12th Standard Business Maths and Statistics State Board (Tamilnadu) - study material, free online tests, previous year question papers, answer keys, topper answers, centum question paper, exam tips

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the rank of the matrix \(\begin{pmatrix} 1 & 5 \\ 3 & 9 \end{pmatrix}\)
2)
Find the rank of the matrix \(\begin{pmatrix} -5 & -7 \\ 5 & 7 \end{pmatrix}\)
3)
Find the rank of the matrix A = \(\left( \begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 5 & 7 \end{matrix} \right) \)
4)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix} \right) \)
5)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 1 & -1 \\ 3 & -6 \end{matrix} \right) \)

12th Standard English Medium Business Maths Subject Differential Equations Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Solve: \(\frac { 1+{ x }^{ 2 } }{ 1+y } =xy\frac { dy }{ dx } \)
2)
Solve: log\(\left( \frac { dy }{ dx } \right) \) = ax + by
3)
Find the order and degree of the following differential equation
\(\frac { { d }^{ 2 }y }{ { dx }^{ 3 } } -3{ \left( \frac { dy }{ dx } \right) }^{ 6 }+2y={ x }^{ 2 }\)
4)
Find the order and degree of the following differential equation
y' + (y'')² = (x + y'')²
5)
Find the order and degree of the following differential equation
\(y=2{ \left( \frac { dy }{ dx } \right) }^{ 2 }\)+ 4x\(\frac { dx }{ dy } \)

12th Standard English Medium Business Maths Subject Differential Equations Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Solve \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -4\frac { dy }{ dx } +5y\) = 0
2)
Solve the following differential equations
\(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -4\frac { dy }{ dx } +4y=0\)
3)
Solve the following differential equations
\(\frac{d^2 y}{dx^2}-2k\frac{dy}{dx}+k^2y = 0\)
4)
A manufacturing company has found that the cost C of operating and maintaining the equipment is related to the length ‘m’ of intervals between overhauls by the equation m²\(\frac{dC}{dm}\) + 2mC = 2 and c = 4 and when m = 2. Find the relationship between C and m.
5)
Find the order and degree of the following differential equations.
\(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =0\)

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find (i) Δe^ax
(ii) Δ²e^x
(iii) Δ log x
2)
Evaluate \({ \Delta }^{ 2 }\left( \frac { 1 }{ x } \right) \) by taking ‘1’ as the interval of differencing.
3)
If f (x) = e^ax then show that f(0), Δf(0), Δ²f(0) are in G.P
4)
Prove that
(1 + Δ)(1 - ∇) = 1
5)
Prove that
∇Δ = Δ - ∇

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
What are the properties of Mathematical expectation?
2)
What do you understand by Mathematical expectation?
3)
How do you define variance in terms of Mathematical expectation?
4)
State the definition of Mathematical expectation using continuous random variable.
5)
Let X be a random variable and Y = 2X + 1. What is the variance of Y if variance of X is 5 ?

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
How do you define variance in terms of Mathematical expectation?
2)
State the definition of Mathematical expectation using continuous random variable.
3)
Let X be a random variable and Y = 2X + 1. What is the variance of Y if variance of X is 5 ?
4)
Prove that, V(aX) = a²V(X)
5)
The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function
\(f(x)= \begin{cases}2 e^{-2 x}, & x>0 \\ 0,& \text { otherwise }\end{cases}\)
Find the expected life of this piece of equipment.

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The mean of a binomial distribution is 5 and standard deviation is 2. Determine the distribution.
2)
Define Poisson distribution.
3)
Write the conditions for which the poisson distribution is a limiting case of binomial distribution.
4)
Define Normal distribution.
5)
Write down the conditions in which the Normal distribution is a limiting case of binomial distribution.

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Verfy the following statement:
The mean of a Binomial distribution is 12 and its standard deviation is 4.
2)
In a book of 520 pages, 390 typo-graphical errors occur. Assuming Poisson law for the number of errors per page, find the probability that a random sample of 5 pages will contain no error.
3)
Define Bernoulli trials.
4)
If the probability of success is 0.09, how many trials are needed to have a probability of atleast one success as 1/3 or more ?
5)
The mean of a binomial distribution is 5 and standard deviation is 2. Determine the distribution.

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
What is population?
2)
What is statistic?
3)
What is sampling distribution of a statistic?
4)
State any two merits of simple random sampling.
5)
State any two merits for systematic random sampling.

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
What is interval estimation?
2)
What is null hypothesis? Give an example.
3)
Define critical region.
4)
Define level of significance.
5)
What is single tailed test.

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Define true value ratio.
2)
Define Family Budget Method.
3)
Define Statistical Quality Control.
4)
Define Chance Cause.
5)
What do you mean by product control?

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
What do you mean by product control?
2)
Define a control chart.
3)
Define mean chart.
4)
What are the uses of statistical quality control?
5)
Write the control limits for the R chart.

12th Standard English Medium Business Maths Subject Operations Research Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Write mathematical form of transportation problem.
2)
What is feasible solution and non degenerate solution in transportation problem?
3)
What do you mean by balanced transportation problem?
4)
What is the Assignment problem?
5)
What is the difference between Assignment Problem and Transportation Problem?

12th Standard English Medium Business Maths Subject Operations Research Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
What is transportation problem?
2)
Write mathematical form of transportation problem.
3)
What do you mean by balanced transportation problem?
4)
Give mathematical form of assignment problem.
5)
What is the difference between Assignment Problem and Transportation Problem?

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 3 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If A=\(\left( \begin{matrix} 1 & 1 & -1 \\ 2 & -3 & 4 \\ 3 & -2 & 3 \end{matrix} \right) \) and B=\(\left( \begin{matrix} 1 & -2 & 3 \\ -2 & 4 & -6 \\ 5 & 1 & -1 \end{matrix} \right) \), then find the rank of AB and the rank of BA.
2)
Solve the equations 2x + 3y = 7, 3x + 5y = 9 by Cramer’s rule.
3)
The following table represents the number of shares of two companies A and B during the month of January and February and it also gives the amount in rupees invested by Ravi during these two months for the purchase of shares of two companies. Find the the price per share of A and B purchased during both the months

Months Number of Shares of
the company Amount invested by Ravi
(in Rs)

A B

January 10 5 125

February 9 12 150
4)
The total cost of 11 pencils and 3 erasers is Rs. 64 and the total cost of 8 pencils and 3 erasers is Rs. 49. Find the cost of each pencil and each eraser by Cramer’s rule.
5)
A total of Rs. 8,600 was invested in two accounts. One account earned \(4\frac { 3 }{ 4 } %\)% annual interest and the other earned \(6\frac { 1 }{ 2 } %\)% annual interest. If the total interest for one year was Rs. 431.25, how much was invested in each account? (Use determinant method).

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 3 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 2 & -1 & 1 \\ 3 & 1 & -5 \\ 1 & 1 & 1 \end{matrix} \right) \)
2)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} -1 & 2 & -2 \\ 4 & -3 & 4 \\ -2 & 4 & -4 \end{matrix} \right) \)
3)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 1 & 2 & -1 \\ 2 & 4 & 1 \\ 3 & 6 & 3 \end{matrix}\begin{matrix} 3 \\ -2 \\ -7 \end{matrix} \right) \)
4)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 1 & -2 & 3 \\ -2 & 4 & -1 \\ -1 & 2 & 7 \end{matrix}\begin{matrix} 4 \\ -3 \\ 6 \end{matrix} \right) \)
5)
Solve the following equation by using Cramer’s rule
5x + 3y = 17; 3x + 7y = 31

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 3 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Evaluate \(\int \frac{a x^{2}+b x+c}{\sqrt{x}} d x\)
2)
Evaluate \(\int { \frac { 1 }{ \sqrt { x+2 } -\sqrt { x-2 } } } dx\)
3)
Integrate the following with respect to x.
\(\sqrt{x}\)(x³− 2x + 3)
4)
Evaluate \(\int { \frac { { x }^{ 2 }+2x+3 }{ x+1 } dx}\)
5)
Integrate the following with respect x.
\(\frac { { x }^{ 3 }+3x^{ 2 }-7x+11 }{ x+5 } \)

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 3 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Evaluate \(\int { \frac { { x }^{ 3 } }{ { \left( { x }^{ 2 }+1 \right) }^{ 3 } } dx } \)
2)
Integrate the following with respect to x.
\(\frac { { e }^{ 3logx } }{ { x }^{ 4 }+1 } \)
3)
Evaluate ഽ\(\frac { dx }{ x^{ 2 }-3x+2 } \)
4)
Integrate the following with respect to x
\(\frac { 1 }{ \sqrt { { x }^{ 2 }-3x+2 } } \)
5)
Using second fundamental theorem, evaluate the following:
\(\int _{ 1 }^{ e }{ \frac { dx }{ x(1{ +logx) }^{ 3 } } } \)

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 3 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The demand and supply function of a commodity are p_d = 18− 2x − x² and p_s = 2x − 3 . Find the consumer’s surplus and producer’s surplus at equilibrium price.
2)
The demand function for a commodity is p = e^−x. Find the consumer’s surplus when p = 0.5.
3)
If the supply function for a product is p = 3x + 5x². Find the producer’s surplus when x = 4.
4)
A company has determined that marginal cost function for x product of a particular commodity is given by MC = 125 +10x − \(\frac { { x }^{ 2 } }{ 9 } \). Where C is the cost of producing x units of the commodity. If the fixed cost is Rs. 250 what is cost of producing 15 units
5)
Find the area of the region bounded by the curve between the parabola y = 8x² − 4x + 6 the y-axis and the ordinate at x = 2.

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 3 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Using integration, find the area of the region bounded by the line y −1 = x, the x axis and the ordinates x = –2, x = 3.
2)
The marginal cost function of manufacturing x shoes is 6 +10x − 6x². The cost producing a pair of shoes is Rs. 12. Find the total and average cost function.
3)
The rate of new product is given by f (x) = 100 − 90 e^−xwhere x is the number of days the product is on the market. Find the total sale during the first four days. (e^–4= 0.018)
4)
A company receives a shipment of 200 cars every 30 days. From experience it is known that the inventory on hand is related to the number of days. Since the last shipment, I(x)=200 − 0.2x. Find the daily holding cost for maintaining inventory for 30 days if the daily holding cost is Rs. 3.5
5)
The marginal cost function of a product is given by \(\frac { dC }{ dx } \) = 100 −10x + 0.1x²where x is the output. Obtain the total and the average cost function of the firm under the assumption, that its fixed cost is Rs. 500.

12th Standard English Medium Business Maths Subject Differential Equations Book Back 3 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Solve \(\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } -\frac { 3dx }{ dt } +2x\) = 0 given that when t = 0, x = 0 and \(\frac { dx }{ dt } \) = 1
2)
Solve the following differential equations: (4D²+4D−3)y = e^2x
3)
Form the differential equation having for its general solution y = ax²+ bx
4)
Solve x \(\frac{dy}{dx}\) + 2y = x⁴
5)
Find the order and degree of the following differential equations.
\(\frac{d^{3} y}{d x^{3}}+3\left(\frac{d y}{d x}\right)^{3}+2 \frac{d y}{d x}=0\)

12th Standard English Medium Business Maths Subject Differential Equations Book Back 3 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Form the differential equation by eliminating α and β from (x − α)² + (y − β)² = r²
2)
Find the differential equation of all circles passing through the origin and having their centers on the y axis.
3)
Find the differential equation of the family of parabola with foci at the origin and axis along the x-axis.
4)
Find the differential equation of the family of curves \(y=\frac { a }{ x } +b\) where a and b are arbitrary constants
5)
Solve \(\frac { dy }{ dx } \) = e^x−y+ x²e^{− y}

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 3 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Construct a forward difference table for y = f(x) = x³+2x+1 for x = 1,2,3,4,5
2)
Prove that f(4) = f(3) + Δf(2) + Δ² f(1) + Δ³ f(1) taking ‘1’ as the interval of differencing.
3)
Given y₃= 2, y₄= −6, y₅= 8, y₆= 9 and y₇ = 17 Calculate Δ⁴y₃
4)
Evaluate ∆(log ax).
5)
If f(x) = x²+ 3x then show that Δf(x) = 2x + 4

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 3 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If h = 1 then prove that (E⁻¹Δ)x³= 3x²− 3x + 1.
2)
If f(x) = x²+ 3x then show that Δf(x) = 2x + 4
3)
Using graphic method, find the value of y when x = 48 from the following data:

x 40 50 60 70

y 6.2 7.2 9.1 12

4)

The following data relates to indirect labour expenses and the level of output

Months	Jan	Feb	Mar	Apr	May	June
Units of output	200	300	400	640	540	580
Indirect labour expenses (Rs)	2500	2800	3100	3820	3220	3640

Estimate the expenses at a level of output of 350 units, by using graphic method

5)
A second degree polynomial passes though the point (1,-1) (2,-1) (3,1) (4,5). Find the polynomial.

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 3 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
What are the properties of
(i) discrete random variable and
(ii) continuous random variable?
2)
State the properties of distribution function.
3)
A fair die is thrown. Find out the expected value of its outcomes.
4)
Suppose the probability mass function of the discrete random variable is

X=x 0 1 2 3

p(x) 0.2 0.1 0.4 0.3

What is the value of E(3X + 2X²) ?
5)
If f (x) is defined by f(x)=ke^-2x, 0\(\le\)x<\(\infty\) is a density function. Determine the constant k and also find mean.

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 3 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Two unbiased dice are thrown simultaneously and sum of the upturned faces considered as random variable. Construct a probability mass function.
2)
The following table is describing about the probability mass function of the random variable X

x 3 4 5

P(x) 0.1 0.1 0.2

Find the standard deviation of x.
3)
The number of miles an automobile tire lasts before it reaches a critical point in tread wear can be represented by a p.d.f.
\(f(x)= \begin{cases}\frac{1}{30} e^{-\frac{x}{30}}, & \text { for } x>0 \\ 0, & \text { for } x \leq 0\end{cases}\)
Find the expected number of miles (in thousands) a tire would last until it reaches the critical tread wear point.
4)
The probability distribution function of a discrete random variable X is
\(F(x)=\left\{\begin{array}{l} 2k, x = 1 \\ 3k, x = 3 \\ 4k, x = 5 \\ 0, \text{otherwise} \end{array}\right.\)
where k is some constant. Find (a) k and (b) P(X>2).
5)
Consider a random variable X with p.d.f
\(f(x)=\left\{\begin{array}{l} 3 x^{2}, \text { if } 0< x< 1 \\ 0, \text { otherwise } \end{array}\right.\)
Find E(X) and V(3X-2).

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 3 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The mean of Binomials distribution is 20 and standard deviation is 4. Find the parameters of the distribution.
2)
What is the probability of guessing correctly atleast six of the ten answers in a TRUE/FALSE objective test?
3)
Assuming one in 80 births is a case of twins, calculate the probability of 2 or more sets of twins on a day when 30 births occur.
4)
Weights of fish caught by a traveler are approximately normally distributed with a mean weight of 2.25 kg and a standard deviation of 0.25 kg. What percentage of fish weigh less than 2 kg?
5)
Among 28 professors of a certain department, 18 drive foreign cars and 10 drive local made cars. If 5 of these professors are selected at random, what is the probability that atleast 3 of them drive foreign cars?

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Solve: 2x + 3y = 4 and 4x + 6y = 8 using Cramer's rule.
2)
If A and B are non-singular matrices, prove that AB is non-singular.
3)
For what value of x, the matrix
\(A=\left| \begin{matrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ x & 2 & -3 \end{matrix} \right| \) is singular?
4)
If \(\left( \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix} \right) \left( \begin{matrix} x \\ y \\ z \end{matrix} \right) =\left( \begin{matrix} 1 \\ -1 \\ 0 \end{matrix} \right) \) find x, y and z
5)
Two newspapers A and B are published in a city . Their market shares are 15% for A and 85% for B of those who bought A the previous year, 65% continue to buy it again while 35% switch over to B. Of those who bought B the previous year, 55% buy it again and 45% switch over to A. Find their market shares after one year

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 3 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The mortality rate for a certain disease is 7 in 1000. What is the probability for just 2 deaths on account of this disease in a group of 400? [Given e^(–2.8)= 0.06]
2)
It is given that 5% of the electric bulbs manufactured by a company are defective. Using poisson distribution find the probability that a sample of 120 bulbs will contain no defective bulb.
3)
Hospital records show that of patients suffering from a certain disease 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover?
4)
If electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week.
5)
The birth weight of babies is Normally distributed with mean 3,500 g and standard deviation 500 g. What is the probability that a baby is born that weighs less than 3,100 g?

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 3 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)

Using the following random number table (Kendall-Babington Smith)

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13

Draw a random sample of 10 four- figure numbers starting from 1550 to 8000.

2)
Explain in detail about sampling error.
3)
A sample of 1000 students whose mean weight is 119 lbs(pounds) from a school in Tamil Nadu State was taken and their average weight was found to be 120 lbs with a standard deviation of 30 lbs. Calculate standard error of mean.
4)
Explain the procedures of testing of hypothesis
5)
Determine the standard error of proportion for a random sample of 500 pineapples was taken from a large consignment and 65 were found to be bad.

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 3 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
From the following data, select 68 random samples from the population of heterogeneous group with size of 500 through stratified random sampling, considering the following categories as strata.
Category 1: Lower income class - 39%
Category 2: Middle income class - 38%
Category 3: Upper income class - 23%
2)
Find the sample size for the given standard deviation 10 and the standard error with respect of sample mean is 3.

3)

Using the following Tippet’s random number table.

2952	6641	3992	9792	7969	5911	3170	5624
4167	9524	1545	1396	7203	5356	1300	2693
2670	7483	3408	2762	3563	1089	6913	7991
0560	5246	1112	6107	6008	8125	4233	8776
2754	9143	1405	9025	7002	6111	8816	6446

Draw a sample of 10 three digit numbers which are even numbers.

4)
A sample of 1000 students whose mean weight is 119 lbs(pounds) from a school in Tamil Nadu State was taken and their average weight was found to be 120 lbs with a standard deviation of 30 lbs. Calculate standard error of mean.
5)
A sample of 100 items, draw from a universe with mean value 4 and S.D 3, has a mean value 63.5. Is the difference in the mean significant at 0.05 level of significance?

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 3 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Write a brief note on seasonal variations
2)
State the different methods of measuring trend.
3)
Calculate by a suitable method, the index number of price from the following data:

Commodity 2002 2012

Price Quantity Price Quantity

A 10 20 16 10

B 12 34 18 42

C 15 30 20 26
4)
From the following data, calculate the trend values using fourly moving averages.

Year 1990 1991 1992 199 1994 1995 1996 1997 1998

Sales 506 620 1036 673 588 696 1116 738 663

5)

An Enquiry was made into the budgets of the middle class families in a city gave the following information.

Expenditure	Food	Rent	Clothing	Fuel	Rice
Price(2010)	150	50	100	20	60
Price(2011)	174	60	125	25	90
Weights	35	15	20	10	20

What changes in the cost of living have taken place in the middle class families of a city?

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Creative 2 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the rank of the matrix \(\left[ \begin{matrix} 7 & -1 \\ 2 & 1 \end{matrix} \right] \)
2)
Find the rank of the matrix \(\left( \begin{matrix} 2 & -4 \\ -1 & 2 \end{matrix} \right) \)
3)
Solve x + 2y = 3 and x +y = 2 using Cramer's rule.
4)
Solve: x + 2y = 3 and 2x + 4y = 6 using rank method.
5)
Show that the equations x + y + z = 6, x + 2y + 3z = 14 and x + 4y + 7z = 30 are consistent

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 3 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Fit a trend line by the method of semi-averages for the given data.

Year 2000 2001 2002 2003 2004 2005 2006

Production 105 115 120 100 110 125 135
2)
Calculate four-yearly moving averages of number of students studying in a higher secondary school in a particular city from the following data.

Year 2001 2002 2003 2004 2005 2006 2007 2008 2009

Sales 124 120 135 140 145 158 162 170 175

3)

You are given below the values of sample mean ( \(\bar{X}\) ) and the range ( R ) for ten samples of size 5 each. Draw mean chart and comment on the state of control of the process.

Sample number	1	2	3	4	5	6	7	8	9	10
\(\overset{-}{X}\)	43	49	37	44	45	37	51	46	43	47
R	5	6	5	7	7	4	8	6	4	6

Given the following control chart constraint for : n = 5, A₂= 0.58, D₃= 0 and D₄= 2.115

4)
Explain the method of fitting a straight line.
5)
The following figures relates to the profits of a commercial concern for 8 years

Year 1986 1987 1988 1989 1990 1991 1992 1993

Profit (Rs.) 15,420 15,470 15,520 21,020 26,500 31,950 35,600 34,900

Find the trend of profits by the method of three yearly moving averages.

12th Standard English Medium Business Maths Subject Operations Research Book Back 3 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Given the following pay-off matrix(in rupees) for three strategies and two states of nature.

Strategy States-of-nature

E₁ E₂

S₁ 40 60

S₂ 10 -20

S₃ -40 150

Select a strategy using each of the following rule
(i) Maximin
(ii) Minimax

2)

A farmer wants to decide which of the three crops he should plant on his 100-acre farm. The profit from each is dependent on the rainfall during the growing season. The farmer has categorized the amount of rainfall as high medium and low. His estimated profit for each is shown in the table.

Rainfall	Estimated Conditional Profit(Rs.)
Rainfall	crop A	crop B	crop C
High	8000	3500	5000
Medium	4500	4500	5000
Low	2000	5000	4000

If the farmer wishes to plant only crop, decide which should be his best crop using
(i) Maximin
(ii) Minimax

3)

The research department of Hindustan Ltd. has recommended to pay marketing department to launch a shampoo of three different types. The marketing types of shampoo to be launched under the following estimated pay-offs for various level of sales.

Types of shampoo	Estimated Sales (in Units)
Types of shampoo	15000	10000	5000
Egg shampoo	30	10	10
Clinic Shampoo	40	15	5
Deluxe Shampoo	55	20	3

What will be the marketing manager’s decision if
(i) Maximin and
(ii) Minimax principle applied?

4)
The following table summarizes the supply, demand and cost information for four factors S₁, S₂, S₃, S₄. shipping goods to three warehouses D₁, D₂, D₃.

Find an initial solution by using north west corner rule. What is the total cost for this solution?

5)

A person wants to invest in one of three alternative investment plans: Stock, Bonds and Debentures. It is assumed that the person wishes to invest all of the funds in a plan. The pay-off matrix based on three potential economic conditions is given in the following table:

Alternative	Economic conditions
Alternative	High growth(Rs.)	Normal growth(Rs.)	Slow growth (Rs.)s
Stocks	10000	7000	3000
Bonds	8000	6000	1000
Debentures	6000	6000	6000

Determine the best investment plan using each of following criteria i) Maxmin ii) Minimax.

12th Standard English Medium Business Maths Subject Operations Research Book Back 3 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Determine an initial basic feasible solution to the following transportation problem using North West corner rule.

Here O_i and D_j represent i^th origin and j^th destination.
2)
Determine how much quantity should be stepped from factory to various destinations for the following transportation problem using the least cost method

Cost are expressed in terms of rupees per unit shipped.

3)

Consider the following pay-off (profit) matrix Action States

Action	States
Action	(s₁)	(s₂)	(s₃)	(s₄)
A₁	5	10	18	25
A₂	8	7	8	23
A₃	21	18	12	21
A₄	30	22	19	15

Determine best action using maximin principle.

4)

Consider the following pay-off matrix

Alternative	Pay – offs (Conditional events)
Alternative	A₁	A₂	A₃	A₄
E₁	7	12	20	27
E₂	10	9	10	25
E₃	23	20	14	23
E₄	32	24	21	17

Using minmax principle, determine the best alternative.

5)
Determine an initial basic feasible solution of the following transportation problem by north west corner method

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find k, if the equations x + y + z = 7, x + 2y + 3z = 18, y + kz = 6 are inconsistent
2)
Investigate for what values of ‘a’ and ‘b’ the following system of equations x + y + z = 6,x + 2y + 3z = 10, x + 2y + az = b have
(i) no solution
(ii) a unique solution
(iii) an infinite number of solutions.
3)
For what values of the parameter λ, will the following equations fail to have unique solution: 3x − y+λz = 1, 2x + y + z = 2, x + 2y − λz = −1 by rank method.
4)
An amount of Rs. 5,000/- is to be deposited in three different bonds bearing 6%, 7% and 8% per year respectively. Total annual income is Rs. 358/-. If the income from first two investments is Rs. 70/- more than the income from the third, then find the amount of investment in each bond by rank method.
5)
An automobile company uses three types of Steel S₁, S₂ and S₃ for providing three different types of Cars C₁, C₂and C₃. Steel requirement R (in tonnes) for each type of car and total available steel of all the three types are summarized in the following table.

Types of Steel Types of Car Total Steel available

C₁ C₂ C₃

S₁ 3 2 4 28

S₂ 1 1 2 13

S₃ 2 2 2 14

Determine the number of Cars of each type which can be produced by Cramer’s rule.

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Evaluate \(\int { { a }^{ 3{ log }_{ a }x } } dx\)
2)
Evaluate \(\int { \frac { 2{ cos }^{ 2 }x-cos2x }{ { sin }^{ 2 }x } } \)
3)
Evaluate ∫ tan²x dx
4)
Evaluate \(\int { \frac { 2+3cosx }{ { sin }^{ 2 }x } } dx\)
5)
Evaluate \(\int { \frac { { 2 }^{ x }+{ 3 }^{ x } }{ { 5 }^{ x } } dx } \)

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The subscription department of a magazine sends out a letter to a large mailing list inviting subscriptions for the magazine. Some of the people receiving this letter already subscribe to the magazine while others do not. From this mailing list, 45% of those who already subscribe will subscribe again while 30% of those who do not now subscribe will subscribe. On the last letter, it was found that 40% of those receiving it ordered a subscription. What percent of those receiving the current letter can be expected to order a subscription?
2)
Find k if the equations x + y + z = 1, 3x − y − z = 4, x+ 5y + 5z = k are inconsistent.
3)
The cost of 2kg of wheat and 1kg of sugar is Rs. 100. The cost of 1kg of wheat and 1kg of rice is Rs. 80. The cost of 3kg of wheat, 2kg of sugar and 1kg of rice is Rs. 220. Find the cost of each per kg using Cramer’s rule.
4)
Solve the following equation by using Cramer’s rule
2x + y −z = 3, x + y + z =1, x− 2y− 3z = 4
5)
Solve the following equation by using Cramer’s rule
x + 4y + 3z = 2, 2x−6y + 6z = −3, 5x− 2y + 3z = −5

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Evaluate \(\int _{ 2 }^{ 3 }{ \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } } dx\)
2)
Evaluate \(\int _{ a }^{ b }{ \frac { \sqrt { \log x } }{ x } dx } \) a, b > 0
3)
Evaluate \(\int _{ 0 }^{ \infty }{ { x }^{ 2 } } { e }^{ { -x }^{ 3 } }dx\)
4)
Evaluate \(\int _{ 1 }^{ e }{ \log x } \) dx
5)
If \(\int _{ a }^{ b }{ dx } =1\) and \(\int _{ a }^{ b }{ xdx } =1\), then find a and b

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 2 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If f'(x) = 8x³ -2x², f(2) = 1, find f(x)
2)
Evaluate \(\int { x } \sqrt { x+2 } dx\)
3)
If \(\int _{ 0 }^{ 1 }{ \left( { 3x }^{ 2 }+2x+k \right) } dx=0\), find k.
4)
Evaluate \(\int _{ 0 }^{ \pi }{ { sin }^{ 2 } } x\ dx\)
5)
If \(\int _{ 0 }^{ a }{ { 3x }^{ 2 } } dx=8\) find the value of a

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Evaluate the following using properties of definite integrals:
\(\int _{ 0 }^{ 1 }{ \log\left( \frac { 1 }{ x } -1 \right) dx } \)
2)
Evaluate the integral as the limit of a sum: \(\int _{ 1 }^{ 2 }{ (2x+1) } dx\)
3)
Evaluate the following integrals as the limit of the sum:
\(\int _{ 0 }^{ 1 }{ (x+4) } \)dx
4)
Evaluate the following integrals as the limit of the sum:
\(\int _{ 0 }^{ 1 }{ { x }^{ 2 } } dx\)
5)
Evaluate the following integrals:
\(\int _{ 0 }^{ 3 }{ \frac { xdx }{ \sqrt { x+1 } +\sqrt { 5x+1 } } } \)

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The marginal cost at a production level of x units is given by C '(x) = 85 +\(\frac{375}{x^2}\). Find the cost of producing 10 in elemental units after 15 units have been produced?
2)
The marginal cost function is MC = \(\frac{100}{x}\). Find the cost function C(x) if C(16) = 100.
3)
Find the demand function for which the elasticity of demand is 1
4)
Find the consumer's surplus for the demand function p = 25 - x -x² when P_o= 19
5)
Find the producer's surplus for the supply function p = x² + x + 3 when x_o = 4

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the area bounded by y = 4x + 3 with x- axis between the lines x = 1 and x = 4
2)
Sketch the graph \(y=\left| x+3 \right| \) and evaluate \(\int _{ -6 }^{ 0 }{ \left| x+3 \right| } \) dx.
3)
Using integration find the area of the region bounded between the line x = 4 and the parabola y² = 16x.
4)
Find the area bounded by the curve y = x² and the line y = 4
5)
The marginal cost and marginal revenue with respect to commodity of a firm are given by C'(x) = 8 + 6x and R'(x)= 24. Find the total Profit given that the total cost at zero output is zero.

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 2 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the area of the region bounded by the parabola x² = 4y, y = 2, y = 4 and the y-axis.
2)
Find the area under the curve y = 4x² - 8x + 6 bounded by the Y-axis, X-axis and the ordinate at x = 2.
3)
Find the area under the curve y = 4x - x² included between x = 0, x = 3 and the X-axis.
4)
The marginal cost function of manufacturing x units of a commodity is 3x² - 2x + 8. If there is no fixed cost, find the total cost function?
5)
If the marginal revenue for a commodity is MR = 9 - 6x² + 2x, find the total revenue function.

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
When the Elasticity function is \(\frac { x }{ x-2 } \). Find the function when x = 6 and y = 16.
2)
A firm’s marginal revenue function is MR = 20e^-x/10 \(\left( 1-\frac { x }{ 10 } \right) \). Find the corresponding demand function.
3)
The marginal cost of production of a firm is given by C'(x) = 5 + 0.13x, the marginal revenue is given by R'(x) = 18 and the fixed cost is Rs. 120. Find the profit function.
4)
The demand equation for a products is x = \(\sqrt { 100-p } \) and the supply equation is x = \(\frac{p}{2}\) -10. Determine the consumer’s surplus and producer’s surplus, under market equilibrium.
5)
A company requires f(x) number of hours to produce 500 units. It is represented by f (x) = 1800x^−0.4. Find out the number of hours required to produce additional 400 units. [(900)^0.6= 59.22, (500)^0.6= 41.63]

12th Standard English Medium Business Maths Subject Differential Equations Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Write down the order and degree of the following differential equations.
\(\left( \frac { dy }{ dx } \right) ^{ 3 }-4\left( \frac { dy }{ dx } \right) \)+y = 3e^x
2)
Write down the order and degree of the following differential equations.
\(\left( \frac { dy }{ dx } \right) ^{ 2 }-7\frac { d^{ 3 }y }{ { dx }^{ 3 } } +y\frac { { d }^{ 2 }y }{ dx^{ 2 } } +4\frac { dy }{ dx } \)- log x = 0
3)
Write down the order and degree of the following differential equations.
\(\sqrt { 1+\left( \frac { dy }{ dx } \right) ^{ 2 } } \)= 4x
4)
Write down the order and degree of the following differential equations.
\(\left[ 1+\left( \frac { dy }{ dx } \right) ^{ 2 } \right] ^{ \frac { 2 }{ 3 } }=\frac { d^{ 2 }y }{ { dx }^{ 2 } } \)
5)
Find the differential equation for y = mx + \(\frac { a }{ m } \) where m is arbitrary constant.

12th Standard English Medium Business Maths Subject Differential Equations Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the differential equation of the family of straight lines y = mx + c when
(i) m is the arbitrary constant
(ii) c is the arbitrary constant
(iii) m and c both are arbitrary constants.
2)
Solve : x - y \(\frac { dx }{ dy } =a\left( { x }^{ 2 }+\frac { dx }{ dy } \right) \)
3)
Solve the differential equation y²dx + (xy + x²)dy = 0
4)
Solve the following homogeneous differential equations.
\(\frac { dy }{ dx } =\frac { 3x-2y }{ 2x-3y } \)
5)
Solve (x² + 1)\(\frac { dy }{ dx } \) + 2xy = 4x²

12th Standard English Medium Business Maths Subject Differential Equations Creative 2 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Solve: (x² - ay)dx = (ax-y²)dy
2)
Solve: \(\frac { dy }{ dx } \)+ ay = e^x (where a ≠ -1)
3)
The change in the cost of ordering and holding C as quantity q is given by \(\frac { dC }{ dq } =a-\frac { c }{ q } \) where a is a Constanst. Find C as a function of q.
4)
Solve: 3\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } -5\frac { dy }{ dx } \)+ 2y = 0
5)
Solve: (D²-6D+25)y = 0

12th Standard English Medium Business Maths Subject Differential Equations Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Solve 3e^xtan ydx +(1 + e^x)sec²ydy = 0 given y(0) = \(\frac { \pi }{ 4 } \)
2)
Solve the differential equation y²dx + (xy + x²)dy = 0
3)
If the marginal cost of producing x shoes is given by (3xy + y²)dx + (x²+ xy)dy = 0 and the total cost of producing a pair of shoes is given by Rs. 12. Then find the total cost function.
4)
An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x²+ y²)dy = xydx where x represents the number of units (in thousands). What is the total revenue function?
5)
Solve the following differential equations (D²+D−6)y=e^3x+ e^−3x

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Determine whether the following is a probability distribution of a random variable X.

X 0 1 2

P(X) 0.6 0.1 0.2
2)
An unbiased die is rolled. If the random variable X is defined as
X(w) = {1, the outcome w is an even number
{0, if the outcome w is an odd number
Find the probability distribution of X.
3)
Two eggs are drawn at random without replacement from a bag containing two bad eggs and eight good eggs. Find the probability of getting two bad eggs?
4)
A random variable X has the probability mass function

X -2 3 1

P(X=x) \(\frac{k}{6}\) \(\frac{k}{4}\) \(\frac{k}{12}\)

then find k
5)
A discrete random variable. X has the following probability distribution

X 0 1 2 3 4 5 6 7 8

P(X) a 3a 5a 7a 9a 11a 13a 15a 17a

Pind the value of a and P(X< 3)

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The values of y = f(x) for x = 0,1,2, ...,6 are given by

x 0 1 2 3 4 5 6

y 2 4 10 16 20 24 38

Estimate the value of y (3.2) using forward interpolation formula by choosing the four values that will give the best approximation.
2)
Using appropriate interpolation formula find the number of students whose weight is between 60 and 70 from the data given below

Weight in lbs 0-40 40-60 60-80 80-100 100-120

No.of.students 250 120 100 70 50
3)
Evaluate \(\Delta \)\(\left[ \frac { 5x+12 }{ { x }^{ 2 }+5x+6 } \right] \) by taking ‘1’ as the interval of differencing.
4)
Calculate the value of y when x = 7.5 from the table given below

x 1 2 3 4 5 6 7 8

y 1 8 27 64 125 216 343 512
5)
Find a polynomial of degree two which takes the values

x 0 1 2 3 4 5 6 7

y 1 2 4 7 11 16 22 29

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 2 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Verify whether \(f(x)=\begin{cases} \frac { 2x }{ 9 } ,\quad 0\le x\le \\ 0,\quad elsewhere \end{cases}\) is a probability density function
2)
A continuous random variable. X has the p.d.f. defined by \(f(x)=\left\{\begin{array}{l} C e^{-a x}, \quad 0<x<\infty \\ 0, \quad \text { elsewhere } \end{array}\right.\) Find the value of C if a> 0
3)
In an entrance examination a student has to answer all the 120 questions. Each question has four options and only one option is correct. A student gets 1 mark for a correct answer and loses \(\frac{1}{2}\) mark for a wrong answer. What is the expectation of the mark scored by a student if he chooses the answer to each question at random?
4)
In a gambling game a man wins Rs. 10 if he gets all heads or all tails and loses Rs. 5 if he gets 1 or 2 heads when 3 coins are tossed once. Find his expectation of gain.
5)
Find the mean for the probability density function \(f(x)=\begin{cases} \frac { 1 }{ 24 } ,-12\le x\le 12 \\ 0,\quad otherwise \end{cases}\)

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Using interpolation estimate the business done in 1985 from the following data

Year 1982 1983 1984 1986

Business done (in lakhs) 150 235 365 525
2)
Find the missing figures in the following table

x 0 5 10 15 20 25

y 7 11 - 18 - 32
3)
Using Lagrange’s interpolation formula find a polynomial which passes through the points (0, –12), (1, 0), (3, 6) and (4,12).
4)
If u₀ = 560, u₁ = 556, u₂ = 520, u₄ = 385, show that u₃= 465
5)
The area A of circle of diameter ‘d’ is given for the following values

D 80 85 90 95 100

A 5026 5674 6362 7088 7854

Find the approximate values for the areas of circles of diameter 82 and 91 respectively

12th Standard English Medium Business Maths Subject Probability Distributions Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Students of a class were given an aptitude test. Marks were found to be normally distributed with mean 60 and S.D. 5. Find the percentage of students who scored more than 60 marks.
2)
In a packet of 50 pens, 10 are defective, 10 pens are selected at random. What is the probability that atleast one is defective.
3)
The random variable X has the normal distribution f(x) = \(C{ e }^{ -\left( \frac { x-100 }{ 50 } \right) ^{ 2 } }\), then find the value of C.
4)
If you buy a lottery ticket in 50 lotteries, in each which your chance of winning a prize is \(\frac { 1 }{ 100 } \). What is the approximate probability that you will win a prize at least once (e-0.5 = 0.6066).
5)
The probability of the happening of an event X is 0.002 in an experiment. If an experiment is reported 1000 times, find the probability that the event X happens exactly twice? (e^-2 = 0.1353)

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Determine the mean and variance of the random variable X having the following probability distribution.

X=x 1 2 3 4 5 6 7 8 9 10

P(x) 0.15 0.10 0.10 0.01 0.08 0.01 0.05 0.02 0.28 0.20
2)
Suppose the life in hours of a radio tube has the probability density function
\(f(x)=\left\{\begin{array}{l} e^{-\frac{x}{100}}, \text { when } x \geq 100 \\ 0, \quad \text { when } x<100 \end{array}\right.\)
Find the mean of the life of a radio tube.
3)
The probability function of a random variable X is given by
\(p(x)=\left\{\begin{array}{l} \frac{1}{4}, \text { for } x=-2 \\ \frac{1}{4}, \text { for } x=0 \\ \frac{1}{2}, \text { for } x=10 \\ 0, \text { elsewhere } \end{array}\right.\)
Evaluate the following probabilities.
P(\(\le\))0
4)
The probability density function of a continuous random variable X is
\(f(x)=\left\{\begin{array}{l} a+b x^{2}, 0 \leq x \leq 1 \\ 0, \text { otherwise } \end{array}\right.\)
where a and b are some constants. Find
(i) a and b if E(X)\(\frac{3}{5}\)
(ii) Var(X).
5)
The probability function of a random variable X is given by
\(p(x)=\left\{\begin{array}{l} \frac{1}{4}, \text { for } x=-2 \\ \frac{1}{4}, \text { for } x=0 \\ \frac{1}{2}, \text { for } x=10 \\ 0, \text { elsewhere } \end{array}\right.\)
Evaluate the following probabilities.
P(|X|\(\le\)2)

12th Standard English Medium Business Maths Subject Probability Distributions Creative 2 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
In a Poisson distribution 3 P(X = 2) = P(X = 4), then find the parameter of the distribution.
2)
If the mean of the binomial distribution with 9 trial is 6, then find the variance.
3)
If the mean of the binomial distribution is 20 and standard deviation is 4, then find the number of events.
4)
Suppose X is a binomial variate X ~ B (5, p) and P(X = 2) = P(X = 3), then find p.
5)
If 10 coins are tossed, find the probability that exactly 5 heads appears.

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Determine the mean and variance of a discrete random variable, given its distribution as follows.

X = x 1 2 3 4 5 6

F_x(x) \(\frac{1}{6}\) \(\frac{2}{6}\) \(\frac{3}{6}\) \(\frac{4}{6}\) \(\frac{5}{6}\) 1
2)
The probability density function of a random variable X is f(x) = ke^-|x|, -∞ < x < ∞ Find the value of k and also find mean and variance for the random variable.
3)
Let X be a random variable with cumulative distribution function
\(F(x)=\left\{\begin{array}{l} 0, \text { if } x<0 \\ \frac{x}{8}, \text { if } 0 \leq x<1 \\ \frac{1}{4}+\frac{x}{8}, \text { if } 1 \leq x<2 \\ \frac{3}{4}+\frac{x}{12}, \text { if } 2 \leq x<3 \\ 1, \text { for } 3 \leq x \end{array}\right.\)
(a) Compute: (i) P(1\(\le\)X\(\le\)2) and
(ii) P(X=3)
(b) Is X a discrete random variable? Justify your answer.
4)
The probability function of a random variable X is given by
\(p(x)=\left\{\begin{array}{l} \frac{1}{4}, \text { for } x=-2 \\ \frac{1}{4}, \text { for } x=0 \\ \frac{1}{2}, \text { for } x=10 \\ 0, \text { elsewhere } \end{array}\right.\)
Evaluate the following probabilities.
P(X<0)
5)
The probability function of a random variable X is given by
\(p(x)=\left\{\begin{array}{l} \frac{1}{4}, \text { for } x=-2 \\ \frac{1}{4}, \text { for } x=0 \\ \frac{1}{2}, \text { for } x=10 \\ 0, \text { elsewhere } \end{array}\right.\)
Evaluate the following probabilities.
P(0\(\le\)X\(\le\)10)

12th Standard English Medium Business Maths Subject Numerical Methods Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the missing term from the following data.

x 20 30 40

y 51 - 34
2)
If f(0) = 5, f(1) = 6, f(3) = 50, find f(2) by using Lagrange's formula.
3)
Find the missing term from the following data

x 1 2 3 4

f(x) 100 - 126 157
4)
When h = 1, find Δ (x³).
5)
Find the second order backward differences of f(x).

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
A random sample of size 50 with mean 67.9 is drawn from a normal population. If it is known that the standard error of the sample \(\sqrt { 0.7 } \) , find 95% confidence interval for the population mean.
2)
Out of 1000 T.V. viewers, 320 watched a particular programme. Calculate the standard error.
3)
Out of 1500 school students, a sample of 150 selected to test the accuracy of solving a problem in B.M. and of them 10 did a mistake. Calculate the standard error of sample proportion.
4)
A sample of 400 students is found to have mean height of 171.38 cms, Can it reasonable be regarded as a sample from a large population with mean height of 171.17 cms and standard deviation of 3.3 cms (Test at 5% level)
5)
The income distribution of the population of a village has a mean of Rs. 6000 and a variance of Rs. 32,400. Could a sample of 64 persons with a mean income of Rs. 5950 belong to this population. (Test at 1% level of significance).

12th Standard English Medium Business Maths Subject Applied Statistics Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Using the method ofleast squares, fit a straight line trend for Σx = 10, Σy = 16.9, Σx² = 30, Σxy = 47.4 and n = 7.

2)

Calculate the 3-yearlymoving averages of the production figures (in tonnes) for the following data.

Year	1973	1974	1975	1976	1977	1978	1979	1980	1981	1982	1983	1984	1985	1986	1987
Production	15	21	30	36	42	46	50	56	63	70	74	82	90	95	102

3)
Calculate the seasonal indices by the method of simple average for the following data.

Year I quarter II quarter III quarter IV quarter

1985 68 62 61 63

1986 65 58 66 61

1987 68 63 63 67

4)

Construct the cost of living index for 2003 on the basis of 2000 from the following data using family budget method.

Item	Price(Rs.)		Weights
Food	2000	2003	30
Rent	200	280	30
Clothing	150	120	20
Fuel & lighting	50	100	10
Miscellaneous	100	200	20

5)

The following data shows the value of sample mean (\(\bar{X}\)) and the range R for 10 samples of size 5 each. Calculate the control limits for : mean chart and range chart.

Sample No.	1	2	3	4	5	6	7	8	9	10
Mean \(\bar{X}\)	11.2	11.8	10.8	11.6	11.0	9.6	10.4	9.6	10.6	10.0
Range	7	4	8	5	7	4	8	4	7	9

(Given for n = 5, A₂ = .577, D₃ = 0, D₄ = 2.115)

12th Standard English Medium Business Maths Subject Operations Research Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Obtain the initial solution for the following problem using north-west corner rule.
2)
Determine an initial basic feasible solution to the following transportation problem using feast cost method.
3)
Consider the following pay-off (profit) matrix action, states

Action States

B₁ B₂

_A1 8 6

_A2 9 2

_A3 6 4

Determine the best action using maximin principle.
4)
For the given pay-off matrix, find the optimal decision under the minimax principle.
5)
The following is the pay-off matrix (in rupees) for three strategies and three states of nature. Select a strategy using maximin principle.

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Creative 3 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the rank of the matrix
\(A=\left( \begin{matrix} 2 & 4 & 5 \\ 4 & 8 & 10 \\ -6 & -12 & -15 \end{matrix} \right) \)
2)
Find the rank of the matrix \(A=\left( \begin{matrix} 1 & 2 & -4 \\ 2 & -1 & 3 \\ 8 & 1 & 9 \end{matrix}\begin{matrix} 5 \\ 6 \\ 7 \end{matrix} \right) \)
3)
Show that the equations 2x - y + z = 7, 3x + y - 5z = 13, x + y + z = 5 are consistent and have a unique solution.
4)
Show that the equations x + 2y = 3, y - z = 2, x + y + z = 1 are consistent and have infinite sets of solution.
5)
Show that the equations x- 3y + 4z = 3, 2x - 5y + 7z = 6, 3x - 8y + 11z = 1 are inconsistent

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Creative 3 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Solve: 2x - 3y - 1 = 0, 5x + 2y - 12 = 0 by Cramer's rule.
2)
If \(\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 2 \\ -1 \\ 3 \end{matrix} \right] \) find x,y and z
3)
If \(A=\left( \begin{matrix} 2 & 4 \\ 4 & 3 \end{matrix} \right) ,X=\left( \begin{matrix} n \\ 1 \end{matrix} \right) B=\left( \begin{matrix} 8 \\ 11 \end{matrix} \right) \) and AX = B then find n.
4)
Solve: 2x + 3y = 5, 6x + 5y = 11
5)
Two products A and B currently share the market with shares 60% and 40% each respectively. Each week some brand switching latees place. Of those who bought A the previous week 70% buy it again whereas 30% switch over to B. Of those who bought B the previous week, 80% buy it again whereas 20% switch over to A. Find their shares after one week and after two weeks.

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 3 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Evaluate \(\int { \frac { { { x }^{ 4 }+{ x }^{ 4 }+1 } }{ { x }^{ 2 }-x+1 } } \)
2)
Evaluate \(\int { \frac { cos2x-cos2\alpha }{ cosx-cos\alpha } } dx\)
3)
Evaluate \(\int { \frac { { ({ a }^{ x }{ +b }^{ x }) }^{ 2 } }{ { a }^{ x }b^{ x } } dx } \)
4)
If f' (x) = 3x² - \(\frac { 2 }{ { x }^{ 3 } } \) and f(1) = 0, find f(x)
5)
Evaluate \(\int { \frac { { 8 }^{ 1+x }+{ 4 }^{ 1-x } }{ { 2 }^{ x } } } dx\)

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 3 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Evaluate \(\int { \frac { { sec }^{ 2 }x }{ 3+tanx } } dx\)
2)
Evaluate ഽ sin³ x cos x dx
3)
Evaluate \(\int { \frac { 1 }{ \sqrt { { 16x }^{ 2 }+25 } } } dx\)
4)
Evaluate ഽe^x \(\left( \frac { 1+sinxcosx }{ { cos }^{ 2 }x } \right) dx\)
5)
Evaluate \(\int _{ 1 }^{ 2 }{ \frac { log\quad x }{ { x }^{ 2 } } } dx\)

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 3 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the area contained between the x-axis and one arc of the curve y = cos x bounded between
\(x=-\frac { \pi }{ 2 } and\quad x=\frac { \pi }{ 2 } \)
2)
Find the area under the demand curve xy = 1 bounded by the ordinates x = 3, x = 9 and x-axis
3)
Find the area bounded by one arc of the curve y = sin ax and the x-axis.
4)
Determine the cost of producing 3000 units of commodity if the marginal cost in rupees per unit is C'(x) = \(\frac{x}{3000}+2.50\)
5)
The marginal revenue function is given by \(R'(x)=\frac { 3 }{ { x }^{ 2 } } -\frac { 2 }{ x } \). Find the revenue function and demand function if R(1) = 6

12th Standard English Medium Business Maths Subject Differential Equations Creative 3 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Solve: (x+y)²\(\frac { dy }{ dx } \) = 1
2)
Find the equation of the curve passing through (1, 0) and which has slope 1+ \(\frac { y }{ x } \) at (x, y).
3)
Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y = 2(e^x-x-1).
4)
Solve: (D²+1)y = 0 when x = 0, y = 2 and when x = \(\frac { \pi }{ 2 } \), y = -2.
5)
A man plans to invest some amount in a small saving scheme with a guaranteed compound in crest compounded continuously at the ratio of 12 percent for 5 years. How much should he invest if he wants an amount of Rs. 25000 at the end of 5 year period? (e^-0.6 = 0.5488)

12th Standard English Medium Business Maths Subject Differential Equations Creative 3 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the differential equation of all circles x² +y² + 2gx = 0 which pass through the origin and whose centres are on the X-axis.
2)
Form the differential equation for \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \)=1 where a & b are arbitrary constants.
3)
Form the differential equation for y = (A + Bx)e^3x where A and B are constants.
4)
Solve: sec 2x dy - sin 5x sec² y dx = 0
5)
Solve: cos²x dy + y.e^tanx dx = 0

Stateboard 12th Standard Business Maths Subject Public Question Paper - March 2022 updated Previous Year Question Papers - by QB Admin - May 13, 2022 - View & Read

12th Standard English Medium Business Maths Subject Numerical Methods Creative 3 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
From the following data, estimate the population for the year 1986 graphically.

year 1960 1970 1980 1990 2000

Population (in thousands) 12 15 20 26 33
2)
Using graphic method, find the value of y when x=27.

x 10 15 20 25 30

y 35 32 29 26 23
3)
Find y when x = 0.2 given that

x 0 1 2 3 4

y 176 185 194 202 212
4)
If y₇₅ = 2459, y₅₀ = 2018, y₈₅ = 1180, and y₉₀ =402, find y₈₂

x 75 80 85 90

y 2459 2018 1180 402
5)
Find the number of men getting wages between Rs. 30 and Rs. 35 from the following table.

Wages (x) 20 - 30 30 - 40 40 - 50 50 - 60

No. of men (y) 9 30 35 42

12th Standard English Medium Business Maths Subject Numerical Methods Creative 3 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
From the following data, estimate the population for the year 1986 graphically.

year 1960 1970 1980 1990 2000

Population (in thousands) 12 15 20 26 33
2)
Find the number of men getting wages between Rs. 30 and Rs. 35 from the following table.

Wages (x) 20 - 30 30 - 40 40 - 50 50 - 60

No. of men (y) 9 30 35 42
3)
Estimate the population for the year 1995.

year (x) 1961 1971 1981 1991 2001

population in thousands (y) 46 66 81 93 101
4)
Using Lagrange's formula, find the value of y when x = 42 from the following table

x 40 50 60 70

y 31 73 124 159
5)
Using Lagrange's formula and y(x) from the following table.

x 6 7 10 12

y 13 14 15 17

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 3 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The probability distribution of a discrete random variable. X is given by

X -2 2 5

P(X=x) \(\frac{1}{4}\) \(\frac{1}{4}\) \(\frac{1}{2}\)

then find 4E(X²)- Var (2X)
2)
A random variable. X has following distribution

X -1 0 1 2

P(X=x) \(\frac{1}{3}\) \(\frac{1}{6}\) \(\frac{1}{6}\) \(\frac{1}{3}\)

Find E(2X+3)²
3)
If a continuous random variable. X has the p.d.f. f(x) = 4k(x-1)³, 1 ≤ x ≤ 3 then find p[-2 ≤ X ≤ 2]
4)
A player tosses two unbiased coins. He wins Rs. 5 if two heads appear, Rs. 2 if one head appear and Rs.1 if no head appear. Find the expected amount to win.
5)
If the probability density function of a random variable. X is given by f(x) = \(\frac{2x}{9}\),0

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 3 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If a random variable. X has the probability distribution

X 0 1 2 3 4 5

P(X=x) a 2a 3a 4a 5a 6a

then find F(4)
2)
Let X denote the number of hours you study during a randomly selected school day. The probability distribution function is
\(P(X=x)=\begin{cases} \begin{matrix} 0.1 & if\quad x=0 \end{matrix} \\ \begin{matrix} kx & if\quad x=1\quad or\quad 2 \end{matrix} \\ \begin{matrix} k(5-x) & if\quad x=3\quad or\quad 4 \end{matrix} \\ \begin{matrix} 0, & otherwise \end{matrix} \end{cases}\)
Find the value of k and what is the probability that you study atleast 2 hours.
3)
A random variable X can take all nonnegative integral values and the probabilities that X takes the value r is proportional to aT (0 < ∝ < 1). Find P(X = 0)
4)
Two cards are drawn from a pack of 52 playing cards. Find the probability distribution of the number of aces.
5)
An urn contains 4 white and 6 red balls. Four balls are drawn at random from the urn. Find the probability distribution of the number of white balls.

12th Standard English Medium Business Maths Subject Probability Distributions Creative 3 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
A die is thrown 120 times and getting 1 or 5 is considered a success. Find the mean and variance of the number of successes.
2)
If on an average 1 ship out of 10 do not arrive safely to ports. Find the mean and the standard deviation of ships returning safely out of a total of 500 ships.
3)
Alpha particles are emitted by a radio active source at an average rate of 5 in a 20 minutes interval. Using Poisson distribution find the probability that there will be atleast 2 emission in a particular 20 minutes interval (e^-5 = 0.0067).
4)
Suppose that the amount of cosmic radiation to which a person is exposed when flying by jet across USA is a random vertical. having a normal distribution with mean of 4.35m rem and a standard deviation of 0.59m rem. What is the probability that a person will be exposed to more than 5.20 m rem of cosmic radiation of such a flight?
5)
The life of army shoes is normally distributed with mean 8 months and standard deviation 2 months. If 5000 pairs are issued, how many pairs would be expected to need replacement within 12 months.

12th Standard English Medium Business Maths Subject Probability Distributions Creative 3 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The probability that an event A happens in one treat of an experiment is 0.4. Three independent treats of the experiment are performed. Find the p!probability that the event A happens at least once.
2)
The standard deviation of a binomial distribution (q +p)¹⁶ is 2. Find its mean.
3)
If a random variable X follows Poisson distribution such that P(X = 2) = 9. P(X = 4) + 90 P(X = 6) then find the mean and variance.
4)
Find the value of K if X is a normal variate whose p.d.f is given by f(x) = \(\frac { 1 }{ K } \)e^8x-4x2, -∞
5)
Obtain K, μ and σ2 of of the normal distribution whose probability distribution function is f(x) = \(K{ e }^{ -2x^{ 2 }+4x-2 }\), -∞

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Creative 3 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
A random sample of 500 apples was taken from large consignment and 45 of them were found to be bad. Find the limits at which the bad apples lie at 99% confidence level.
2)
A sample of five measurements of the diameter of a sphere were recorded by a scientist as 6.33, 6.37,6.36,6.32 and 6.37 mm. Determine the point estimate of
(a) mean
(b) variance.
3)
A random sample of marks in mathematics secured by 50 students out of 200 students showed a mean of 75 and a standard deviation of 10. Find the 95% confidence limits for the estimate of their mean marks.
4)
A company market car tyres. Their lives are normally distributed with a mean of 50,000 kms and standard derivation of 2000 kms. A test sample of 64 tyres has a mean life of 51250 km. Can you conclude that the sample mean differs significantly from the population mean? (Test at 5% level).
5)
The mean life time of 50 electric bulbs produced by a manufacturing company is estimated to be 825 hours with the S.D. of 110 hours. If II is the mean life time of all the bulbs produced by the company, test the hypothesis that μ = 900 hours at 5% level of significance.

12th Standard English Medium Business Maths Subject Applied Statistics Creative 3 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Fit a straight line trend for the following data using the method of least squares.

x 0 1 2 3 4

y 1 1 3 4 6
2)
Fit a trend line to the following data by graphic method.

Year 1978 1979 1980 1981 1982 1983 1984 1985 1986

Production of steel 20 22 24 21 23 25 23 26 25
3)
Find a trend line to the following data by the method of sami-averages.

Years 1980 1981 1982 1983 1984 1985 1986

Sales 102 105 114 110 108 116 112

4)

Calculate the seasonal indices for the following data by the method of simple average.

Year	Quarters
Year	I	II	III	IV
1994	78	66	84	80
1995	76	74	82	78
1996	72	68	80	70
1997	74	70	84	74
1998	76	74	86	82

5)

Compute Fisher's price index number for the following data.

Commodity	Base Year		Current Year
Commodity	Price	Quantity	Price	Quantity
A	10	12	12	15
B	7	15	5	20
C	5	24	9	20
D	16	5	14	5

12th Standard English Medium Business Maths Subject Operations Research Creative 3 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
For the given pay-off matrix, choose the best alternative for the given states of nature under
(i) Maximin (ii) Minimax princple

Alternative States of Nature

Good Fair Bad

A 100 60 +50

B 80 50 +10

C 40 20 +5
2)
Determine an initial basic feasible solution to the following transportation problem using North West corner rule.
3)
Determine how much quantity should be stepped from factory to various destinations for the following transportation problem using the least cost method.
4)
Find the initial basic feasible solution for the following transportation problem by Vogel's approximation method.
5)
Solve the following assignment problem. Cell values represent cost of assigning job A, B, C and D to the operators I, II, III and IV.

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Evaluate ഽ sin (log x) + cos (log x) dx
2)
Evaluate \(\int { \frac { \left( { x }^{ 2 }+1 \right) dx }{ { \left( x-1 \right) }^{ 2 }\left( x+3 \right) } } \)
3)
Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 4 } }{ sin } 3xsin\ 2x\ dx\)
4)
Prove that \(\int _{ a }^{ b }{ \frac { f\left( x \right) }{ f\left( x \right) +f(a+b-x) } } dx=\frac { b-a }{ 2 } \)
5)
Using integrals as limit of sums, evaluate \(\int _{ 2 }^{ 4 }{ (2x-1) } dx\)

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 5 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If f'(x) = a sin x + b cos x and f'(0) = 4, f(0) = 3, f\(\left( \frac { \pi }{ 2 } \right) \) = 5, find f(x).
2)
Evaluate \(\int { \frac { { x }^{ 7 } }{ { x }^{ 5 }+1 } } dx\)
3)
Evaluate ഽ x³ sin (x⁴) dx
4)
Evaluate \(\int { \frac { 1 }{ { 3x }^{ 2 }+13x-10 } } dx\)
5)
Evaluate ഽx. log (1 + x) dx

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the area of the region bounded by the line y = x - 5, the x-axis and between the ordinates x = 3and x = 7
2)
The Marginal revenue for a commodity is MR=\(\frac { { e }^{ x } }{ 100 } +x+{ x }^{ 2 }\), find the revenue function.
3)
The elasticity of demand with respect to price for a commodity-is a constant and is equal to 2. Find the demand function and hence the total revenue function, given that when the price is 1, the demand is 4.
4)
A company determines that the marginal cost of producing x units is C'(x) = 10.6x. The fixed cost is Rs. 50. The selling price per unit is Rs.5. Find the profit function.
5)
The demand and supply functions under pure competition are P_d = 16 - x² and p_s = 2x² + 4. Find the consumer's surplus and producer's surplus at the market equilibrium price.

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 5 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The marginal cost C' (x) and marginal revenue R' (x) are given by C' (x) = 20 +\(\frac{x}{20}\) and R' (x) = 30. The fixed cost is Rs.200. Determine the maximum profit.
2)
The marginal revenue function (in thousands of rupees) of a commodity is 7+^e-0.05x where x is the number of units sold. Find the total revenue from the sale of 100 units (e^-5 = 0.0067)
3)
The marginal cost function of a commodity in a firm is 2 + e^3x where X is the output. Find the total cost and average cost function if the fixed cost is Rs. 500.
4)
Find the area of the region bounded by the curve y = 3 x² - x, X-axis and the lines between x = -1 and x= 1
5)
Find the area of the region bounded by the parabola y² = 4x and the line 2x - y = 4.

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The sum of three numbers is 6. If we multiply the third number by 2 and add the first number to the result we get 7. By adding second and third numbers to three times the first number we get 12. Find the numbers using rank method
2)
A mixture is to be made of three foods A, B, C. The three foods A, B, C contain nutrients P, Q, R as shown below

Ounces per pound of Nutrient

Food P Q R

A 1 2 5

B 3 1 1

C 4 2 1

How to form a mixture which will have 8 ounces of P, 5 ounces of Q and 7 ounces of R? (Cramer's rule).
3)
For what values of k, the system of equations kx+ y+z = 1, x+ ky+z= 1, x+ y+kz = 1 have
(I) Unique solution
(ii) More than one solution
(iii) no solution
4)
Using determinants, find the quadratic defined by f(x) = ax² + bx + c if
f(1) = 0,
f(2) = - 2 and
f(3) = -6.
5)
A new transit system has just gone into operation in a city. Of those who use the transit system this year, 10% will switch over to using their own car next year and 90% will continue to use the transit system. Of those who use their cars this year, 80% will continue to use their cars next year and 20% will switch over to the transit system. Suppose the population of the city remains constant and that 50% of the commuters use the transit system and 50% of the commuters use their own car this year,
(i) What percent of commuters will be using the transit system after one year?
(ii) What percent of commuters will be using the transit system in the long run?

12th Standard English Medium Business Maths Subject Differential Equations Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The net profit p and quantity x satisfy the differential equation \(\frac { dp }{ dx } =\frac { 2{ p }^{ 3 }-{ x }^{ 3 } }{ 3x{ p }^{ 2 } } \). Find the relationship between the net profit and demand given that p = 20, when x = 10.
2)
The rate of increase in the cost Cof ordering holding as the size q of the order increases is given by the differential equation \(\frac { dc }{ dq } =\frac { { c }^{ 2 }+2cq }{ { q }^{ 2 } } \). Find the relationship between c and q if c = 1 when q = 1.
3)
The total cost of production y and the level of output x are related to the marginal cost of production by the equation (6x²+2y²)dx-(x²+4xy)dy = 0. What is the relation between total cost and output if y = 2 when x = 1?
4)
Equipment maintenance and operating costs (are related to the overhaul interval x by the equation \({ x }^{ 2 }\frac { dc }{ dx } -10xc=-10\) with c = c₀ and x = x₀. Find c as a function of x.
5)
Suppose that the quantity needed Q_d = 42 -4p-4\(\frac { dp }{ dt } +\frac { { d }^{ 2 }p }{ { dt }^{ 2 } } \) and quantity supplied Q_s= -6 + 8p where p is the price. Find the s equilibrium price for market clearance.

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
X is normally distributed with mean 12 and sd 4. Find P(X ≤ 20) and P(0 ≤ X ≤ 12)
2)
In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take less than 16.35 seconds to develop prints.
3)
A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain
(a) no more than 2 rejects?
(b) at least 2 rejects?
4)
The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time .
a) less than 19.5 hours?
b) between 20 and 22 hours?
5)
X is a normally normally distributed variable with mean μ = 30 and standard deviation σ = 4. Find
(a) P(x < 40)
(b) P(x > 21)
(c) P(30 < x < 35)

12th Standard English Medium Business Maths Subject Differential Equations Creative 5 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Solve: \(\frac { dy }{ dx } \) = sin(x + y)
2)
Solve: x²\(\frac { dy }{ dx } \) = y²+2xy given that y = 1, when x = 1
3)
Solve: (y-x)\(\frac { dy }{ dx } \) = a²
4)
Solve: (D² + 14D + 49)y = e^-7x + 4.
5)
The rate of increase in the cost Cof ordering holding as the size q of the order increases is given by the differential equation \(\frac { dc }{ dq } =\frac { { c }^{ 2 }+2cq }{ { q }^{ 2 } } \). Find the relationship between c and q if c = 1 when q = 1.

12th Standard English Medium Business Maths Subject Numerical Methods Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Estimate the production for 1962 and 1965 from the following data

year 1961 1962 1963 1964 1965 1966 1967

Production in tonnes 200 - 260 306 - 390 430
2)
From the following data, calculate the value of e^1.75

x 1.7 1.8 1.9 2.0 2.1

e^x 5.474 6.050 6.686 7.386 8.166
3)
From the data, find the number of students whose height is between 80 cm and 90 cm

Height in cm (x) 40-60 60-80 80 - 100 100-120 120-140

No. of. students (y) 250 120 100 70 50
4)
From the following table, estimate the premium for a policy maturing at the age of 58.

Age (x) 40 45 50 55 60

Premium (y) 114.84 96.16 83.32 74.48 68.48
5)
Using Lagrange's formula find the value of y when x = 4 from the following table.

x 0 3 5 6 8

y 276 460 414 343 110

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
A discrete random variable X has the following probability distribution.

x 1 2 3 4 5 6 7

P(X) c 2c 2c 3c c² 2c² 7c²+c

Find the value of e. Also, find the mean of the distribution.
2)
The probability distribution of a random variation X is given below.

X 0 1 2 3 4

P(X) 0.1 0.25 0.3 0.2 0.15

Find
(i) V(X)
ii) V\((\frac{X}{2})\)
3)
The probability distribution of the discrete random variables X and Y are given below

X 0 1 2 3

P(X) \(\frac{1}{5}\) \(\frac{2}{5}\) \(\frac{1}{5}\) \(\frac{1}{5}\)

Y 0 1 2 3

P(Y) \(\frac{1}{5}\) \(\frac{3}{10}\) \(\frac{2}{5}\) \(\frac{1}{10}\)

Prove that E(Y²) = 2E(X).
4)
The random variable X tan take only the values 0,1,2. Given that P(X = 0) = P(X = 1) = P and E(X²) = E(X), find the value of p.
5)
The probability distribution of a random variable X is

X 1 2 4 2A 3A 5A

P(X) \(\frac{1}{2}\) \(\frac{1}{5}\) \(\frac{3}{25}\) \(\frac{1}{10}\) \(\frac{1}{25}\) \(\frac{1}{25}\)

Calculate
(i) A if E(X) = 2.94
(ii) V(X)

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If the average rain falls on 9 days in every thirty days, find the probability that rain will fall on atleast two days of a given week.
2)
An insurance company has discovered that only about 0.1 per cent of the population is involved in a certain type of accident each year. If its 10,000 policy holders were randomly selected from the population, what is the probability that not more than 5 of its clients are involved in such an accident next year? (e⁻¹⁰=.000045)
3)
If the probability that an individual suffers a bad reaction from injection of a given serum is 0.001, determines the probability that out of 2,000 individuals
(a) exactly 3, and
(b) more than 2 individuals will suffer a bad reaction.
4)
If X is a normal variate with mean 30 and SD 5. Find the probabilities that
(i) 26 ≤ X ≤ 40
(ii) X > 45
5)
The marks obtained in a certain exam follow normal distribution with mean 45 and SD 10. If 1,300 students appeared at the examination, calculate the number of students scoring
(i) less than 35 marks and
(ii) more than 65 marks.

12th Standard English Medium Business Maths Subject Probability Distributions Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Four coins are tossed simultaneously. What is the probability of getting
a) atleast 2 heads
b) atmost 2 heads.
2)
20% of the bolts produced in a factory are found to be defective. Find the probability that in a sample of 10 bolts chosen at random exactly 2 will be defective using
(i) Binomial distribution
(ii) Poisson distribution (e^-2 = 0.1353)
3)
The mean weight of 500 male students in a certain college is 151 pounds and the S.D is 15 pounds. Assuming the weights are normally distributed, find how many students weight
(i) between 120 and 155 pounds
(ii) more than 185 pounds.
4)
If the height of 300 students are normally distributed with mean 64.5 inches and standard deviation 3.3 inches find the height below which 99% of the student lie?
5)
Marks in an aptitude test given to 800 students of a school was found to be normally distributed 10% of the students scored below 40 marks and 10% of the students scored above 90 marks. Find the number of students scored between 40 and 90?

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
A machine produces a component of a product with a standard deviation of 1.6 cm in length. A random sample of 64 componentsvwas selected from the output and this sample has a mean length of 90 cm. The customer will reject the part if it is either less than 88 cm or more than 92 cm. Does the 95% confidence interval for the true mean length of all the components produced ensure acceptance by the customer?
2)
The mean life time of a sample of 169 light bulbs manufactured by a company is found to be 1350 hours with a standard deviation of 100 hours. Establish 90% confidence limits within which the mean life time of light bulbs is expected to lie.
3)
A manufacturer of ball pens claims that a certain pen he manufactures has a mean writing life of 400 pages with a standard deviation of 20 pages. A purchasing agent selects a sample of 100 pens and puts them for test. The mean writing life for the sample was 390 pages. Should the purchasing agent reject the manufactures claim at 1% level?
4)
The mean weekly sales of soap bars in departmental stores were 146.3 bars per store. After an advertising campaign the mean weekly sales in 400 stores for a typical week increased to 153.7 and showed a standard deviation of 17.2. Was the advertising campaign successful at 95% confidence limit?
5)
An ambulance service claims that it takes on the average 8.9 minutes to reach its destination in emergency calls. To check on this claim, the agency which licenses ambulance services has them timed on 50 emergency calls, getting a mean of 9.3 minutes with a standard deviation of 1.6 minutes. What can they conclude at 5% level of significance.

12th Standard English Medium Business Maths Subject Applied Statistics Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Fit a straight line trend to the following data using the method of least square. Estimate the trend for 2007.

year 2000 2001 2002 2003 2004

Sales (in tonnes) 1 1.8 3.3 4.5 6.3

2)

From the data given below, calculate seasonal indices.

Quarter	Year
	1984	1985	1986	1987	1988
I	40	42	41	45	44
II	35	37	35	36	38
III	38	39	38	36	38
IV	40	38	40	41	42

3)

Compute
(i) Laspeyre's
(ii) Paasche's
(iii) Fisher's price index number for 2000 from the following data.

Commodity	Price		Quantity
	1990	2000	1990	2000
A	2	4	8	6
B	5	6	10	5
C	4	5	14	10
D	2	2	19	13

4)

Calculate Fisher's ideal index from the following data and verify that it satisfies both time reversal and factor reversal test

Commodity	Price		Quantity
	1985	1986	1985	1986
A	8	20	50	60
B	2	6	15	10
C	1	2	20	25
D	2	5	10	8
E	1	5	40	30

5)

The followingdata relateto the life(inhours) of 10 samples of 6 electricbulbs each drawn at an intervalof one hour from a production process.Draw the controlchart for \(\overline { X } \) and \(\overline { R } \) and comment.

Sample No	Lifetime (inhour)
	1	2	3	4	5	6
1	620	687	666	689	738	686
2	501	585	524	585	653	668
3	673	701	686	567	619	660
4	646	626	572	628	631	743
5	494	984	659	643	660	640
6	634	755	625	582	683	555
7	619	710	664	693	770	534
8	630	723	614	535	550	570
9	482	791	533	612	497	499
10	706	524	626	503	661	754

(For n = 6,A₂= 0.483,D₃ = 0,D₄ = 2.004)

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
An ambulance service claims that it takes on the average 8.9 minutes to reach its destination in emergency calls. To check on this claim, the agency which licenses ambulance services has them timed on 50 emergency calls, getting a mean of 9.3 minutes with a standard deviation of 1.6 minutes. What can they conclude at 5% level of significance.
2)
Explain the stratified random sampling with a suitable example.
3)
A random sample of 60 observations was drawn from a large population and its standard deviation was found to be 2.5. Calculate the suitable standard error that this sample is taken from a population with standard deviation 3?
4)
A sample of 400 individuals is found to have a mean height of 67.47 inches. Can it be reasonably regarded as a sample from a large population with mean height of 67.39 inches and standard deviation 1.30 inches at 0.05 level of significance?
5)
The mean breaking strength of cables supplied by a manufacturer is 1,800 with a standard deviation 100. By a new technique in the manufacturing process it is claimed that the breaking strength of the cables has increased. In order to test this claim a sample of 50 cables is tested. It is found that the mean breaking strength is 1,850. Can you support the claim at 0.01 level of significance.

12th Standard English Medium Business Maths Subject Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The rank of an n x n matrix each of whose elements is 2 is __________
2)
If \(\int { \frac { { 2 }^{ \frac { 1 }{ x } } }{ { x }^{ 2 } } } dx=k{ 2 }^{ \frac { 1 }{ x } }\) +c, then k is ___________
3)
The area of the region bounded by the ellipse __________
4)
If y = k.e^λx then its differential equation where k is arbitrary constant is _____________
5)
∇f(x+ 3h) ______________

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The following data gives the readings for 8 samples of size 6 each in the production of a certain product. Find the control limits using mean chart.

Sample 1 2 3 4 5 6

Mean 300 342 351 319 326 333

Range 25 37 20 28 30 22

Given for n = 6, A₂ = 0.483,

2)

Compute the average seasonal movement for the following series

Year	Quarterly Production
Year	I	II	III	IV
2002	3.5	3.8	3.7	3.5
2003	3.6	4.2	3.4	4.1
2004	3.4	3.9	3.7	4.2
2005	4.2	4.5	3.8	4.4
2006	3.9	4.4	4.2	4.6

3)
Determine the equation of a straight line which best fits the following data

Year 2000 2001 2002 2003 2004

Sales(Rs.000) 35 36 79 80 40

Compute the trend values for all years from 2000 to 2004

4)

Use the method of monthly averages to find the monthly indices for the following data of production of a commodity for the years 2002, 2003 and 2004.

2002	15	18	17	19	16	20	21	18	17	15	14	18
2003	20	18	16	13	12	15	22	16	18	20	17	15
2004	18	25	21	11	14	16	19	20	17	16	18	20

5)
The following table shows the number of salesmen working for a certain concern:

Year 1992 1993 1994 1995 1996

No. of salesmen 46 48 42 56 52

Use the method of least squares to fit a straight line and estimate the number of salesmen in 1997.

12th Standard English Medium Business Maths Subject Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If A, B are two n x n non-singular matrices, then ___________
2)
If \(\int { \frac { 1 }{ \left( x+2 \right) \left( { x }^{ 2 }+1 \right) } } \) dx = a log \(\left| 1+{ x }^{ 2 } \right| \) +b tan^-1 x + \(\frac { 1 }{ 5 } log\left| x+2 \right| \) +c then ___________
3)
The Consumer's surplus for the demand function P =f(x) for the quantity X_o and price P_o is_________
4)
The integrating factor of \(\frac { dy }{ dx } +\frac { 2y }{ x } \)= x³ is _____________
5)
Δ is ____________

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Given below are the data relating to the production of sugarcane in a district.
Fit a straight line trend by the method of least squares and tabulate the trend values.

Year 2000 2001 2002 2003 2004 2005 2006

Prod.of Sugarcane 40 45 46 42 47 50 46

2)

Calculate the seasonal index for the monthly sales of a product using the method of simple averages.

Months	Jan	Feb	Mar	Apr	May	June	July	Aug	Sep	Oct	Nov	Dec
Year	Jan	Feb	Mar	Apr	May	June	July	Aug	Sep	Oct	Nov	Dec
2001	15	41	25	31	29	47	41	19	35	38	40	30
2002	20	21	27	19	17	25	29	31	35	39	30	44
2003	18	16	20	28	24	25	30	34	30	38	37	39

3)

the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Commodities	Price		Quandity
Commodities	2000	2010	2000	2010
Rice	38	35	6	7
Wheat	12	18	7	10
Rent	10	15	10	15
Fuel	25	30	12	16
Miscellaneous	30	33	8	10

4)

Calculate Fisher’s price index number and show that it satisfies both Time Reversal Test and Factor Reversal Test for data given below.

Commodities	Price		Quandity
Commodities	2003	2009	2003	2009
Rice	10	13	4	6
Wheat	125	18	7	8
Rent	25	29	5	9
Fuel	11	14	8	10
Miscellaneous	14	17	6	7

5)

Construct Fisher’s price index number and prove that it satisfies both Time Reversal Test and Factor Reversal Test for data following data.

Commodities	Base Year		Current Year
Commodities	Price	Quantity	Price	Quantity
Rice	40	5	48	4
Wheat	45	2	42	3
Rent	90	4	95	6
Fuel	85	3	80	2
Transport	50	5	65	8
Miscellaneous	65	1	72	3

12th Standard English Medium Business Maths Subject Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Solve: x + 2y = 3 and 2x + 4y = 6 using rank method.
2)
Evaluate \(\int { \frac { 2{ cos }^{ 2 }x-cos2x }{ { sin }^{ 2 }x } } \)
3)
Find the area under the curve y = 4x² - 8x + 6 bounded by the Y-axis, X-axis and the ordinate at x = 2.
4)
Write down the order and degree of the following differential equations.
\(\left( \frac { dy }{ dx } \right) ^{ 2 }-7\frac { d^{ 3 }y }{ { dx }^{ 3 } } +y\frac { { d }^{ 2 }y }{ dx^{ 2 } } +4\frac { dy }{ dx } \)- log x = 0
5)
Find the missing term from the following data.

x 20 30 40

y 51 - 34

12th Standard English Medium Business Maths Subject Operations Research Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Obtain an initial basic feasible solution to the following transportation problem using Vogel’s approximation method.
2)
Consider the problem of assigning five jobs to five persons. The assignment costs are given as follows. Determine the optimum assignment schedule.
3)
A computer centre has got three expert programmers. The centre needs three application programmes to be developed. The head of the computer centre, after studying carefully the programmes to be developed, estimates the computer time in minitues required by the experts to the application programme as follows.

Assign the programmers to the programme in such a way that the total computer time is least.
4)
Find the optimal solution for the assignment problem with the following cost matrix.

12th Standard English Medium Business Maths Subject Creative 2 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If A and B are non-singular matrices, prove that AB is non-singular.
2)
Evaluate \(\int _{ 0 }^{ \pi }{ { sin }^{ 2 } } x\ dx\)
3)
Find the consumer's surplus for the demand function p = 25 - x -x² when P_o= 19
4)
Solve: \(\frac { dy }{ dx } \)+ ay = e^x (where a ≠ -1)
5)
When h = 1, find Δ (x³).

12th Standard English Medium Business Maths Subject Operations Research Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Assign four trucks 1, 2, 3 and 4 to vacant spaces A, B, C, D, E and F so that distance travelled is minimized. The matrix below shows the distance.
2)
Determine an initial basic feasible solution to the following transportation problem by using North West Corner rule
3)
Explain Vogel’s approximation method by obtaining initial feasible solution of the following transportation problem.
4)
A car hire company has one car at each of five depots a,b,c,d and e. A customer in each of the fine towers A,B,C,D and E requires a car. The distance (in miles) between the depots (origins) and the towers(destinations) where the customers are given in the following distance matrix.

How should the cars be assigned to the customers so as to minimize the distance travelled?
5)
A natural truck-rental service has a surplus of one truck in each of the cities 1,2,3,4,5 and 6 and a deficit of one truck in each of the cities 7,8,9,10,11 and 12. The distance(in kilometers) between the cities with a surplus and the cities with a deficit are displayed below:

How should the truck be dispersed so as to minimize the total distance travelled?

12th Standard English Medium Business Maths Subject Creative 3 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the rank of the matrix \(A=\left( \begin{matrix} 1 & 2 & -4 \\ 2 & -1 & 3 \\ 8 & 1 & 9 \end{matrix}\begin{matrix} 5 \\ 6 \\ 7 \end{matrix} \right) \)
2)
Evaluate \(\int { \frac { cos2x-cos2\alpha }{ cosx-cos\alpha } } dx\)
3)
Find the area under the demand curve xy = 1 bounded by the ordinates x = 3, x = 9 and x-axis
4)
Form the differential equation for y = (A + Bx)e^3x where A and B are constants.
5)
Using graphic method, find the value of y when x=27.

x 10 15 20 25 30

y 35 32 29 26 23

12th Standard English Medium Business Maths Subject Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The rank of m x n matrix whose elements are unity is ________.
2)
\(\int \frac{\sin 5 x-\sin x}{\cos 3 x} d x\) is _______.
3)
The given demand and supply function are given by D(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is ________.
4)
The differential equation of y = mx + c is ______.(m and c are arbitrary constants)
5)
E ≡ _______.

12th Standard English Medium Business Maths Subject Creative 3 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Solve: 2x + 3y = 5, 6x + 5y = 11
2)
Evaluate ഽe^x \(\left( \frac { 1+sinxcosx }{ { cos }^{ 2 }x } \right) dx\)
3)
Determine the cost of producing 3000 units of commodity if the marginal cost in rupees per unit is C'(x) = \(\frac{x}{3000}+2.50\)
4)
Solve: (D²+1)y = 0 when x = 0, y = 2 and when x = \(\frac { \pi }{ 2 } \), y = -2.
5)
Using Lagrange's formula, find the value of y when x = 42 from the following table

x 40 50 60 70

y 31 73 124 159

12th Standard English Medium Business Maths Subject Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If \(\rho (A)\) = r then which of the following is correct?
2)
ഽ\(\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } } \) dx is _______.
3)
If the marginal revenue MR = 35 + 7x − 3x², then the average revenue AR is ________.
4)
The complementary function of (D²+ 4)y = e^2x is ______.
5)
E f (x)= _______.

12th Standard English Medium Business Maths Subject Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
For what values of k, the system of equations kx+ y+z = 1, x+ ky+z= 1, x+ y+kz = 1 have
(I) Unique solution
(ii) More than one solution
(iii) no solution
2)
Evaluate \(\int { \frac { 1 }{ { 3x }^{ 2 }+13x-10 } } dx\)
3)
The elasticity of demand with respect to price for a commodity-is a constant and is equal to 2. Find the demand function and hence the total revenue function, given that when the price is 1, the demand is 4.
4)
Solve: (y-x)\(\frac { dy }{ dx } \) = a²
5)
From the following data, calculate the value of e^1.75

x 1.7 1.8 1.9 2.0 2.1

e^x 5.474 6.050 6.686 7.386 8.166

12th Standard English Medium Business Maths Subject Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the rank of the matrix \(\begin{pmatrix} -5 & -7 \\ 5 & 7 \end{pmatrix}\)
2)
Integrate the following with respect to x.
\(\sqrt { 3x+5 } \)
3)
Find the area of the region bounded by the parabola \(y=4{ - }x^{ 2 }\) , x −axis and the lines x = 0, x = 2.
4)
Solve: \(\frac { dy }{ dx } \) = y sin 2x
5)
Evaluate \({ \Delta }^{ 2 }\left( \frac { 1 }{ x } \right) \) by taking ‘1’ as the interval of differencing.

12th Standard English Medium Business Maths Subject Creative 5 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
A new transit system has just gone into operation in a city. Of those who use the transit system this year, 10% will switch over to using their own car next year and 90% will continue to use the transit system. Of those who use their cars this year, 80% will continue to use their cars next year and 20% will switch over to the transit system. Suppose the population of the city remains constant and that 50% of the commuters use the transit system and 50% of the commuters use their own car this year,
(i) What percent of commuters will be using the transit system after one year?
(ii) What percent of commuters will be using the transit system in the long run?
2)
Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 4 } }{ sin } 3xsin\ 2x\ dx\)
3)
The marginal revenue function (in thousands of rupees) of a commodity is 7+^e-0.05x where x is the number of units sold. Find the total revenue from the sale of 100 units (e^-5 = 0.0067)
4)
The total cost of production y and the level of output x are related to the marginal cost of production by the equation (6x²+2y²)dx-(x²+4xy)dy = 0. What is the relation between total cost and output if y = 2 when x = 1?
5)
Using Lagrange's formula find the value of y when x = 4 from the following table.

x 0 3 5 6 8

y 276 460 414 343 110

12th Standard English Medium Business Maths Subject Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 1 & -1 \\ 3 & -6 \end{matrix} \right) \)
2)
Integrate the following with respect to x.
\({ \left( \sqrt { 2x } -\frac { 1 }{ \sqrt { 2x } } \right) }^{ 2 }\)
3)
Evaluate the following using properties of definite integrals:
\(\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ { x }^{ 3 }{ cos }^{ 3 }xdx } \)
4)
Find the order and degree of the following differential equation
\({ \left[ 1+\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right] }^{ \frac { 3 }{ 2 } }=a\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } }\)
5)
Describe what is meant by a random variable.

12th Standard English Medium Business Maths Subject Book Back 3 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the rank of the matrix \(\left( \begin{matrix} 1 & 2 & -1 \\ 2 & 4 & 1 \\ 3 & 6 & 3 \end{matrix}\begin{matrix} 3 \\ -2 \\ -7 \end{matrix} \right) \)
2)
Evaluate \(\int { \frac { x+2 }{ \sqrt { 2x+3 } } } dx\)
3)
Using integration, find the area of the region bounded by the line y −1 = x, the x axis and the ordinates x = –2, x = 3.
4)
Find the differential equation of the following
y = cx + c − c³
5)
Construct a forward difference table for y = f(x) = x³+2x+1 for x = 1,2,3,4,5

12th Standard English Medium Business Maths Subject Book Back 3 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Solve the following equations by using Cramer’s rule
2x + 3y = 7; 3x + 5y = 9
2)
Integrate the following with respect to x.
\(\frac { 1 }{ { \sin }^{ 2 }x{ \cos }^{ 2 }x } [Hint:\sin ^{ 2 }+{ \cos }^{ 2 }x=1]\)
3)
The demand and supply function of a commodity are p_d = 18− 2x − x² and p_s = 2x − 3 . Find the consumer’s surplus and producer’s surplus at equilibrium price.
4)
Solve yx²dx + e ^{− x}dy = 0
5)
Using graphic method, find the value of y when x = 48 from the following data:

x 40 50 60 70

y 6.2 7.2 9.1 12

12th Standard English Medium Business Maths Subject Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find k, if the equations x + y + z = 7, x + 2y + 3z = 18, y + kz = 6 are inconsistent
2)
Integrate the following with respect to x.
\(\frac { { 3x }^{ 2 }-2x+5 }{ { \left( x-1 \right) }\left( x^{ 2 }+5 \right) } \)
3)
Using integration find the area of the region bounded between the line x = 4 and the parabola y² = 16x.
4)
The sum of Rs. 2,000 is compounded continuously, the nominal rate of interest being 5% per annum. In how many years will the amount be double the original principal? (log_e2 = 0.6931)
5)
Using appropriate interpolation formula find the number of students whose weight is between 60 and 70 from the data given below

Weight in lbs 0-40 40-60 60-80 80-100 100-120

No.of.students 250 120 100 70 50

12th Standard English Medium Business Maths Subject Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The price of 3 Business Mathematics books, 2 Accountancy books and one Commerce book is Rs. 840. The price of 2 Business Mathematics books, one Accountancy book and one Commerce book is Rs. 570. The price of one Business Mathematics book, one Accountancy book and 2 Commerce books is Rs. 630. Find the cost of each book by using Cramer’s rule.
2)
Evaluate the following integrals as the limit of the sum:
\(\int _{ 1 }^{ 3 }{ xdx } \)
3)
Find the consumer’s surplus and producer’s surplus for the demand function p_d = 25 − 3x and supply function p_s = 5 + 2x.
4)
Solve: (D²− 2D + 1)y = e^2x+ e^x
5)
Calculate the value of y when x = 7.5 from the table given below

x 1 2 3 4 5 6 7 8

y 1 8 27 64 125 216 343 512

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The rank of an n x n matrix each of whose elements is 2 is __________
2)
The value of \(\left| \begin{matrix} { 5 }^{ 2 } & { 5 }^{ 3 } & { 5 }^{ 4 } \\ { 5 }^{ 3 } & { 5 }^{ 4 } & { 5^{ 5 } } \\ { 5 }^{ 4 } & { 5 }^{ 5 } & { 5 }^{ 6 } \end{matrix} \right| \)
3)
If \(\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right| \) then x =
4)
If A is a singular matrix, then Adj A is ___________
5)
If A, B are two n x n non-singular matrices, then ___________

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
\(\int { { \left| x \right| }^{ 3 } } \)dx = ________________ +c
2)
\(\int { \frac { 2 }{ { \left( { e }^{ x }+{ e }^{ -x } \right) }^{ 2 } } } \) dx = ____________ +c
3)
\(\int { { e }^{ x } } \) (1-cot x +cot² x) dx = _______________ +c
4)
\(\int { { e }^{ x } } \) f(x) + f' (x) dx = _____________ +c
5)
If ∫ x sin x dx = - x cos x + α then α = __________ +c

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
∫ e^x (sin x + cos x) dx = ________________ +c.
2)
\(\int _{ 4 }^{ 9 }{ \frac { 1 }{ \sqrt { 2 } } } \) dx =
3)
\(\int _{ 0 }^{ 1 }{ \frac { 1 }{ 2x-3 } } \) dx = ____________
4)
\(\int _{ 1 }^{ 4 }{ f\left( x \right) } dx,\) where f(x) = \(\begin{cases} 7x+3\quad if\quad 1\le x\le 3 \\ 8x\quad if\quad 3\le x\le 4 \end{cases}\) is _____________.
5)
\(\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 71 } } x\) dx = ____________

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The area of the region bounded by the line y = 3x + 2, the X-axis and the ordinates x = - 1 and x = 1is_________ sq. units.
2)
The value of \(\int _{ -3 }^{ 2 }{ |x+1| } dx\) is______.
3)
The area lying above the X-axis and under the parabola y = 4x - x² is ______ sq. units
4)
The area of the region bounded by the curve y² = 2y - x and the y-axis _____ sq. units
5)
The area bounded by the curve y = 4ax and the lines y² = 2a and Y-axis is _______ sq. units.

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The are bounded by the demand curve xy = 1, the X-axis, x = 1 and x = 2 is ________
2)
The area above the supply curve p = g(x) and below the line p = p_o is ________.
3)
The area below the demand curve p = f(x) and above the line p = p_o is________.
4)
Profit = Total revenue - __________.
5)
Profit function is maximum when \(\frac{dp}{dx}\) = 0 and \(\frac{d^2p}{dx^2}\) is _________.

12th Standard English Medium Business Maths Subject Differential Equations Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The amount present in a radio active element disintegrates at a rate proportional to its amount. The differential equation corresponding to the above statement is _____________ (k is negative).
2)
The differential equation satisfied by all the straight lines in xy plane is _____________
3)
If y = k.e^λx then its differential equation where k is arbitrary constant is _____________
4)
The differential equation obtained by eliminating a and b from y = a e^3x + b e^-3x is _____________
5)
The differential equation formed by eliminating A and B from y = e^x (A cos x + B sin x) is _____________

12th Standard English Medium Business Maths Subject Differential Equations Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
On putting y = vx; homogeneous differential equation x²dy + y(x + y)dx = 0 becomes ______
2)
The I.F. of \(\frac { dy }{ dx } \)- y tan x = cos x is _____
3)
The P.I. of (3D²+D-14)y = 13 e^2x is ______
4)
The P.I. of the differential equation f(D)y = e^ax where f(D) = (D-a) g(D), g(a) ≠0 is _____
5)
The equation of ydx + xdy = e^-xy dx if it cuts the Y-axis is ______

12th Standard English Medium Business Maths Subject Numerical Methods Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
∆f(x + 3h) ______________
2)
Δ can be defined as Δf(x) =f(x + h) -f(x) where h is the __________ interval of spacing
3)
If c is a constant, then Δc = ______________
4)
Δ(f(x) + g(x)) = ________
5)
If c is a constant, then Δc.f(x) ______________

12th Standard English Medium Business Maths Subject Numerical Methods Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The nationality of the mathematician Joseph Louis Laguange is _________
2)
The knowledge of ______ is essential for the study of Numerical Analysis
3)
The forward difference operator Δ is ______________
4)
The backward difference operator ∇ is ______________
5)
Δ is ____________

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
X is a random variable. Taking the values 3, 4 and 12 with probabilities \(\frac{1}{3},\frac{1}{4}\)and \(\frac{5}{12}\).Then E(X) is
2)
Variance of the random variable. X is 4, Its mean is 2. Then E(X²) is _________
3)
μ₂= 20, μ¹₂ = 276 for a discrete random variable X. Then the mean of the random variable. X is _________
4)
V(4X + 3) is _________
5)
If E(X) = \(\frac{1}{2}, E(X^2)=\frac{1}{4}\), then V(X) is ________

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If X is a discrete random variable. then P(X≥a)=________.
2)
If X is a continuous random variable. then P(X≥a)= _________.
3)
If X is a discrete random variable., then which of the following is correct?
4)
Which of the following are correct?
(i) E(aX+b) = a E(X) + b
(ii) μ₂= μ₂¹ - (μ₁¹)²
(iii) μ²= variance
(iv) V (a X + b) = a² V(x)
5)
A discrete random variable. X has the probability mass function p(x), then __________ is true.

12th Standard English Medium Business Maths Subject Probability Distributions Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The probability that a normal variate X lies in the interval (μ-σ, μ+σ) is ___________
2)
In case of normal distribution, skewness is ___________
3)
For a normal distribution if the mean is m, mode is n and median is m, then ___________
4)
If the mean of the binomial distribution is 25, then its standard deviation lies in the interval ___________
5)
The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, the probability that he hits the target is ___________

12th Standard English Medium Business Maths Subject Probability Distributions Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If the variance of a Poisson distribution is 0.5. Then p(X = 3) is _________ (e^-0.5= 0.6066)
2)
For a binomial distribution with mean 2 and variance \(\frac{4}{3}\), p = _________
3)
In a binomial distribution if n = 5, p(x = 3) = 2. p(x = 2), then p = _________
4)
For a standard normal distribution, the mean and variance are _________
5)
The normal distribution curve is _______

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Probability of rejecting null hypothesis. when it is true is _______
2)
The number of ways in which one can select 2 customers out of 10 customers is __________
3)
The standard error of the sample mean is __________
4)
Which of the following statements is true?
5)
The Z-value that is used to establish a 95% confidence interval for the estimation of a population parameter is __________

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
There are _______ branches of statistical inference.
2)
An _______ is a specific observed value of a statistic
3)
If 55 is the mean mark obtained by a sample of 5 students randomly drawn from a class of 100 students is considered to the means marks of the entire class. This single value 55 is a
4)
If α is the level of significance. then the confidence Co-efficient is
5)
Any hypothesis which is complementary to the null hypothesis is _______ hypothesis.

12th Standard English Medium Business Maths Subject Applied Statistics Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Most commonly used index numbers are _________ index number
2)
Chance variation in the manufactured product is __________
3)
Variation due to assignable causes in the product occur due to, _____
4)
The causes leading to vast variation in the specification of a product are usually due to _____
5)
Most frequently used index number formulae are_____

12th Standard English Medium Business Maths Subject Applied Statistics Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Time series consists of data arranged
2)
Seasonal variations are __________
3)
The components used in the time series y = T + S + C + l are __________
4)
The methods of measurements of trends are __________
5)
Seasonal variations can be measured when the data are available in season wise __________

12th Standard English Medium Business Maths Subject Operations Research Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
To assign different jobs to the different machines to minimize the overall cost is ___________
2)
The optimum_______schedule remains, unaltered if we add or subtract a constant from all the elements of the row or which of the cost________matrix.
3)
If the number of rows is____tothenumber of columns, then the assignment problem is said to be balanced.
4)
______ method provides optimum assignment schedule in an assignment problem.
5)
_____determines the lowest out comes for each alternative.

12th Standard English Medium Business Maths Subject Operations Research Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
_____determines the highest out come for each alternative.
2)
Operation research is an analytical method of ___________
3)
The methods of funding feasible solution to a transportation problem ___________
4)
The least cost method is more economical than North West Corner Rule, since it starts with the ___________
5)
The penalty is the difference between the ___ costs in each row and column.

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If \(\rho (A)=\rho (A,B)\) the number of unknowns, then the system is______.
2)
If the number of variables in a non-homogeneous system AX = B is n, then the system possesses a unique solution only when _______.
3)
If \(\left| A \right| \neq 0,\) then A is _______.
4)
Cramer’s rule is applicable only to get an unique solution when _______.
5)
Rank of a null matrix is _______.

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The rank of m x n matrix whose elements are unity is ________.
2)
The rank of the matrix \(\left( \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 4 & 9 \end{matrix} \right) \) is ________.
3)
If A =\(\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right) \) then the rank of AA^Tis ________.
4)
If \(T=\begin{array}{l} A \\ B \end{array}\left(\begin{array}{ll} 0.7 & 0.3 \\ 0.6 & x \end{array}\right)\) is a transition probability matrix, then the value of x is ________.
5)
If \(\rho (A)=\rho (A,B)\) the number of unknowns, then the system is______.

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
ഽ\(\frac { sin2x }{ 2sinx } dx\) is _______.
2)
ഽ\(\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } } \) dx is _______.
3)
ഽ\(\frac { { e }^{ x } }{ { e }^{ x }+1 } \) dx is _______.
4)
ഽ\(\frac { dx }{ \sqrt { { x }^{ 2 }-{ 36 } } } \) is _______.
5)
\(\int _{ 2 }^{ 4 }{ \frac { dx }{ x } } \) is _______.

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The value of \(\int _{ -\frac{\pi}{2}}^{ \frac{\pi}{2}}\) cos x dx is _______.
2)
The value of \(\int _{ 2 }^{ 3 }{ f(5-x) } dx-\int _{ 2 }^{ 3 }{ f(x) } dx\) is _______.
3)
Using the factorial representation of the gamma function, which of the following is the solution for the gamma function \(\Gamma \)(n) when n = 8 _______.
4)
If n > 0, then \(\Gamma \)(n) is _______.
5)
\(\int _{ 0 }^{ \infty }{ { x }^{ 4 }{ e }^{ -x } } \)dx is _______.

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The demand and supply functions are given by D(x)= 16 − x² and S(x) = 2x² + 4 are under perfect competition, then the equilibrium price x is ________.
2)
The given demand and supply function are given by D(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is ________.
3)
The profit of a function p(x) is maximum when ________.
4)
The demand function for the marginal function MR = 100 − 9x² is ________.
5)
When x₀ = 2 and P₀ = 12 the producer’s surplus for the supply function P_s = 2x² + 4 is ________.

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The marginal cost function is MC = 100 \(\sqrt x\). find AC given that TC = 0 when the out put is zero is ________.
2)
If MR and MC denote the marginal revenue and marginal cost and MR − MC = 36x − 3x² − 81 , then the maximum profit at x is equal to ________.
3)
If the marginal revenue of a firm is constant, then the demand function is ________.
4)
Area bounded by y = e^x between the limits 0 to 1 is ________.
5)
Area bounded by y = \(\left| x \right| \) between the limits 0 and 2 is ________.

12th Standard English Medium Business Maths Subject Differential Equations Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The degree of the differential equation \(\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3\) ______.
2)
The differential equation \({ \left( \frac { dx }{ dy } \right) }^{ 3 }+2{ y }^{ \frac { 1 }{ 2 } }\) = x is ______.
3)
If y = cx + c− c³ then its differential equation is ______.
4)
The particular integral of the differential equation is \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -8\frac { dy }{ dx } \) + 16y = 2e^4x ______.
5)
The integrating factor of x \(\frac { dy }{ dx } \) - y = x² is ______.

12th Standard English Medium Business Maths Subject Differential Equations Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The integrating factor of x \(\frac { dy }{ dx } \) - y = x² is ______.
2)
The particular integral of the differential equation f(D)y = e^ax where f(D) = (D−a)² ______.
3)
The P.I of (3D²+ D − 14)y = 13e^2x is ______.
4)
A homogeneous differential equation of the form \(\frac { dx }{ dy } \) = f\(\left( \frac { y }{ x } \right) \) can be solved by making substitution,______.
5)
The solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } +\frac { f\left( \frac { y }{ x } \right) }{ f'\left( \frac { y }{ x } \right) } \) is ______.

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Δ²y₀ = _______.
2)
E ≡ _______.
3)
If c is a constant then Δc = _______.
4)
If ‘n’ is a positive integer Δⁿ[ Δ^-n f(x)] _______.
5)
∇ ≡ _______.

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
If c is a constant then Δc = _______.
2)
If ‘n’ is a positive integer Δⁿ[ Δ^-n f(x)] _______.
3)
∇ ≡ _______.
4)
For the given points (x₀, y₀) and (x₁, y₁) the Lagrange’s formula is _______.
5)
If f (x)=x²+ 2x + 2 and the interval of differencing is unity then Δf (x) _______.

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
A variable which can assume finite or countably infinite number of values is known as ________.
2)
If p(x) =\(\frac{1}{10}\), c = 10, then E(X) is ________.
3)
In a discrete probability distribution the sum of all the probabilities is always equal to ________.
4)
A discrete probability function p(x) is always non-negative and always lies between ________.
5)
The height of persons in a country is a random variable of the type ________.

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0.29, 0.40, 0.35. Profit per unit is 0.50 paisa then expected profits for three days are ________.
2)
Given E(X)=5 and E(Y)=−2, then E(X−Y) is ________.
3)
A formula or equation used to represent the probability distribution of a continuous random variable is called ________.
4)
Which of the following is not possible in probability distribution?
5)
A discrete probability distribution may be represented by ________.

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Using the standard normal table, the sum of the probabilities to the right of z = 2.18 and to the left of z = -1.75 is ________.
2)
The time until first failure of a brand of inkjet printers is normally distributed with a mean of 1,500 hours and a standard deviation of 200 hours. What proportion of printers fails before 1000 hours?
3)
Monthly expenditure on their credit cards, by credit card holders from a certain bank, follows a normal distribution with a mean of Rs. 1,295.00 and a standard deviation of Rs. 750.00. What proportion of credit card holders spend more than Rs. 1,500.00 on their credit cards per month?
4)
Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be: ________.
5)
If the area to the left of a value of z (z has a standard normal distribution) is 0.0793, what is the value of z?

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
A manufacturer produces switches and experiences that 2 per cent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is ________.
2)
An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is ________.
3)
If for a binomial distribution b(n,p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to ________.
4)
Forty percent of the passengers who fly on a certain route do not check in any luggage. The planes on this route seat 15 passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?
5)
Which of the following statements is/are true regarding the normal distribution curve?

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
A _______is one where each item in the universe has an equal chance of known opportunity of being selected.
2)
A random sample is a sample selected in such a way that every item in the population has an equal chance of being included ______.
3)
Which one of the following is probability sampling
4)
In ________ the heterogeneous groups are divided into homogeneous groups.
5)
Errors in sampling are of ______.

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
In simple random sampling from a population of N units, the probability of drawing any unit at the first draw is ______.
2)
In ________ the heterogeneous groups are divided into homogeneous groups.
3)
If probability \(P[|\hat{\theta}-\theta|<\varepsilon] \rightarrow 1\) as \(n \rightarrow \infty\), for any positive \(\varepsilon \) then \(\hat{\theta}\) is said to ________ estimator of \(\theta\).
4)
An estimator is said to be ________ if it contains all the information in the data about the parameter it estimates.
5)
An estimate of a population parameter given by two numbers between which the parameter would be expected to lie is called an………..interval estimate of the parameter.

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The quantities that can be numerically measured can be plotted on a ________.
2)
How many causes of variation will affect the quality of a product?
3)
Variations due to natural disorder is known as ________.
4)
The assignable causes can occur due to ________.
5)
A typical control charts consists of ________.

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The components of a time series which is attached to short term fluctuation is ________.
2)
Factors responsible for seasonal variations are ________.
3)
The additive model of the time series with the components T, S, C and I is ________.
4)
Least square method of fitting a trend is ________.
5)
The value of ‘b’ in the trend line y = a + bx is ________.

12th Standard English Medium Business Maths Subject Operations Research Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
The purpose of a dummy row or column in an assignment problem is to _______.
2)
The solution for an assignment problem is optimal if _______.
3)
In an assignment problem involving four workers and three jobs, total number of assignments possible are _______.
4)
Decision theory is concerned with _______.
5)
A type of decision –making environment is _______.

12th Standard English Medium Business Maths Subject Operations Research Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
North-West Corner refers to ________.
2)
Solution for transportation problem using ________method is nearer to an optimal solution.
3)
In an assignment problem the value of decision variable x_ij is ______.
4)
If number of sources is not equal to number of destinations, the assignment problem is called______.
5)
The purpose of a dummy row or column in an assignment problem is to _______.

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the rank of the matrix \(\begin{pmatrix} 1 & 5 \\ 3 & 9 \end{pmatrix}\)
2)
Find the rank of the matrix A = \(\left( \begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 5 & 7 \end{matrix} \right) \)
3)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix} \right) \)
4)
Find the rank of the matrix A =\(\left( \begin{matrix} 1 & -3 \\ 9 & 1 \end{matrix}\begin{matrix} 4 & 7 \\ 2 & 0 \end{matrix} \right) \)
5)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 1 & 4 \\ 2 & 8 \end{matrix} \right) \)

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the area of the region bounded by the line x − 2y − 12 = 0 , the y-axis and the lines y = 2, y = 5.
2)
Using Integration, find the area of the region bounded the line 2y + x = 8, the x axis and the lines x = 2, x = 4.
3)
Find the area bounded by the lines y − 2x − 4 = 0, y = 1, y = 3 and the y-axis
4)
If MR = 20 − 5x + 3x², find total revenue function.
5)
For the marginal revenue function MR = 6 − 3x² − x³, Find the revenue function and demand function.

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Find the area of the region bounded by the parabola \(y=4{ - }x^{ 2 }\) , x −axis and the lines x = 0, x = 2.
2)
Find the area bounded by the lines y − 2x − 4 = 0, y = 1, y = 3 and the y-axis
3)
If MR = 20 − 5x + 3x², find total revenue function.
4)
If MR = 14 − 6x + 9x², find the demand function.
5)
For the marginal revenue function MR = 6 − 3x² − x³, Find the revenue function and demand function.

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Integrate the following with respect to x.
\(\frac { 8x+13 }{ \sqrt { 4x+7 } } \)
2)
Integrate the following with respect to x.
\({ \left( \sqrt { 2x } -\frac { 1 }{ \sqrt { 2x } } \right) }^{ 2 }\)
3)
Evaluate ∫(2sin x − 5cos x)dx
4)
Integrate the following with respect to x.
2cos x − 3sin x + 4sec² x − 5cosec²x
5)
Integrate the following with respect to x.
x⁸(1+x⁹)⁵

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

1)
Evaluate the following using properties of definite integrals:
\(\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ { x }^{ 3 }{ cos }^{ 3 }xdx } \)
2)
Evaluate the following integrals:
ഽ\(\sqrt { 2{ x }^{ 2 }-3 } \) dx
3)
Evaluate the following
\(\int _{ 0 }^{ \infty }{ { e }^{ -mx } } { x }^{ 6 }dx\)
4)
Evaluate
\(\Gamma(\frac{7}{2})\)
5)
Evaluate
\(\int _{ 0 }^{ \infty }{ { e }^{ -2x }{ x }^{ 5 }dx } \)

12th Standard English Medium Business Maths Subject Creative 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
A new transit system has just gone into operation in a city. Of those who use the transit system this year, 10% will switch over to using their own car next year and 90% will continue to use the transit system. Of those who use their cars this year, 80% will continue to use their cars next year and 20% will switch over to the transit system. Suppose the population of the city remains constant and that 50% of the commuters use the transit system and 50% of the commuters use their own car this year,
(i) What percent of commuters will be using the transit system after one year?
(ii) What percent of commuters will be using the transit system in the long run?
2)
Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 4 } }{ sin } 3xsin\ 2x\ dx\)
3)
The marginal revenue function (in thousands of rupees) of a commodity is 7+^e-0.05x where x is the number of units sold. Find the total revenue from the sale of 100 units (e^-5 = 0.0067)
4)
The total cost of production y and the level of output x are related to the marginal cost of production by the equation (6x²+2y²)dx-(x²+4xy)dy = 0. What is the relation between total cost and output if y = 2 when x = 1?
5)
Using Lagrange's formula find the value of y when x = 4 from the following table.

x 0 3 5 6 8

y 276 460 414 343 110

12th Standard English Medium Business Maths Subject Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
For what values of k, the system of equations kx+ y+z = 1, x+ ky+z= 1, x+ y+kz = 1 have
(I) Unique solution
(ii) More than one solution
(iii) no solution
2)
Evaluate \(\int { \frac { 1 }{ { 3x }^{ 2 }+13x-10 } } dx\)
3)
The elasticity of demand with respect to price for a commodity-is a constant and is equal to 2. Find the demand function and hence the total revenue function, given that when the price is 1, the demand is 4.
4)
Solve: (y-x)\(\frac { dy }{ dx } \) = a²
5)
From the following data, calculate the value of e^1.75

x 1.7 1.8 1.9 2.0 2.1

e^x 5.474 6.050 6.686 7.386 8.166

12th Standard English Medium Business Maths Subject Creative 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Solve: 2x + 3y = 5, 6x + 5y = 11
2)
Evaluate ഽe^x \(\left( \frac { 1+sinxcosx }{ { cos }^{ 2 }x } \right) dx\)
3)
Determine the cost of producing 3000 units of commodity if the marginal cost in rupees per unit is C'(x) = \(\frac{x}{3000}+2.50\)
4)
Solve: (D²+1)y = 0 when x = 0, y = 2 and when x = \(\frac { \pi }{ 2 } \), y = -2.
5)
Using Lagrange's formula, find the value of y when x = 42 from the following table

x 40 50 60 70

y 31 73 124 159

12th Standard English Medium Business Maths Subject Creative 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Find the rank of the matrix \(A=\left( \begin{matrix} 1 & 2 & -4 \\ 2 & -1 & 3 \\ 8 & 1 & 9 \end{matrix}\begin{matrix} 5 \\ 6 \\ 7 \end{matrix} \right) \)
2)
Evaluate \(\int { \frac { cos2x-cos2\alpha }{ cosx-cos\alpha } } dx\)
3)
Find the area under the demand curve xy = 1 bounded by the ordinates x = 3, x = 9 and x-axis
4)
Form the differential equation for y = (A + Bx)e^3x where A and B are constants.
5)
Using graphic method, find the value of y when x=27.

x 10 15 20 25 30

y 35 32 29 26 23

12th Standard English Medium Business Maths Subject Creative 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
If A and B are non-singular matrices, prove that AB is non-singular.
2)
Evaluate \(\int _{ 0 }^{ \pi }{ { sin }^{ 2 } } x\ dx\)
3)
Find the consumer's surplus for the demand function p = 25 - x -x² when P_o= 19
4)
Solve: \(\frac { dy }{ dx } \)+ ay = e^x (where a ≠ -1)
5)
When h = 1, find Δ (x³).

12th Standard English Medium Business Maths Subject Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Solve: x + 2y = 3 and 2x + 4y = 6 using rank method.
2)
Evaluate \(\int { \frac { 2{ cos }^{ 2 }x-cos2x }{ { sin }^{ 2 }x } } \)
3)
Find the area under the curve y = 4x² - 8x + 6 bounded by the Y-axis, X-axis and the ordinate at x = 2.
4)
Write down the order and degree of the following differential equations.
\(\left( \frac { dy }{ dx } \right) ^{ 2 }-7\frac { d^{ 3 }y }{ { dx }^{ 3 } } +y\frac { { d }^{ 2 }y }{ dx^{ 2 } } +4\frac { dy }{ dx } \)- log x = 0
5)
Find the missing term from the following data.

x 20 30 40

y 51 - 34

12th Standard English Medium Business Maths Subject Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
If A, B are two n x n non-singular matrices, then ___________
2)
If \(\int { \frac { 1 }{ \left( x+2 \right) \left( { x }^{ 2 }+1 \right) } } \) dx = a log \(\left| 1+{ x }^{ 2 } \right| \) +b tan^-1 x + \(\frac { 1 }{ 5 } log\left| x+2 \right| \) +c then ___________
3)
The Consumer's surplus for the demand function P =f(x) for the quantity X_o and price P_o is_________
4)
The integrating factor of \(\frac { dy }{ dx } +\frac { 2y }{ x } \)= x³ is _____________
5)
Δ is ____________

12th Standard English Medium Business Maths Subject Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
The rank of an n x n matrix each of whose elements is 2 is __________
2)
If \(\int { \frac { { 2 }^{ \frac { 1 }{ x } } }{ { x }^{ 2 } } } dx=k{ 2 }^{ \frac { 1 }{ x } }\) +c, then k is ___________
3)
The area of the region bounded by the ellipse __________
4)
If y = k.e^λx then its differential equation where k is arbitrary constant is _____________
5)
∇f(x+ 3h) ______________

12th Standard English Medium Business Maths Subject Applied Statistics Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Fit a straight line trend to the following data using the method of least square. Estimate the trend for 2007.

year 2000 2001 2002 2003 2004

Sales (in tonnes) 1 1.8 3.3 4.5 6.3

2)

From the data given below, calculate seasonal indices.

Quarter	Year
	1984	1985	1986	1987	1988
I	40	42	41	45	44
II	35	37	35	36	38
III	38	39	38	36	38
IV	40	38	40	41	42

3)

Compute
(i) Laspeyre's
(ii) Paasche's
(iii) Fisher's price index number for 2000 from the following data.

Commodity	Price		Quantity
	1990	2000	1990	2000
A	2	4	8	6
B	5	6	10	5
C	4	5	14	10
D	2	2	19	13

4)

Calculate Fisher's ideal index from the following data and verify that it satisfies both time reversal and factor reversal test

Commodity	Price		Quantity
	1985	1986	1985	1986
A	8	20	50	60
B	2	6	15	10
C	1	2	20	25
D	2	5	10	8
E	1	5	40	30

5)

The followingdata relateto the life(inhours) of 10 samples of 6 electricbulbs each drawn at an intervalof one hour from a production process.Draw the controlchart for \(\overline { X } \) and \(\overline { R } \) and comment.

Sample No	Lifetime (inhour)
	1	2	3	4	5	6
1	620	687	666	689	738	686
2	501	585	524	585	653	668
3	673	701	686	567	619	660
4	646	626	572	628	631	743
5	494	984	659	643	660	640
6	634	755	625	582	683	555
7	619	710	664	693	770	534
8	630	723	614	535	550	570
9	482	791	533	612	497	499
10	706	524	626	503	661	754

(For n = 6,A₂= 0.483,D₃ = 0,D₄ = 2.004)

12th Standard English Medium Business Maths Subject Probability Distributions Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Four coins are tossed simultaneously. What is the probability of getting
a) atleast 2 heads
b) atmost 2 heads.
2)
20% of the bolts produced in a factory are found to be defective. Find the probability that in a sample of 10 bolts chosen at random exactly 2 will be defective using
(i) Binomial distribution
(ii) Poisson distribution (e^-2 = 0.1353)
3)
The mean weight of 500 male students in a certain college is 151 pounds and the S.D is 15 pounds. Assuming the weights are normally distributed, find how many students weight
(i) between 120 and 155 pounds
(ii) more than 185 pounds.
4)
If the height of 300 students are normally distributed with mean 64.5 inches and standard deviation 3.3 inches find the height below which 99% of the student lie?
5)
Marks in an aptitude test given to 800 students of a school was found to be normally distributed 10% of the students scored below 40 marks and 10% of the students scored above 90 marks. Find the number of students scored between 40 and 90?

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
A discrete random variable X has the following probability distribution.

x 1 2 3 4 5 6 7

P(X) c 2c 2c 3c c² 2c² 7c²+c

Find the value of e. Also, find the mean of the distribution.
2)
The probability distribution of a random variation X is given below.

X 0 1 2 3 4

P(X) 0.1 0.25 0.3 0.2 0.15

Find
(i) V(X)
ii) V\((\frac{X}{2})\)
3)
The probability distribution of the discrete random variables X and Y are given below

X 0 1 2 3

P(X) \(\frac{1}{5}\) \(\frac{2}{5}\) \(\frac{1}{5}\) \(\frac{1}{5}\)

Y 0 1 2 3

P(Y) \(\frac{1}{5}\) \(\frac{3}{10}\) \(\frac{2}{5}\) \(\frac{1}{10}\)

Prove that E(Y²) = 2E(X).
4)
The random variable X tan take only the values 0,1,2. Given that P(X = 0) = P(X = 1) = P and E(X²) = E(X), find the value of p.
5)
The probability distribution of a random variable X is

X 1 2 4 2A 3A 5A

P(X) \(\frac{1}{2}\) \(\frac{1}{5}\) \(\frac{3}{25}\) \(\frac{1}{10}\) \(\frac{1}{25}\) \(\frac{1}{25}\)

Calculate
(i) A if E(X) = 2.94
(ii) V(X)

12th Standard English Medium Business Maths Subject Numerical Methods Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Estimate the production for 1962 and 1965 from the following data

year 1961 1962 1963 1964 1965 1966 1967

Production in tonnes 200 - 260 306 - 390 430
2)
From the following data, calculate the value of e^1.75

x 1.7 1.8 1.9 2.0 2.1

e^x 5.474 6.050 6.686 7.386 8.166
3)
From the data, find the number of students whose height is between 80 cm and 90 cm

Height in cm (x) 40-60 60-80 80 - 100 100-120 120-140

No. of. students (y) 250 120 100 70 50
4)
From the following table, estimate the premium for a policy maturing at the age of 58.

Age (x) 40 45 50 55 60

Premium (y) 114.84 96.16 83.32 74.48 68.48
5)
Using Lagrange's formula find the value of y when x = 4 from the following table.

x 0 3 5 6 8

y 276 460 414 343 110

12th Standard English Medium Business Maths Subject Differential Equations Creative 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Solve: \(\frac { dy }{ dx } \) = sin(x + y)
2)
Solve: x²\(\frac { dy }{ dx } \) = y²+2xy given that y = 1, when x = 1
3)
Solve: (y-x)\(\frac { dy }{ dx } \) = a²
4)
Solve: (D² + 14D + 49)y = e^-7x + 4.
5)
The rate of increase in the cost Cof ordering holding as the size q of the order increases is given by the differential equation \(\frac { dc }{ dq } =\frac { { c }^{ 2 }+2cq }{ { q }^{ 2 } } \). Find the relationship between c and q if c = 1 when q = 1.

12th Standard English Medium Business Maths Subject Differential Equations Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
The net profit p and quantity x satisfy the differential equation \(\frac { dp }{ dx } =\frac { 2{ p }^{ 3 }-{ x }^{ 3 } }{ 3x{ p }^{ 2 } } \). Find the relationship between the net profit and demand given that p = 20, when x = 10.
2)
The rate of increase in the cost Cof ordering holding as the size q of the order increases is given by the differential equation \(\frac { dc }{ dq } =\frac { { c }^{ 2 }+2cq }{ { q }^{ 2 } } \). Find the relationship between c and q if c = 1 when q = 1.
3)
The total cost of production y and the level of output x are related to the marginal cost of production by the equation (6x²+2y²)dx-(x²+4xy)dy = 0. What is the relation between total cost and output if y = 2 when x = 1?
4)
Equipment maintenance and operating costs (are related to the overhaul interval x by the equation \({ x }^{ 2 }\frac { dc }{ dx } -10xc=-10\) with c = c₀ and x = x₀. Find c as a function of x.
5)
Suppose that the quantity needed Q_d = 42 -4p-4\(\frac { dp }{ dt } +\frac { { d }^{ 2 }p }{ { dt }^{ 2 } } \) and quantity supplied Q_s= -6 + 8p where p is the price. Find the s equilibrium price for market clearance.

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
The sum of three numbers is 6. If we multiply the third number by 2 and add the first number to the result we get 7. By adding second and third numbers to three times the first number we get 12. Find the numbers using rank method
2)
A mixture is to be made of three foods A, B, C. The three foods A, B, C contain nutrients P, Q, R as shown below

Ounces per pound of Nutrient

Food P Q R

A 1 2 5

B 3 1 1

C 4 2 1

How to form a mixture which will have 8 ounces of P, 5 ounces of Q and 7 ounces of R? (Cramer's rule).
3)
For what values of k, the system of equations kx+ y+z = 1, x+ ky+z= 1, x+ y+kz = 1 have
(I) Unique solution
(ii) More than one solution
(iii) no solution
4)
Using determinants, find the quadratic defined by f(x) = ax² + bx + c if
f(1) = 0,
f(2) = - 2 and
f(3) = -6.
5)
A new transit system has just gone into operation in a city. Of those who use the transit system this year, 10% will switch over to using their own car next year and 90% will continue to use the transit system. Of those who use their cars this year, 80% will continue to use their cars next year and 20% will switch over to the transit system. Suppose the population of the city remains constant and that 50% of the commuters use the transit system and 50% of the commuters use their own car this year,
(i) What percent of commuters will be using the transit system after one year?
(ii) What percent of commuters will be using the transit system in the long run?

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
The marginal cost C' (x) and marginal revenue R' (x) are given by C' (x) = 20 +\(\frac{x}{20}\) and R' (x) = 30. The fixed cost is Rs.200. Determine the maximum profit.
2)
The marginal revenue function (in thousands of rupees) of a commodity is 7+^e-0.05x where x is the number of units sold. Find the total revenue from the sale of 100 units (e^-5 = 0.0067)
3)
The marginal cost function of a commodity in a firm is 2 + e^3x where X is the output. Find the total cost and average cost function if the fixed cost is Rs. 500.
4)
Find the area of the region bounded by the curve y = 3 x² - x, X-axis and the lines between x = -1 and x= 1
5)
Find the area of the region bounded by the parabola y² = 4x and the line 2x - y = 4.

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Find the area of the region bounded by the line y = x - 5, the x-axis and between the ordinates x = 3and x = 7
2)
The Marginal revenue for a commodity is MR=\(\frac { { e }^{ x } }{ 100 } +x+{ x }^{ 2 }\), find the revenue function.
3)
The elasticity of demand with respect to price for a commodity-is a constant and is equal to 2. Find the demand function and hence the total revenue function, given that when the price is 1, the demand is 4.
4)
A company determines that the marginal cost of producing x units is C'(x) = 10.6x. The fixed cost is Rs. 50. The selling price per unit is Rs.5. Find the profit function.
5)
The demand and supply functions under pure competition are P_d = 16 - x² and p_s = 2x² + 4. Find the consumer's surplus and producer's surplus at the market equilibrium price.

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
If f'(x) = a sin x + b cos x and f'(0) = 4, f(0) = 3, f\(\left( \frac { \pi }{ 2 } \right) \) = 5, find f(x).
2)
Evaluate \(\int { \frac { { x }^{ 7 } }{ { x }^{ 5 }+1 } } dx\)
3)
Evaluate ഽ x³ sin (x⁴) dx
4)
Evaluate \(\int { \frac { 1 }{ { 3x }^{ 2 }+13x-10 } } dx\)
5)
Evaluate ഽx. log (1 + x) dx

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Evaluate ഽ sin (log x) + cos (log x) dx
2)
Evaluate \(\int { \frac { \left( { x }^{ 2 }+1 \right) dx }{ { \left( x-1 \right) }^{ 2 }\left( x+3 \right) } } \)
3)
Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 4 } }{ sin } 3xsin\ 2x\ dx\)
4)
Prove that \(\int _{ a }^{ b }{ \frac { f\left( x \right) }{ f\left( x \right) +f(a+b-x) } } dx=\frac { b-a }{ 2 } \)
5)
Using integrals as limit of sums, evaluate \(\int _{ 2 }^{ 4 }{ (2x-1) } dx\)

12th Standard English Medium Business Maths Subject Operations Research Creative 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
For the given pay-off matrix, choose the best alternative for the given states of nature under
(i) Maximin (ii) Minimax princple

Alternative States of Nature

Good Fair Bad

A 100 60 +50

B 80 50 +10

C 40 20 +5
2)
Determine an initial basic feasible solution to the following transportation problem using North West corner rule.
3)
Determine how much quantity should be stepped from factory to various destinations for the following transportation problem using the least cost method.
4)
Find the initial basic feasible solution for the following transportation problem by Vogel's approximation method.
5)
Solve the following assignment problem. Cell values represent cost of assigning job A, B, C and D to the operators I, II, III and IV.

12th Standard English Medium Business Maths Subject Applied Statistics Creative 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Fit a straight line trend for the following data using the method of least squares.

x 0 1 2 3 4

y 1 1 3 4 6
2)
Fit a trend line to the following data by graphic method.

Year 1978 1979 1980 1981 1982 1983 1984 1985 1986

Production of steel 20 22 24 21 23 25 23 26 25
3)
Find a trend line to the following data by the method of sami-averages.

Years 1980 1981 1982 1983 1984 1985 1986

Sales 102 105 114 110 108 116 112

4)

Calculate the seasonal indices for the following data by the method of simple average.

Year	Quarters
Year	I	II	III	IV
1994	78	66	84	80
1995	76	74	82	78
1996	72	68	80	70
1997	74	70	84	74
1998	76	74	86	82

5)

Compute Fisher's price index number for the following data.

Commodity	Base Year		Current Year
Commodity	Price	Quantity	Price	Quantity
A	10	12	12	15
B	7	15	5	20
C	5	24	9	20
D	16	5	14	5

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Creative 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
A random sample of 500 apples was taken from large consignment and 45 of them were found to be bad. Find the limits at which the bad apples lie at 99% confidence level.
2)
A sample of five measurements of the diameter of a sphere were recorded by a scientist as 6.33, 6.37,6.36,6.32 and 6.37 mm. Determine the point estimate of
(a) mean
(b) variance.
3)
A random sample of marks in mathematics secured by 50 students out of 200 students showed a mean of 75 and a standard deviation of 10. Find the 95% confidence limits for the estimate of their mean marks.
4)
A company market car tyres. Their lives are normally distributed with a mean of 50,000 kms and standard derivation of 2000 kms. A test sample of 64 tyres has a mean life of 51250 km. Can you conclude that the sample mean differs significantly from the population mean? (Test at 5% level).
5)
The mean life time of 50 electric bulbs produced by a manufacturing company is estimated to be 825 hours with the S.D. of 110 hours. If II is the mean life time of all the bulbs produced by the company, test the hypothesis that μ = 900 hours at 5% level of significance.

12th Standard English Medium Business Maths Subject Probability Distributions Creative 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
The probability that an event A happens in one treat of an experiment is 0.4. Three independent treats of the experiment are performed. Find the p!probability that the event A happens at least once.
2)
The standard deviation of a binomial distribution (q +p)¹⁶ is 2. Find its mean.
3)
If a random variable X follows Poisson distribution such that P(X = 2) = 9. P(X = 4) + 90 P(X = 6) then find the mean and variance.
4)
Find the value of K if X is a normal variate whose p.d.f is given by f(x) = \(\frac { 1 }{ K } \)e^8x-4x2, -∞
5)
Obtain K, μ and σ2 of of the normal distribution whose probability distribution function is f(x) = \(K{ e }^{ -2x^{ 2 }+4x-2 }\), -∞

12th Standard English Medium Business Maths Subject Probability Distributions Creative 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
A die is thrown 120 times and getting 1 or 5 is considered a success. Find the mean and variance of the number of successes.
2)
If on an average 1 ship out of 10 do not arrive safely to ports. Find the mean and the standard deviation of ships returning safely out of a total of 500 ships.
3)
Alpha particles are emitted by a radio active source at an average rate of 5 in a 20 minutes interval. Using Poisson distribution find the probability that there will be atleast 2 emission in a particular 20 minutes interval (e^-5 = 0.0067).
4)
Suppose that the amount of cosmic radiation to which a person is exposed when flying by jet across USA is a random vertical. having a normal distribution with mean of 4.35m rem and a standard deviation of 0.59m rem. What is the probability that a person will be exposed to more than 5.20 m rem of cosmic radiation of such a flight?
5)
The life of army shoes is normally distributed with mean 8 months and standard deviation 2 months. If 5000 pairs are issued, how many pairs would be expected to need replacement within 12 months.

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
If a random variable. X has the probability distribution

X 0 1 2 3 4 5

P(X=x) a 2a 3a 4a 5a 6a

then find F(4)
2)
Let X denote the number of hours you study during a randomly selected school day. The probability distribution function is
\(P(X=x)=\begin{cases} \begin{matrix} 0.1 & if\quad x=0 \end{matrix} \\ \begin{matrix} kx & if\quad x=1\quad or\quad 2 \end{matrix} \\ \begin{matrix} k(5-x) & if\quad x=3\quad or\quad 4 \end{matrix} \\ \begin{matrix} 0, & otherwise \end{matrix} \end{cases}\)
Find the value of k and what is the probability that you study atleast 2 hours.
3)
A random variable X can take all nonnegative integral values and the probabilities that X takes the value r is proportional to aT (0 < ∝ < 1). Find P(X = 0)
4)
Two cards are drawn from a pack of 52 playing cards. Find the probability distribution of the number of aces.
5)
An urn contains 4 white and 6 red balls. Four balls are drawn at random from the urn. Find the probability distribution of the number of white balls.

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
The probability distribution of a discrete random variable. X is given by

X -2 2 5

P(X=x) \(\frac{1}{4}\) \(\frac{1}{4}\) \(\frac{1}{2}\)

then find 4E(X²)- Var (2X)
2)
A random variable. X has following distribution

X -1 0 1 2

P(X=x) \(\frac{1}{3}\) \(\frac{1}{6}\) \(\frac{1}{6}\) \(\frac{1}{3}\)

Find E(2X+3)²
3)
If a continuous random variable. X has the p.d.f. f(x) = 4k(x-1)³, 1 ≤ x ≤ 3 then find p[-2 ≤ X ≤ 2]
4)
A player tosses two unbiased coins. He wins Rs. 5 if two heads appear, Rs. 2 if one head appear and Rs.1 if no head appear. Find the expected amount to win.
5)
If the probability density function of a random variable. X is given by f(x) = \(\frac{2x}{9}\),0

12th Standard English Medium Business Maths Subject Numerical Methods Creative 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
From the following data, estimate the population for the year 1986 graphically.

year 1960 1970 1980 1990 2000

Population (in thousands) 12 15 20 26 33
2)
Find the number of men getting wages between Rs. 30 and Rs. 35 from the following table.

Wages (x) 20 - 30 30 - 40 40 - 50 50 - 60

No. of men (y) 9 30 35 42
3)
Estimate the population for the year 1995.

year (x) 1961 1971 1981 1991 2001

population in thousands (y) 46 66 81 93 101
4)
Using Lagrange's formula, find the value of y when x = 42 from the following table

x 40 50 60 70

y 31 73 124 159
5)
Using Lagrange's formula and y(x) from the following table.

x 6 7 10 12

y 13 14 15 17

12th Standard English Medium Business Maths Subject Numerical Methods Creative 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
From the following data, estimate the population for the year 1986 graphically.

year 1960 1970 1980 1990 2000

Population (in thousands) 12 15 20 26 33
2)
Using graphic method, find the value of y when x=27.

x 10 15 20 25 30

y 35 32 29 26 23
3)
Find y when x = 0.2 given that

x 0 1 2 3 4

y 176 185 194 202 212
4)
If y₇₅ = 2459, y₅₀ = 2018, y₈₅ = 1180, and y₉₀ =402, find y₈₂

x 75 80 85 90

y 2459 2018 1180 402
5)
Find the number of men getting wages between Rs. 30 and Rs. 35 from the following table.

Wages (x) 20 - 30 30 - 40 40 - 50 50 - 60

No. of men (y) 9 30 35 42

12th Standard English Medium Business Maths Subject Differential Equations Creative 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Find the differential equation of all circles x² +y² + 2gx = 0 which pass through the origin and whose centres are on the X-axis.
2)
Form the differential equation for \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \)=1 where a & b are arbitrary constants.
3)
Form the differential equation for y = (A + Bx)e^3x where A and B are constants.
4)
Solve: sec 2x dy - sin 5x sec² y dx = 0
5)
Solve: cos²x dy + y.e^tanx dx = 0

12th Standard English Medium Business Maths Subject Differential Equations Creative 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Solve: (x+y)²\(\frac { dy }{ dx } \) = 1
2)
Find the equation of the curve passing through (1, 0) and which has slope 1+ \(\frac { y }{ x } \) at (x, y).
3)
Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y = 2(e^x-x-1).
4)
Solve: (D²+1)y = 0 when x = 0, y = 2 and when x = \(\frac { \pi }{ 2 } \), y = -2.
5)
A man plans to invest some amount in a small saving scheme with a guaranteed compound in crest compounded continuously at the ratio of 12 percent for 5 years. How much should he invest if he wants an amount of Rs. 25000 at the end of 5 year period? (e^-0.6 = 0.5488)

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Find the area contained between the x-axis and one arc of the curve y = cos x bounded between
\(x=-\frac { \pi }{ 2 } and\quad x=\frac { \pi }{ 2 } \)
2)
Find the area under the demand curve xy = 1 bounded by the ordinates x = 3, x = 9 and x-axis
3)
Find the area bounded by one arc of the curve y = sin ax and the x-axis.
4)
Determine the cost of producing 3000 units of commodity if the marginal cost in rupees per unit is C'(x) = \(\frac{x}{3000}+2.50\)
5)
The marginal revenue function is given by \(R'(x)=\frac { 3 }{ { x }^{ 2 } } -\frac { 2 }{ x } \). Find the revenue function and demand function if R(1) = 6

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Evaluate \(\int { \frac { { sec }^{ 2 }x }{ 3+tanx } } dx\)
2)
Evaluate ഽ sin³ x cos x dx
3)
Evaluate \(\int { \frac { 1 }{ \sqrt { { 16x }^{ 2 }+25 } } } dx\)
4)
Evaluate ഽe^x \(\left( \frac { 1+sinxcosx }{ { cos }^{ 2 }x } \right) dx\)
5)
Evaluate \(\int _{ 1 }^{ 2 }{ \frac { log\quad x }{ { x }^{ 2 } } } dx\)

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Evaluate \(\int { \frac { { { x }^{ 4 }+{ x }^{ 4 }+1 } }{ { x }^{ 2 }-x+1 } } \)
2)
Evaluate \(\int { \frac { cos2x-cos2\alpha }{ cosx-cos\alpha } } dx\)
3)
Evaluate \(\int { \frac { { ({ a }^{ x }{ +b }^{ x }) }^{ 2 } }{ { a }^{ x }b^{ x } } dx } \)
4)
If f' (x) = 3x² - \(\frac { 2 }{ { x }^{ 3 } } \) and f(1) = 0, find f(x)
5)
Evaluate \(\int { \frac { { 8 }^{ 1+x }+{ 4 }^{ 1-x } }{ { 2 }^{ x } } } dx\)

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Creative 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Solve: 2x - 3y - 1 = 0, 5x + 2y - 12 = 0 by Cramer's rule.
2)
If \(\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 2 \\ -1 \\ 3 \end{matrix} \right] \) find x,y and z
3)
If \(A=\left( \begin{matrix} 2 & 4 \\ 4 & 3 \end{matrix} \right) ,X=\left( \begin{matrix} n \\ 1 \end{matrix} \right) B=\left( \begin{matrix} 8 \\ 11 \end{matrix} \right) \) and AX = B then find n.
4)
Solve: 2x + 3y = 5, 6x + 5y = 11
5)
Two products A and B currently share the market with shares 60% and 40% each respectively. Each week some brand switching latees place. Of those who bought A the previous week 70% buy it again whereas 30% switch over to B. Of those who bought B the previous week, 80% buy it again whereas 20% switch over to A. Find their shares after one week and after two weeks.

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Creative 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Find the rank of the matrix
\(A=\left( \begin{matrix} 2 & 4 & 5 \\ 4 & 8 & 10 \\ -6 & -12 & -15 \end{matrix} \right) \)
2)
Find the rank of the matrix \(A=\left( \begin{matrix} 1 & 2 & -4 \\ 2 & -1 & 3 \\ 8 & 1 & 9 \end{matrix}\begin{matrix} 5 \\ 6 \\ 7 \end{matrix} \right) \)
3)
Show that the equations 2x - y + z = 7, 3x + y - 5z = 13, x + y + z = 5 are consistent and have a unique solution.
4)
Show that the equations x + 2y = 3, y - z = 2, x + y + z = 1 are consistent and have infinite sets of solution.
5)
Show that the equations x- 3y + 4z = 3, 2x - 5y + 7z = 6, 3x - 8y + 11z = 1 are inconsistent

12th Standard English Medium Business Maths Subject Operations Research Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Obtain the initial solution for the following problem using north-west corner rule.
2)
Determine an initial basic feasible solution to the following transportation problem using feast cost method.
3)
Consider the following pay-off (profit) matrix action, states

Action States

B₁ B₂

_A1 8 6

_A2 9 2

_A3 6 4

Determine the best action using maximin principle.
4)
For the given pay-off matrix, find the optimal decision under the minimax principle.
5)
The following is the pay-off matrix (in rupees) for three strategies and three states of nature. Select a strategy using maximin principle.

12th Standard English Medium Business Maths Subject Applied Statistics Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Using the method ofleast squares, fit a straight line trend for Σx = 10, Σy = 16.9, Σx² = 30, Σxy = 47.4 and n = 7.

2)

Calculate the 3-yearlymoving averages of the production figures (in tonnes) for the following data.

Year	1973	1974	1975	1976	1977	1978	1979	1980	1981	1982	1983	1984	1985	1986	1987
Production	15	21	30	36	42	46	50	56	63	70	74	82	90	95	102

3)
Calculate the seasonal indices by the method of simple average for the following data.

Year I quarter II quarter III quarter IV quarter

1985 68 62 61 63

1986 65 58 66 61

1987 68 63 63 67

4)

Construct the cost of living index for 2003 on the basis of 2000 from the following data using family budget method.

Item	Price(Rs.)		Weights
Food	2000	2003	30
Rent	200	280	30
Clothing	150	120	20
Fuel & lighting	50	100	10
Miscellaneous	100	200	20

5)

The following data shows the value of sample mean (\(\bar{X}\)) and the range R for 10 samples of size 5 each. Calculate the control limits for : mean chart and range chart.

Sample No.	1	2	3	4	5	6	7	8	9	10
Mean \(\bar{X}\)	11.2	11.8	10.8	11.6	11.0	9.6	10.4	9.6	10.6	10.0
Range	7	4	8	5	7	4	8	4	7	9

(Given for n = 5, A₂ = .577, D₃ = 0, D₄ = 2.115)

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
A random sample of size 50 with mean 67.9 is drawn from a normal population. If it is known that the standard error of the sample \(\sqrt { 0.7 } \) , find 95% confidence interval for the population mean.
2)
Out of 1000 T.V. viewers, 320 watched a particular programme. Calculate the standard error.
3)
Out of 1500 school students, a sample of 150 selected to test the accuracy of solving a problem in B.M. and of them 10 did a mistake. Calculate the standard error of sample proportion.
4)
A sample of 400 students is found to have mean height of 171.38 cms, Can it reasonable be regarded as a sample from a large population with mean height of 171.17 cms and standard deviation of 3.3 cms (Test at 5% level)
5)
The income distribution of the population of a village has a mean of Rs. 6000 and a variance of Rs. 32,400. Could a sample of 64 persons with a mean income of Rs. 5950 belong to this population. (Test at 1% level of significance).

12th Standard English Medium Business Maths Subject Numerical Methods Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Find the missing term from the following data.

x 20 30 40

y 51 - 34
2)
If f(0) = 5, f(1) = 6, f(3) = 50, find f(2) by using Lagrange's formula.
3)
Find the missing term from the following data

x 1 2 3 4

f(x) 100 - 126 157
4)
When h = 1, find Δ (x³).
5)
Find the second order backward differences of f(x).

12th Standard English Medium Business Maths Subject Probability Distributions Creative 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
In a Poisson distribution 3 P(X = 2) = P(X = 4), then find the parameter of the distribution.
2)
If the mean of the binomial distribution with 9 trial is 6, then find the variance.
3)
If the mean of the binomial distribution is 20 and standard deviation is 4, then find the number of events.
4)
Suppose X is a binomial variate X ~ B (5, p) and P(X = 2) = P(X = 3), then find p.
5)
If 10 coins are tossed, find the probability that exactly 5 heads appears.

12th Standard English Medium Business Maths Subject Probability Distributions Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Students of a class were given an aptitude test. Marks were found to be normally distributed with mean 60 and S.D. 5. Find the percentage of students who scored more than 60 marks.
2)
In a packet of 50 pens, 10 are defective, 10 pens are selected at random. What is the probability that atleast one is defective.
3)
The random variable X has the normal distribution f(x) = \(C{ e }^{ -\left( \frac { x-100 }{ 50 } \right) ^{ 2 } }\), then find the value of C.
4)
If you buy a lottery ticket in 50 lotteries, in each which your chance of winning a prize is \(\frac { 1 }{ 100 } \). What is the approximate probability that you will win a prize at least once (e-0.5 = 0.6066).
5)
The probability of the happening of an event X is 0.002 in an experiment. If an experiment is reported 1000 times, find the probability that the event X happens exactly twice? (e^-2 = 0.1353)

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Verify whether \(f(x)=\begin{cases} \frac { 2x }{ 9 } ,\quad 0\le x\le \\ 0,\quad elsewhere \end{cases}\) is a probability density function
2)
A continuous random variable. X has the p.d.f. defined by \(f(x)=\left\{\begin{array}{l} C e^{-a x}, \quad 0<x<\infty \\ 0, \quad \text { elsewhere } \end{array}\right.\) Find the value of C if a> 0
3)
In an entrance examination a student has to answer all the 120 questions. Each question has four options and only one option is correct. A student gets 1 mark for a correct answer and loses \(\frac{1}{2}\) mark for a wrong answer. What is the expectation of the mark scored by a student if he chooses the answer to each question at random?
4)
In a gambling game a man wins Rs. 10 if he gets all heads or all tails and loses Rs. 5 if he gets 1 or 2 heads when 3 coins are tossed once. Find his expectation of gain.
5)
Find the mean for the probability density function \(f(x)=\begin{cases} \frac { 1 }{ 24 } ,-12\le x\le 12 \\ 0,\quad otherwise \end{cases}\)

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Determine whether the following is a probability distribution of a random variable X.

X 0 1 2

P(X) 0.6 0.1 0.2
2)
An unbiased die is rolled. If the random variable X is defined as
X(w) = {1, the outcome w is an even number
{0, if the outcome w is an odd number
Find the probability distribution of X.
3)
Two eggs are drawn at random without replacement from a bag containing two bad eggs and eight good eggs. Find the probability of getting two bad eggs?
4)
A random variable X has the probability mass function

X -2 3 1

P(X=x) \(\frac{k}{6}\) \(\frac{k}{4}\) \(\frac{k}{12}\)

then find k
5)
A discrete random variable. X has the following probability distribution

X 0 1 2 3 4 5 6 7 8

P(X) a 3a 5a 7a 9a 11a 13a 15a 17a

Pind the value of a and P(X< 3)

12th Standard English Medium Business Maths Subject Differential Equations Creative 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Solve: (x² - ay)dx = (ax-y²)dy
2)
Solve: \(\frac { dy }{ dx } \)+ ay = e^x (where a ≠ -1)
3)
The change in the cost of ordering and holding C as quantity q is given by \(\frac { dC }{ dq } =a-\frac { c }{ q } \) where a is a Constanst. Find C as a function of q.
4)
Solve: 3\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } -5\frac { dy }{ dx } \)+ 2y = 0
5)
Solve: (D²-6D+25)y = 0

12th Standard English Medium Business Maths Subject Differential Equations Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Write down the order and degree of the following differential equations.
\(\left( \frac { dy }{ dx } \right) ^{ 3 }-4\left( \frac { dy }{ dx } \right) \)+y = 3e^x
2)
Write down the order and degree of the following differential equations.
\(\left( \frac { dy }{ dx } \right) ^{ 2 }-7\frac { d^{ 3 }y }{ { dx }^{ 3 } } +y\frac { { d }^{ 2 }y }{ dx^{ 2 } } +4\frac { dy }{ dx } \)- log x = 0
3)
Write down the order and degree of the following differential equations.
\(\sqrt { 1+\left( \frac { dy }{ dx } \right) ^{ 2 } } \)= 4x
4)
Write down the order and degree of the following differential equations.
\(\left[ 1+\left( \frac { dy }{ dx } \right) ^{ 2 } \right] ^{ \frac { 2 }{ 3 } }=\frac { d^{ 2 }y }{ { dx }^{ 2 } } \)
5)
Find the differential equation for y = mx + \(\frac { a }{ m } \) where m is arbitrary constant.

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Find the area of the region bounded by the parabola x² = 4y, y = 2, y = 4 and the y-axis.
2)
Find the area under the curve y = 4x² - 8x + 6 bounded by the Y-axis, X-axis and the ordinate at x = 2.
3)
Find the area under the curve y = 4x - x² included between x = 0, x = 3 and the X-axis.
4)
The marginal cost function of manufacturing x units of a commodity is 3x² - 2x + 8. If there is no fixed cost, find the total cost function?
5)
If the marginal revenue for a commodity is MR = 9 - 6x² + 2x, find the total revenue function.

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
The marginal cost at a production level of x units is given by C '(x) = 85 +\(\frac{375}{x^2}\). Find the cost of producing 10 in elemental units after 15 units have been produced?
2)
The marginal cost function is MC = \(\frac{100}{x}\). Find the cost function C(x) if C(16) = 100.
3)
Find the demand function for which the elasticity of demand is 1
4)
Find the consumer's surplus for the demand function p = 25 - x -x² when P_o= 19
5)
Find the producer's surplus for the supply function p = x² + x + 3 when x_o = 4

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
If f'(x) = 8x³ -2x², f(2) = 1, find f(x)
2)
Evaluate \(\int { x } \sqrt { x+2 } dx\)
3)
If \(\int _{ 0 }^{ 1 }{ \left( { 3x }^{ 2 }+2x+k \right) } dx=0\), find k.
4)
Evaluate \(\int _{ 0 }^{ \pi }{ { sin }^{ 2 } } x\ dx\)
5)
If \(\int _{ 0 }^{ a }{ { 3x }^{ 2 } } dx=8\) find the value of a

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Evaluate \(\int { { a }^{ 3{ log }_{ a }x } } dx\)
2)
Evaluate \(\int { \frac { 2{ cos }^{ 2 }x-cos2x }{ { sin }^{ 2 }x } } \)
3)
Evaluate ∫ tan²x dx
4)
Evaluate \(\int { \frac { 2+3cosx }{ { sin }^{ 2 }x } } dx\)
5)
Evaluate \(\int { \frac { { 2 }^{ x }+{ 3 }^{ x } }{ { 5 }^{ x } } dx } \)

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Creative 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Find the rank of the matrix \(\left[ \begin{matrix} 7 & -1 \\ 2 & 1 \end{matrix} \right] \)
2)
Find the rank of the matrix \(\left( \begin{matrix} 2 & -4 \\ -1 & 2 \end{matrix} \right) \)
3)
Solve x + 2y = 3 and x +y = 2 using Cramer's rule.
4)
Solve: x + 2y = 3 and 2x + 4y = 6 using rank method.
5)
Show that the equations x + y + z = 6, x + 2y + 3z = 14 and x + 4y + 7z = 30 are consistent

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 23, 2021 - View & Read

1)
Solve: 2x + 3y = 4 and 4x + 6y = 8 using Cramer's rule.
2)
If A and B are non-singular matrices, prove that AB is non-singular.
3)
For what value of x, the matrix
\(A=\left| \begin{matrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ x & 2 & -3 \end{matrix} \right| \) is singular?
4)
If \(\left( \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix} \right) \left( \begin{matrix} x \\ y \\ z \end{matrix} \right) =\left( \begin{matrix} 1 \\ -1 \\ 0 \end{matrix} \right) \) find x, y and z
5)
Two newspapers A and B are published in a city . Their market shares are 15% for A and 85% for B of those who bought A the previous year, 65% continue to buy it again while 35% switch over to B. Of those who bought B the previous year, 55% buy it again and 45% switch over to A. Find their market shares after one year

12th Standard English Medium Business Maths Subject Operations Research Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 22, 2021 - View & Read

1)
_____determines the highest out come for each alternative.
2)
Operation research is an analytical method of ___________
3)
The methods of funding feasible solution to a transportation problem ___________
4)
The least cost method is more economical than North West Corner Rule, since it starts with the ___________
5)
The penalty is the difference between the ___ costs in each row and column.

12th Standard English Medium Business Maths Subject Operations Research Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 22, 2021 - View & Read

1)
To assign different jobs to the different machines to minimize the overall cost is ___________
2)
The optimum_______schedule remains, unaltered if we add or subtract a constant from all the elements of the row or which of the cost________matrix.
3)
If the number of rows is____tothenumber of columns, then the assignment problem is said to be balanced.
4)
______ method provides optimum assignment schedule in an assignment problem.
5)
_____determines the lowest out comes for each alternative.

12th Standard English Medium Business Maths Subject Applied Statistics Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 22, 2021 - View & Read

1)
Time series consists of data arranged
2)
Seasonal variations are __________
3)
The components used in the time series y = T + S + C + l are __________
4)
The methods of measurements of trends are __________
5)
Seasonal variations can be measured when the data are available in season wise __________

12th Standard English Medium Business Maths Subject Applied Statistics Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 22, 2021 - View & Read

1)
Most commonly used index numbers are _________ index number
2)
Chance variation in the manufactured product is __________
3)
Variation due to assignable causes in the product occur due to, _____
4)
The causes leading to vast variation in the specification of a product are usually due to _____
5)
Most frequently used index number formulae are_____

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 22, 2021 - View & Read

1)
There are _______ branches of statistical inference.
2)
An _______ is a specific observed value of a statistic
3)
If 55 is the mean mark obtained by a sample of 5 students randomly drawn from a class of 100 students is considered to the means marks of the entire class. This single value 55 is a
4)
If α is the level of significance. then the confidence Co-efficient is
5)
Any hypothesis which is complementary to the null hypothesis is _______ hypothesis.

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 22, 2021 - View & Read

1)
Probability of rejecting null hypothesis. when it is true is _______
2)
The number of ways in which one can select 2 customers out of 10 customers is __________
3)
The standard error of the sample mean is __________
4)
Which of the following statements is true?
5)
The Z-value that is used to establish a 95% confidence interval for the estimation of a population parameter is __________

12th Standard English Medium Business Maths Subject Probability Distributions Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 22, 2021 - View & Read

1)
If the variance of a Poisson distribution is 0.5. Then p(X = 3) is _________ (e^-0.5= 0.6066)
2)
For a binomial distribution with mean 2 and variance \(\frac{4}{3}\), p = _________
3)
In a binomial distribution if n = 5, p(x = 3) = 2. p(x = 2), then p = _________
4)
For a standard normal distribution, the mean and variance are _________
5)
The normal distribution curve is _______

12th Standard English Medium Business Maths Subject Probability Distributions Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 22, 2021 - View & Read

1)
The probability that a normal variate X lies in the interval (μ-σ, μ+σ) is ___________
2)
In case of normal distribution, skewness is ___________
3)
For a normal distribution if the mean is m, mode is n and median is m, then ___________
4)
If the mean of the binomial distribution is 25, then its standard deviation lies in the interval ___________
5)
The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, the probability that he hits the target is ___________

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 22, 2021 - View & Read

1)
If X is a discrete random variable. then P(X≥a)=________.
2)
If X is a continuous random variable. then P(X≥a)= _________.
3)
If X is a discrete random variable., then which of the following is correct?
4)
Which of the following are correct?
(i) E(aX+b) = a E(X) + b
(ii) μ₂= μ₂¹ - (μ₁¹)²
(iii) μ²= variance
(iv) V (a X + b) = a² V(x)
5)
A discrete random variable. X has the probability mass function p(x), then __________ is true.

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 22, 2021 - View & Read

1)
X is a random variable. Taking the values 3, 4 and 12 with probabilities \(\frac{1}{3},\frac{1}{4}\)and \(\frac{5}{12}\).Then E(X) is
2)
Variance of the random variable. X is 4, Its mean is 2. Then E(X²) is _________
3)
μ₂= 20, μ¹₂ = 276 for a discrete random variable X. Then the mean of the random variable. X is _________
4)
V(4X + 3) is _________
5)
If E(X) = \(\frac{1}{2}, E(X^2)=\frac{1}{4}\), then V(X) is ________

12th Standard English Medium Business Maths Subject Numerical Methods Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 22, 2021 - View & Read

1)
The nationality of the mathematician Joseph Louis Laguange is _________
2)
The knowledge of ______ is essential for the study of Numerical Analysis
3)
The forward difference operator Δ is ______________
4)
The backward difference operator ∇ is ______________
5)
Δ is ____________

12th Standard English Medium Business Maths Subject Numerical Methods Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 22, 2021 - View & Read

1)
∆f(x + 3h) ______________
2)
Δ can be defined as Δf(x) =f(x + h) -f(x) where h is the __________ interval of spacing
3)
If c is a constant, then Δc = ______________
4)
Δ(f(x) + g(x)) = ________
5)
If c is a constant, then Δc.f(x) ______________

12th Standard English Medium Business Maths Subject Differential Equations Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 22, 2021 - View & Read

1)
On putting y = vx; homogeneous differential equation x²dy + y(x + y)dx = 0 becomes ______
2)
The I.F. of \(\frac { dy }{ dx } \)- y tan x = cos x is _____
3)
The P.I. of (3D²+D-14)y = 13 e^2x is ______
4)
The P.I. of the differential equation f(D)y = e^ax where f(D) = (D-a) g(D), g(a) ≠0 is _____
5)
The equation of ydx + xdy = e^-xy dx if it cuts the Y-axis is ______

12th Standard English Medium Business Maths Subject Differential Equations Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 22, 2021 - View & Read

1)
The amount present in a radio active element disintegrates at a rate proportional to its amount. The differential equation corresponding to the above statement is _____________ (k is negative).
2)
The differential equation satisfied by all the straight lines in xy plane is _____________
3)
If y = k.e^λx then its differential equation where k is arbitrary constant is _____________
4)
The differential equation obtained by eliminating a and b from y = a e^3x + b e^-3x is _____________
5)
The differential equation formed by eliminating A and B from y = e^x (A cos x + B sin x) is _____________

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 22, 2021 - View & Read

1)
The are bounded by the demand curve xy = 1, the X-axis, x = 1 and x = 2 is ________
2)
The area above the supply curve p = g(x) and below the line p = p_o is ________.
3)
The area below the demand curve p = f(x) and above the line p = p_o is________.
4)
Profit = Total revenue - __________.
5)
Profit function is maximum when \(\frac{dp}{dx}\) = 0 and \(\frac{d^2p}{dx^2}\) is _________.

12th Standard English Medium Business Maths Subject Integral Calculus – II Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 22, 2021 - View & Read

1)
The area of the region bounded by the line y = 3x + 2, the X-axis and the ordinates x = - 1 and x = 1is_________ sq. units.
2)
The value of \(\int _{ -3 }^{ 2 }{ |x+1| } dx\) is______.
3)
The area lying above the X-axis and under the parabola y = 4x - x² is ______ sq. units
4)
The area of the region bounded by the curve y² = 2y - x and the y-axis _____ sq. units
5)
The area bounded by the curve y = 4ax and the lines y² = 2a and Y-axis is _______ sq. units.

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 22, 2021 - View & Read

1)
∫ e^x (sin x + cos x) dx = ________________ +c.
2)
\(\int _{ 4 }^{ 9 }{ \frac { 1 }{ \sqrt { 2 } } } \) dx =
3)
\(\int _{ 0 }^{ 1 }{ \frac { 1 }{ 2x-3 } } \) dx = ____________
4)
\(\int _{ 1 }^{ 4 }{ f\left( x \right) } dx,\) where f(x) = \(\begin{cases} 7x+3\quad if\quad 1\le x\le 3 \\ 8x\quad if\quad 3\le x\le 4 \end{cases}\) is _____________.
5)
\(\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 71 } } x\) dx = ____________

12th Standard English Medium Business Maths Subject Integral Calculus – I Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 22, 2021 - View & Read

1)
\(\int { { \left| x \right| }^{ 3 } } \)dx = ________________ +c
2)
\(\int { \frac { 2 }{ { \left( { e }^{ x }+{ e }^{ -x } \right) }^{ 2 } } } \) dx = ____________ +c
3)
\(\int { { e }^{ x } } \) (1-cot x +cot² x) dx = _______________ +c
4)
\(\int { { e }^{ x } } \) f(x) + f' (x) dx = _____________ +c
5)
If ∫ x sin x dx = - x cos x + α then α = __________ +c

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 22, 2021 - View & Read

1)
The rank of an n x n matrix each of whose elements is 2 is __________
2)
The value of \(\left| \begin{matrix} { 5 }^{ 2 } & { 5 }^{ 3 } & { 5 }^{ 4 } \\ { 5 }^{ 3 } & { 5 }^{ 4 } & { 5^{ 5 } } \\ { 5 }^{ 4 } & { 5 }^{ 5 } & { 5 }^{ 6 } \end{matrix} \right| \)
3)
If \(\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right| \) then x =
4)
If A is a singular matrix, then Adj A is ___________
5)
If A, B are two n x n non-singular matrices, then ___________

12th Standard English Medium Business Maths Subject Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 05, 2021 - View & Read

1)
The price of 3 Business Mathematics books, 2 Accountancy books and one Commerce book is Rs. 840. The price of 2 Business Mathematics books, one Accountancy book and one Commerce book is Rs. 570. The price of one Business Mathematics book, one Accountancy book and 2 Commerce books is Rs. 630. Find the cost of each book by using Cramer’s rule.
2)
Evaluate the following integrals as the limit of the sum:
\(\int _{ 1 }^{ 3 }{ xdx } \)
3)
Find the consumer’s surplus and producer’s surplus for the demand function p_d = 25 − 3x and supply function p_s = 5 + 2x.
4)
Solve: (D²− 2D + 1)y = e^2x+ e^x
5)
Calculate the value of y when x = 7.5 from the table given below

x 1 2 3 4 5 6 7 8

y 1 8 27 64 125 216 343 512

12th Standard English Medium Business Maths Subject Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 05, 2021 - View & Read

1)
Find k, if the equations x + y + z = 7, x + 2y + 3z = 18, y + kz = 6 are inconsistent
2)
Integrate the following with respect to x.
\(\frac { { 3x }^{ 2 }-2x+5 }{ { \left( x-1 \right) }\left( x^{ 2 }+5 \right) } \)
3)
Using integration find the area of the region bounded between the line x = 4 and the parabola y² = 16x.
4)
The sum of Rs. 2,000 is compounded continuously, the nominal rate of interest being 5% per annum. In how many years will the amount be double the original principal? (log_e2 = 0.6931)
5)
Using appropriate interpolation formula find the number of students whose weight is between 60 and 70 from the data given below

Weight in lbs 0-40 40-60 60-80 80-100 100-120

No.of.students 250 120 100 70 50

12th Standard English Medium Business Maths Subject Book Back 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 05, 2021 - View & Read

1)
Solve the following equations by using Cramer’s rule
2x + 3y = 7; 3x + 5y = 9
2)
Integrate the following with respect to x.
\(\frac { 1 }{ { \sin }^{ 2 }x{ \cos }^{ 2 }x } [Hint:\sin ^{ 2 }+{ \cos }^{ 2 }x=1]\)
3)
The demand and supply function of a commodity are p_d = 18− 2x − x² and p_s = 2x − 3 . Find the consumer’s surplus and producer’s surplus at equilibrium price.
4)
Solve yx²dx + e ^{− x}dy = 0
5)
Using graphic method, find the value of y when x = 48 from the following data:

x 40 50 60 70

y 6.2 7.2 9.1 12

12th Standard English Medium Business Maths Subject Book Back 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 05, 2021 - View & Read

1)
Find the rank of the matrix \(\left( \begin{matrix} 1 & 2 & -1 \\ 2 & 4 & 1 \\ 3 & 6 & 3 \end{matrix}\begin{matrix} 3 \\ -2 \\ -7 \end{matrix} \right) \)
2)
Evaluate \(\int { \frac { x+2 }{ \sqrt { 2x+3 } } } dx\)
3)
Using integration, find the area of the region bounded by the line y −1 = x, the x axis and the ordinates x = –2, x = 3.
4)
Find the differential equation of the following
y = cx + c − c³
5)
Construct a forward difference table for y = f(x) = x³+2x+1 for x = 1,2,3,4,5

12th Standard English Medium Business Maths Subject Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 05, 2021 - View & Read

1)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 1 & -1 \\ 3 & -6 \end{matrix} \right) \)
2)
Integrate the following with respect to x.
\({ \left( \sqrt { 2x } -\frac { 1 }{ \sqrt { 2x } } \right) }^{ 2 }\)
3)
Evaluate the following using properties of definite integrals:
\(\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ { x }^{ 3 }{ cos }^{ 3 }xdx } \)
4)
Find the order and degree of the following differential equation
\({ \left[ 1+\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right] }^{ \frac { 3 }{ 2 } }=a\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } }\)
5)
Describe what is meant by a random variable.

12th Standard English Medium Business Maths Subject Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 05, 2021 - View & Read

1)
Find the rank of the matrix \(\begin{pmatrix} -5 & -7 \\ 5 & 7 \end{pmatrix}\)
2)
Integrate the following with respect to x.
\(\sqrt { 3x+5 } \)
3)
Find the area of the region bounded by the parabola \(y=4{ - }x^{ 2 }\) , x −axis and the lines x = 0, x = 2.
4)
Solve: \(\frac { dy }{ dx } \) = y sin 2x
5)
Evaluate \({ \Delta }^{ 2 }\left( \frac { 1 }{ x } \right) \) by taking ‘1’ as the interval of differencing.

12th Standard English Medium Business Maths Subject Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 05, 2021 - View & Read

1)
If \(\rho (A)\) = r then which of the following is correct?
2)
ഽ\(\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } } \) dx is _______.
3)
If the marginal revenue MR = 35 + 7x − 3x², then the average revenue AR is ________.
4)
The complementary function of (D²+ 4)y = e^2x is ______.
5)
E f (x)= _______.

12th Standard English Medium Business Maths Subject Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 05, 2021 - View & Read

1)
The rank of m x n matrix whose elements are unity is ________.
2)
\(\int \frac{\sin 5 x-\sin x}{\cos 3 x} d x\) is _______.
3)
The given demand and supply function are given by D(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is ________.
4)
The differential equation of y = mx + c is ______.(m and c are arbitrary constants)
5)
E ≡ _______.

12th Standard English Medium Business Maths Subject Operations Research Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 05, 2021 - View & Read

1)
Assign four trucks 1, 2, 3 and 4 to vacant spaces A, B, C, D, E and F so that distance travelled is minimized. The matrix below shows the distance.
2)
Determine an initial basic feasible solution to the following transportation problem by using North West Corner rule
3)
Explain Vogel’s approximation method by obtaining initial feasible solution of the following transportation problem.
4)
A car hire company has one car at each of five depots a,b,c,d and e. A customer in each of the fine towers A,B,C,D and E requires a car. The distance (in miles) between the depots (origins) and the towers(destinations) where the customers are given in the following distance matrix.

How should the cars be assigned to the customers so as to minimize the distance travelled?
5)
A natural truck-rental service has a surplus of one truck in each of the cities 1,2,3,4,5 and 6 and a deficit of one truck in each of the cities 7,8,9,10,11 and 12. The distance(in kilometers) between the cities with a surplus and the cities with a deficit are displayed below:

How should the truck be dispersed so as to minimize the total distance travelled?

12th Standard English Medium Business Maths Subject Operations Research Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 05, 2021 - View & Read

1)
Obtain an initial basic feasible solution to the following transportation problem using Vogel’s approximation method.
2)
Consider the problem of assigning five jobs to five persons. The assignment costs are given as follows. Determine the optimum assignment schedule.
3)
A computer centre has got three expert programmers. The centre needs three application programmes to be developed. The head of the computer centre, after studying carefully the programmes to be developed, estimates the computer time in minitues required by the experts to the application programme as follows.

Assign the programmers to the programme in such a way that the total computer time is least.
4)
Find the optimal solution for the assignment problem with the following cost matrix.

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 05, 2021 - View & Read

1)
Given below are the data relating to the production of sugarcane in a district.
Fit a straight line trend by the method of least squares and tabulate the trend values.

Year 2000 2001 2002 2003 2004 2005 2006

Prod.of Sugarcane 40 45 46 42 47 50 46

2)

Calculate the seasonal index for the monthly sales of a product using the method of simple averages.

Months	Jan	Feb	Mar	Apr	May	June	July	Aug	Sep	Oct	Nov	Dec
Year	Jan	Feb	Mar	Apr	May	June	July	Aug	Sep	Oct	Nov	Dec
2001	15	41	25	31	29	47	41	19	35	38	40	30
2002	20	21	27	19	17	25	29	31	35	39	30	44
2003	18	16	20	28	24	25	30	34	30	38	37	39

3)

the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Commodities	Price		Quandity
Commodities	2000	2010	2000	2010
Rice	38	35	6	7
Wheat	12	18	7	10
Rent	10	15	10	15
Fuel	25	30	12	16
Miscellaneous	30	33	8	10

4)

Calculate Fisher’s price index number and show that it satisfies both Time Reversal Test and Factor Reversal Test for data given below.

Commodities	Price		Quandity
Commodities	2003	2009	2003	2009
Rice	10	13	4	6
Wheat	125	18	7	8
Rent	25	29	5	9
Fuel	11	14	8	10
Miscellaneous	14	17	6	7

5)

Construct Fisher’s price index number and prove that it satisfies both Time Reversal Test and Factor Reversal Test for data following data.

Commodities	Base Year		Current Year
Commodities	Price	Quantity	Price	Quantity
Rice	40	5	48	4
Wheat	45	2	42	3
Rent	90	4	95	6
Fuel	85	3	80	2
Transport	50	5	65	8
Miscellaneous	65	1	72	3

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 05, 2021 - View & Read

1)
The following data gives the readings for 8 samples of size 6 each in the production of a certain product. Find the control limits using mean chart.

Sample 1 2 3 4 5 6

Mean 300 342 351 319 326 333

Range 25 37 20 28 30 22

Given for n = 6, A₂ = 0.483,

2)

Compute the average seasonal movement for the following series

Year	Quarterly Production
Year	I	II	III	IV
2002	3.5	3.8	3.7	3.5
2003	3.6	4.2	3.4	4.1
2004	3.4	3.9	3.7	4.2
2005	4.2	4.5	3.8	4.4
2006	3.9	4.4	4.2	4.6

3)
Determine the equation of a straight line which best fits the following data

Year 2000 2001 2002 2003 2004

Sales(Rs.000) 35 36 79 80 40

Compute the trend values for all years from 2000 to 2004

4)

Use the method of monthly averages to find the monthly indices for the following data of production of a commodity for the years 2002, 2003 and 2004.

2002	15	18	17	19	16	20	21	18	17	15	14	18
2003	20	18	16	13	12	15	22	16	18	20	17	15
2004	18	25	21	11	14	16	19	20	17	16	18	20

5)
The following table shows the number of salesmen working for a certain concern:

Year 1992 1993 1994 1995 1996

No. of salesmen 46 48 42 56 52

Use the method of least squares to fit a straight line and estimate the number of salesmen in 1997.

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 05, 2021 - View & Read

1)
An ambulance service claims that it takes on the average 8.9 minutes to reach its destination in emergency calls. To check on this claim, the agency which licenses ambulance services has them timed on 50 emergency calls, getting a mean of 9.3 minutes with a standard deviation of 1.6 minutes. What can they conclude at 5% level of significance.
2)
Explain the stratified random sampling with a suitable example.
3)
A random sample of 60 observations was drawn from a large population and its standard deviation was found to be 2.5. Calculate the suitable standard error that this sample is taken from a population with standard deviation 3?
4)
A sample of 400 individuals is found to have a mean height of 67.47 inches. Can it be reasonably regarded as a sample from a large population with mean height of 67.39 inches and standard deviation 1.30 inches at 0.05 level of significance?
5)
The mean breaking strength of cables supplied by a manufacturer is 1,800 with a standard deviation 100. By a new technique in the manufacturing process it is claimed that the breaking strength of the cables has increased. In order to test this claim a sample of 50 cables is tested. It is found that the mean breaking strength is 1,850. Can you support the claim at 0.01 level of significance.

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 05, 2021 - View & Read

1)
A machine produces a component of a product with a standard deviation of 1.6 cm in length. A random sample of 64 componentsvwas selected from the output and this sample has a mean length of 90 cm. The customer will reject the part if it is either less than 88 cm or more than 92 cm. Does the 95% confidence interval for the true mean length of all the components produced ensure acceptance by the customer?
2)
The mean life time of a sample of 169 light bulbs manufactured by a company is found to be 1350 hours with a standard deviation of 100 hours. Establish 90% confidence limits within which the mean life time of light bulbs is expected to lie.
3)
A manufacturer of ball pens claims that a certain pen he manufactures has a mean writing life of 400 pages with a standard deviation of 20 pages. A purchasing agent selects a sample of 100 pens and puts them for test. The mean writing life for the sample was 390 pages. Should the purchasing agent reject the manufactures claim at 1% level?
4)
The mean weekly sales of soap bars in departmental stores were 146.3 bars per store. After an advertising campaign the mean weekly sales in 400 stores for a typical week increased to 153.7 and showed a standard deviation of 17.2. Was the advertising campaign successful at 95% confidence limit?
5)
An ambulance service claims that it takes on the average 8.9 minutes to reach its destination in emergency calls. To check on this claim, the agency which licenses ambulance services has them timed on 50 emergency calls, getting a mean of 9.3 minutes with a standard deviation of 1.6 minutes. What can they conclude at 5% level of significance.

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 05, 2021 - View & Read

1)
If the average rain falls on 9 days in every thirty days, find the probability that rain will fall on atleast two days of a given week.
2)
An insurance company has discovered that only about 0.1 per cent of the population is involved in a certain type of accident each year. If its 10,000 policy holders were randomly selected from the population, what is the probability that not more than 5 of its clients are involved in such an accident next year? (e⁻¹⁰=.000045)
3)
If the probability that an individual suffers a bad reaction from injection of a given serum is 0.001, determines the probability that out of 2,000 individuals
(a) exactly 3, and
(b) more than 2 individuals will suffer a bad reaction.
4)
If X is a normal variate with mean 30 and SD 5. Find the probabilities that
(i) 26 ≤ X ≤ 40
(ii) X > 45
5)
The marks obtained in a certain exam follow normal distribution with mean 45 and SD 10. If 1,300 students appeared at the examination, calculate the number of students scoring
(i) less than 35 marks and
(ii) more than 65 marks.

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 05, 2021 - View & Read

1)
X is normally distributed with mean 12 and sd 4. Find P(X ≤ 20) and P(0 ≤ X ≤ 12)
2)
In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take less than 16.35 seconds to develop prints.
3)
A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain
(a) no more than 2 rejects?
(b) at least 2 rejects?
4)
The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time .
a) less than 19.5 hours?
b) between 20 and 22 hours?
5)
X is a normally normally distributed variable with mean μ = 30 and standard deviation σ = 4. Find
(a) P(x < 40)
(b) P(x > 21)
(c) P(30 < x < 35)

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Determine the mean and variance of a discrete random variable, given its distribution as follows.

X = x 1 2 3 4 5 6

F_x(x) \(\frac{1}{6}\) \(\frac{2}{6}\) \(\frac{3}{6}\) \(\frac{4}{6}\) \(\frac{5}{6}\) 1
2)
The probability density function of a random variable X is f(x) = ke^-|x|, -∞ < x < ∞ Find the value of k and also find mean and variance for the random variable.
3)
Let X be a random variable with cumulative distribution function
\(F(x)=\left\{\begin{array}{l} 0, \text { if } x<0 \\ \frac{x}{8}, \text { if } 0 \leq x<1 \\ \frac{1}{4}+\frac{x}{8}, \text { if } 1 \leq x<2 \\ \frac{3}{4}+\frac{x}{12}, \text { if } 2 \leq x<3 \\ 1, \text { for } 3 \leq x \end{array}\right.\)
(a) Compute: (i) P(1\(\le\)X\(\le\)2) and
(ii) P(X=3)
(b) Is X a discrete random variable? Justify your answer.
4)
The probability function of a random variable X is given by
\(p(x)=\left\{\begin{array}{l} \frac{1}{4}, \text { for } x=-2 \\ \frac{1}{4}, \text { for } x=0 \\ \frac{1}{2}, \text { for } x=10 \\ 0, \text { elsewhere } \end{array}\right.\)
Evaluate the following probabilities.
P(X<0)
5)
The probability function of a random variable X is given by
\(p(x)=\left\{\begin{array}{l} \frac{1}{4}, \text { for } x=-2 \\ \frac{1}{4}, \text { for } x=0 \\ \frac{1}{2}, \text { for } x=10 \\ 0, \text { elsewhere } \end{array}\right.\)
Evaluate the following probabilities.
P(0\(\le\)X\(\le\)10)

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Determine the mean and variance of the random variable X having the following probability distribution.

X=x 1 2 3 4 5 6 7 8 9 10

P(x) 0.15 0.10 0.10 0.01 0.08 0.01 0.05 0.02 0.28 0.20
2)
Suppose the life in hours of a radio tube has the probability density function
\(f(x)=\left\{\begin{array}{l} e^{-\frac{x}{100}}, \text { when } x \geq 100 \\ 0, \quad \text { when } x<100 \end{array}\right.\)
Find the mean of the life of a radio tube.
3)
The probability function of a random variable X is given by
\(p(x)=\left\{\begin{array}{l} \frac{1}{4}, \text { for } x=-2 \\ \frac{1}{4}, \text { for } x=0 \\ \frac{1}{2}, \text { for } x=10 \\ 0, \text { elsewhere } \end{array}\right.\)
Evaluate the following probabilities.
P(\(\le\))0
4)
The probability density function of a continuous random variable X is
\(f(x)=\left\{\begin{array}{l} a+b x^{2}, 0 \leq x \leq 1 \\ 0, \text { otherwise } \end{array}\right.\)
where a and b are some constants. Find
(i) a and b if E(X)\(\frac{3}{5}\)
(ii) Var(X).
5)
The probability function of a random variable X is given by
\(p(x)=\left\{\begin{array}{l} \frac{1}{4}, \text { for } x=-2 \\ \frac{1}{4}, \text { for } x=0 \\ \frac{1}{2}, \text { for } x=10 \\ 0, \text { elsewhere } \end{array}\right.\)
Evaluate the following probabilities.
P(|X|\(\le\)2)

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Using interpolation estimate the business done in 1985 from the following data

Year 1982 1983 1984 1986

Business done (in lakhs) 150 235 365 525
2)
Find the missing figures in the following table

x 0 5 10 15 20 25

y 7 11 - 18 - 32
3)
Using Lagrange’s interpolation formula find a polynomial which passes through the points (0, –12), (1, 0), (3, 6) and (4,12).
4)
If u₀ = 560, u₁ = 556, u₂ = 520, u₄ = 385, show that u₃= 465
5)
The area A of circle of diameter ‘d’ is given for the following values

D 80 85 90 95 100

A 5026 5674 6362 7088 7854

Find the approximate values for the areas of circles of diameter 82 and 91 respectively

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The values of y = f(x) for x = 0,1,2, ...,6 are given by

x 0 1 2 3 4 5 6

y 2 4 10 16 20 24 38

Estimate the value of y (3.2) using forward interpolation formula by choosing the four values that will give the best approximation.
2)
Using appropriate interpolation formula find the number of students whose weight is between 60 and 70 from the data given below

Weight in lbs 0-40 40-60 60-80 80-100 100-120

No.of.students 250 120 100 70 50
3)
Evaluate \(\Delta \)\(\left[ \frac { 5x+12 }{ { x }^{ 2 }+5x+6 } \right] \) by taking ‘1’ as the interval of differencing.
4)
Calculate the value of y when x = 7.5 from the table given below

x 1 2 3 4 5 6 7 8

y 1 8 27 64 125 216 343 512
5)
Find a polynomial of degree two which takes the values

x 0 1 2 3 4 5 6 7

y 1 2 4 7 11 16 22 29

12th Standard English Medium Business Maths Subject Differential Equations Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Solve 3e^xtan ydx +(1 + e^x)sec²ydy = 0 given y(0) = \(\frac { \pi }{ 4 } \)
2)
Solve the differential equation y²dx + (xy + x²)dy = 0
3)
If the marginal cost of producing x shoes is given by (3xy + y²)dx + (x²+ xy)dy = 0 and the total cost of producing a pair of shoes is given by Rs. 12. Then find the total cost function.
4)
An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x²+ y²)dy = xydx where x represents the number of units (in thousands). What is the total revenue function?
5)
Solve the following differential equations (D²+D−6)y=e^3x+ e^−3x

12th Standard English Medium Business Maths Subject Differential Equations Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Find the differential equation of the family of straight lines y = mx + c when
(i) m is the arbitrary constant
(ii) c is the arbitrary constant
(iii) m and c both are arbitrary constants.
2)
Solve : x - y \(\frac { dx }{ dy } =a\left( { x }^{ 2 }+\frac { dx }{ dy } \right) \)
3)
Solve the differential equation y²dx + (xy + x²)dy = 0
4)
Solve the following homogeneous differential equations.
\(\frac { dy }{ dx } =\frac { 3x-2y }{ 2x-3y } \)
5)
Solve (x² + 1)\(\frac { dy }{ dx } \) + 2xy = 4x²

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
When the Elasticity function is \(\frac { x }{ x-2 } \). Find the function when x = 6 and y = 16.
2)
A firm’s marginal revenue function is MR = 20e^-x/10 \(\left( 1-\frac { x }{ 10 } \right) \). Find the corresponding demand function.
3)
The marginal cost of production of a firm is given by C'(x) = 5 + 0.13x, the marginal revenue is given by R'(x) = 18 and the fixed cost is Rs. 120. Find the profit function.
4)
The demand equation for a products is x = \(\sqrt { 100-p } \) and the supply equation is x = \(\frac{p}{2}\) -10. Determine the consumer’s surplus and producer’s surplus, under market equilibrium.
5)
A company requires f(x) number of hours to produce 500 units. It is represented by f (x) = 1800x^−0.4. Find out the number of hours required to produce additional 400 units. [(900)^0.6= 59.22, (500)^0.6= 41.63]

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Find the area bounded by y = 4x + 3 with x- axis between the lines x = 1 and x = 4
2)
Sketch the graph \(y=\left| x+3 \right| \) and evaluate \(\int _{ -6 }^{ 0 }{ \left| x+3 \right| } \) dx.
3)
Using integration find the area of the region bounded between the line x = 4 and the parabola y² = 16x.
4)
Find the area bounded by the curve y = x² and the line y = 4
5)
The marginal cost and marginal revenue with respect to commodity of a firm are given by C'(x) = 8 + 6x and R'(x)= 24. Find the total Profit given that the total cost at zero output is zero.

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Evaluate the following using properties of definite integrals:
\(\int _{ 0 }^{ 1 }{ \log\left( \frac { 1 }{ x } -1 \right) dx } \)
2)
Evaluate the integral as the limit of a sum: \(\int _{ 1 }^{ 2 }{ (2x+1) } dx\)
3)
Evaluate the following integrals as the limit of the sum:
\(\int _{ 0 }^{ 1 }{ (x+4) } \)dx
4)
Evaluate the following integrals as the limit of the sum:
\(\int _{ 0 }^{ 1 }{ { x }^{ 2 } } dx\)
5)
Evaluate the following integrals:
\(\int _{ 0 }^{ 3 }{ \frac { xdx }{ \sqrt { x+1 } +\sqrt { 5x+1 } } } \)

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Evaluate \(\int _{ 2 }^{ 3 }{ \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } } dx\)
2)
Evaluate \(\int _{ a }^{ b }{ \frac { \sqrt { \log x } }{ x } dx } \) a, b > 0
3)
Evaluate \(\int _{ 0 }^{ \infty }{ { x }^{ 2 } } { e }^{ { -x }^{ 3 } }dx\)
4)
Evaluate \(\int _{ 1 }^{ e }{ \log x } \) dx
5)
If \(\int _{ a }^{ b }{ dx } =1\) and \(\int _{ a }^{ b }{ xdx } =1\), then find a and b

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The subscription department of a magazine sends out a letter to a large mailing list inviting subscriptions for the magazine. Some of the people receiving this letter already subscribe to the magazine while others do not. From this mailing list, 45% of those who already subscribe will subscribe again while 30% of those who do not now subscribe will subscribe. On the last letter, it was found that 40% of those receiving it ordered a subscription. What percent of those receiving the current letter can be expected to order a subscription?
2)
Find k if the equations x + y + z = 1, 3x − y − z = 4, x+ 5y + 5z = k are inconsistent.
3)
The cost of 2kg of wheat and 1kg of sugar is Rs. 100. The cost of 1kg of wheat and 1kg of rice is Rs. 80. The cost of 3kg of wheat, 2kg of sugar and 1kg of rice is Rs. 220. Find the cost of each per kg using Cramer’s rule.
4)
Solve the following equation by using Cramer’s rule
2x + y −z = 3, x + y + z =1, x− 2y− 3z = 4
5)
Solve the following equation by using Cramer’s rule
x + 4y + 3z = 2, 2x−6y + 6z = −3, 5x− 2y + 3z = −5

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Find k, if the equations x + y + z = 7, x + 2y + 3z = 18, y + kz = 6 are inconsistent
2)
Investigate for what values of ‘a’ and ‘b’ the following system of equations x + y + z = 6,x + 2y + 3z = 10, x + 2y + az = b have
(i) no solution
(ii) a unique solution
(iii) an infinite number of solutions.
3)
For what values of the parameter λ, will the following equations fail to have unique solution: 3x − y+λz = 1, 2x + y + z = 2, x + 2y − λz = −1 by rank method.
4)
An amount of Rs. 5,000/- is to be deposited in three different bonds bearing 6%, 7% and 8% per year respectively. Total annual income is Rs. 358/-. If the income from first two investments is Rs. 70/- more than the income from the third, then find the amount of investment in each bond by rank method.
5)
An automobile company uses three types of Steel S₁, S₂ and S₃ for providing three different types of Cars C₁, C₂and C₃. Steel requirement R (in tonnes) for each type of car and total available steel of all the three types are summarized in the following table.

Types of Steel Types of Car Total Steel available

C₁ C₂ C₃

S₁ 3 2 4 28

S₂ 1 1 2 13

S₃ 2 2 2 14

Determine the number of Cars of each type which can be produced by Cramer’s rule.

12th Standard English Medium Business Maths Subject Operations Research Book Back 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Determine an initial basic feasible solution to the following transportation problem using North West corner rule.

Here O_i and D_j represent i^th origin and j^th destination.
2)
Determine how much quantity should be stepped from factory to various destinations for the following transportation problem using the least cost method

Cost are expressed in terms of rupees per unit shipped.

3)

Consider the following pay-off (profit) matrix Action States

Action	States
Action	(s₁)	(s₂)	(s₃)	(s₄)
A₁	5	10	18	25
A₂	8	7	8	23
A₃	21	18	12	21
A₄	30	22	19	15

Determine best action using maximin principle.

4)

Consider the following pay-off matrix

Alternative	Pay – offs (Conditional events)
Alternative	A₁	A₂	A₃	A₄
E₁	7	12	20	27
E₂	10	9	10	25
E₃	23	20	14	23
E₄	32	24	21	17

Using minmax principle, determine the best alternative.

5)
Determine an initial basic feasible solution of the following transportation problem by north west corner method

12th Standard English Medium Business Maths Subject Operations Research Book Back 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Given the following pay-off matrix(in rupees) for three strategies and two states of nature.

Strategy States-of-nature

E₁ E₂

S₁ 40 60

S₂ 10 -20

S₃ -40 150

Select a strategy using each of the following rule
(i) Maximin
(ii) Minimax

2)

A farmer wants to decide which of the three crops he should plant on his 100-acre farm. The profit from each is dependent on the rainfall during the growing season. The farmer has categorized the amount of rainfall as high medium and low. His estimated profit for each is shown in the table.

Rainfall	Estimated Conditional Profit(Rs.)
Rainfall	crop A	crop B	crop C
High	8000	3500	5000
Medium	4500	4500	5000
Low	2000	5000	4000

If the farmer wishes to plant only crop, decide which should be his best crop using
(i) Maximin
(ii) Minimax

3)

The research department of Hindustan Ltd. has recommended to pay marketing department to launch a shampoo of three different types. The marketing types of shampoo to be launched under the following estimated pay-offs for various level of sales.

Types of shampoo	Estimated Sales (in Units)
Types of shampoo	15000	10000	5000
Egg shampoo	30	10	10
Clinic Shampoo	40	15	5
Deluxe Shampoo	55	20	3

What will be the marketing manager’s decision if
(i) Maximin and
(ii) Minimax principle applied?

4)
The following table summarizes the supply, demand and cost information for four factors S₁, S₂, S₃, S₄. shipping goods to three warehouses D₁, D₂, D₃.

Find an initial solution by using north west corner rule. What is the total cost for this solution?

5)

A person wants to invest in one of three alternative investment plans: Stock, Bonds and Debentures. It is assumed that the person wishes to invest all of the funds in a plan. The pay-off matrix based on three potential economic conditions is given in the following table:

Alternative	Economic conditions
Alternative	High growth(Rs.)	Normal growth(Rs.)	Slow growth (Rs.)s
Stocks	10000	7000	3000
Bonds	8000	6000	1000
Debentures	6000	6000	6000

Determine the best investment plan using each of following criteria i) Maxmin ii) Minimax.

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Fit a trend line by the method of semi-averages for the given data.

Year 2000 2001 2002 2003 2004 2005 2006

Production 105 115 120 100 110 125 135
2)
Calculate four-yearly moving averages of number of students studying in a higher secondary school in a particular city from the following data.

Year 2001 2002 2003 2004 2005 2006 2007 2008 2009

Sales 124 120 135 140 145 158 162 170 175

3)

You are given below the values of sample mean ( \(\bar{X}\) ) and the range ( R ) for ten samples of size 5 each. Draw mean chart and comment on the state of control of the process.

Sample number	1	2	3	4	5	6	7	8	9	10
\(\overset{-}{X}\)	43	49	37	44	45	37	51	46	43	47
R	5	6	5	7	7	4	8	6	4	6

Given the following control chart constraint for : n = 5, A₂= 0.58, D₃= 0 and D₄= 2.115

4)
Explain the method of fitting a straight line.
5)
The following figures relates to the profits of a commercial concern for 8 years

Year 1986 1987 1988 1989 1990 1991 1992 1993

Profit (Rs.) 15,420 15,470 15,520 21,020 26,500 31,950 35,600 34,900

Find the trend of profits by the method of three yearly moving averages.

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Write a brief note on seasonal variations
2)
State the different methods of measuring trend.
3)
Calculate by a suitable method, the index number of price from the following data:

Commodity 2002 2012

Price Quantity Price Quantity

A 10 20 16 10

B 12 34 18 42

C 15 30 20 26
4)
From the following data, calculate the trend values using fourly moving averages.

Year 1990 1991 1992 199 1994 1995 1996 1997 1998

Sales 506 620 1036 673 588 696 1116 738 663

5)

An Enquiry was made into the budgets of the middle class families in a city gave the following information.

Expenditure	Food	Rent	Clothing	Fuel	Rice
Price(2010)	150	50	100	20	60
Price(2011)	174	60	125	25	90
Weights	35	15	20	10	20

What changes in the cost of living have taken place in the middle class families of a city?

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
From the following data, select 68 random samples from the population of heterogeneous group with size of 500 through stratified random sampling, considering the following categories as strata.
Category 1: Lower income class - 39%
Category 2: Middle income class - 38%
Category 3: Upper income class - 23%
2)
Find the sample size for the given standard deviation 10 and the standard error with respect of sample mean is 3.

3)

Using the following Tippet’s random number table.

2952	6641	3992	9792	7969	5911	3170	5624
4167	9524	1545	1396	7203	5356	1300	2693
2670	7483	3408	2762	3563	1089	6913	7991
0560	5246	1112	6107	6008	8125	4233	8776
2754	9143	1405	9025	7002	6111	8816	6446

Draw a sample of 10 three digit numbers which are even numbers.

4)
A sample of 1000 students whose mean weight is 119 lbs(pounds) from a school in Tamil Nadu State was taken and their average weight was found to be 120 lbs with a standard deviation of 30 lbs. Calculate standard error of mean.
5)
A sample of 100 items, draw from a universe with mean value 4 and S.D 3, has a mean value 63.5. Is the difference in the mean significant at 0.05 level of significance?

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)

Using the following random number table (Kendall-Babington Smith)

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13

Draw a random sample of 10 four- figure numbers starting from 1550 to 8000.

2)
Explain in detail about sampling error.
3)
A sample of 1000 students whose mean weight is 119 lbs(pounds) from a school in Tamil Nadu State was taken and their average weight was found to be 120 lbs with a standard deviation of 30 lbs. Calculate standard error of mean.
4)
Explain the procedures of testing of hypothesis
5)
Determine the standard error of proportion for a random sample of 500 pineapples was taken from a large consignment and 65 were found to be bad.

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The mortality rate for a certain disease is 7 in 1000. What is the probability for just 2 deaths on account of this disease in a group of 400? [Given e^(–2.8)= 0.06]
2)
It is given that 5% of the electric bulbs manufactured by a company are defective. Using poisson distribution find the probability that a sample of 120 bulbs will contain no defective bulb.
3)
Hospital records show that of patients suffering from a certain disease 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover?
4)
If electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week.
5)
The birth weight of babies is Normally distributed with mean 3,500 g and standard deviation 500 g. What is the probability that a baby is born that weighs less than 3,100 g?

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The mean of Binomials distribution is 20 and standard deviation is 4. Find the parameters of the distribution.
2)
What is the probability of guessing correctly atleast six of the ten answers in a TRUE/FALSE objective test?
3)
Assuming one in 80 births is a case of twins, calculate the probability of 2 or more sets of twins on a day when 30 births occur.
4)
Weights of fish caught by a traveler are approximately normally distributed with a mean weight of 2.25 kg and a standard deviation of 0.25 kg. What percentage of fish weigh less than 2 kg?
5)
Among 28 professors of a certain department, 18 drive foreign cars and 10 drive local made cars. If 5 of these professors are selected at random, what is the probability that atleast 3 of them drive foreign cars?

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Two unbiased dice are thrown simultaneously and sum of the upturned faces considered as random variable. Construct a probability mass function.
2)
The following table is describing about the probability mass function of the random variable X

x 3 4 5

P(x) 0.1 0.1 0.2

Find the standard deviation of x.
3)
The number of miles an automobile tire lasts before it reaches a critical point in tread wear can be represented by a p.d.f.
\(f(x)= \begin{cases}\frac{1}{30} e^{-\frac{x}{30}}, & \text { for } x>0 \\ 0, & \text { for } x \leq 0\end{cases}\)
Find the expected number of miles (in thousands) a tire would last until it reaches the critical tread wear point.
4)
The probability distribution function of a discrete random variable X is
\(F(x)=\left\{\begin{array}{l} 2k, x = 1 \\ 3k, x = 3 \\ 4k, x = 5 \\ 0, \text{otherwise} \end{array}\right.\)
where k is some constant. Find (a) k and (b) P(X>2).
5)
Consider a random variable X with p.d.f
\(f(x)=\left\{\begin{array}{l} 3 x^{2}, \text { if } 0< x< 1 \\ 0, \text { otherwise } \end{array}\right.\)
Find E(X) and V(3X-2).

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
What are the properties of
(i) discrete random variable and
(ii) continuous random variable?
2)
State the properties of distribution function.
3)
A fair die is thrown. Find out the expected value of its outcomes.
4)
Suppose the probability mass function of the discrete random variable is

X=x 0 1 2 3

p(x) 0.2 0.1 0.4 0.3

What is the value of E(3X + 2X²) ?
5)
If f (x) is defined by f(x)=ke^-2x, 0\(\le\)x<\(\infty\) is a density function. Determine the constant k and also find mean.

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
If h = 1 then prove that (E⁻¹Δ)x³= 3x²− 3x + 1.
2)
If f(x) = x²+ 3x then show that Δf(x) = 2x + 4
3)
Using graphic method, find the value of y when x = 48 from the following data:

x 40 50 60 70

y 6.2 7.2 9.1 12

4)

The following data relates to indirect labour expenses and the level of output

Months	Jan	Feb	Mar	Apr	May	June
Units of output	200	300	400	640	540	580
Indirect labour expenses (Rs)	2500	2800	3100	3820	3220	3640

Estimate the expenses at a level of output of 350 units, by using graphic method

5)
A second degree polynomial passes though the point (1,-1) (2,-1) (3,1) (4,5). Find the polynomial.

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Construct a forward difference table for y = f(x) = x³+2x+1 for x = 1,2,3,4,5
2)
Prove that f(4) = f(3) + Δf(2) + Δ² f(1) + Δ³ f(1) taking ‘1’ as the interval of differencing.
3)
Given y₃= 2, y₄= −6, y₅= 8, y₆= 9 and y₇ = 17 Calculate Δ⁴y₃
4)
Evaluate ∆(log ax).
5)
If f(x) = x²+ 3x then show that Δf(x) = 2x + 4

12th Standard English Medium Business Maths Subject Differential Equations Book Back 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Form the differential equation by eliminating α and β from (x − α)² + (y − β)² = r²
2)
Find the differential equation of all circles passing through the origin and having their centers on the y axis.
3)
Find the differential equation of the family of parabola with foci at the origin and axis along the x-axis.
4)
Find the differential equation of the family of curves \(y=\frac { a }{ x } +b\) where a and b are arbitrary constants
5)
Solve \(\frac { dy }{ dx } \) = e^x−y+ x²e^{− y}

12th Standard English Medium Business Maths Subject Differential Equations Book Back 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Solve \(\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } -\frac { 3dx }{ dt } +2x\) = 0 given that when t = 0, x = 0 and \(\frac { dx }{ dt } \) = 1
2)
Solve the following differential equations: (4D²+4D−3)y = e^2x
3)
Form the differential equation having for its general solution y = ax²+ bx
4)
Solve x \(\frac{dy}{dx}\) + 2y = x⁴
5)
Find the order and degree of the following differential equations.
\(\frac{d^{3} y}{d x^{3}}+3\left(\frac{d y}{d x}\right)^{3}+2 \frac{d y}{d x}=0\)

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Using integration, find the area of the region bounded by the line y −1 = x, the x axis and the ordinates x = –2, x = 3.
2)
The marginal cost function of manufacturing x shoes is 6 +10x − 6x². The cost producing a pair of shoes is Rs. 12. Find the total and average cost function.
3)
The rate of new product is given by f (x) = 100 − 90 e^−xwhere x is the number of days the product is on the market. Find the total sale during the first four days. (e^–4= 0.018)
4)
A company receives a shipment of 200 cars every 30 days. From experience it is known that the inventory on hand is related to the number of days. Since the last shipment, I(x)=200 − 0.2x. Find the daily holding cost for maintaining inventory for 30 days if the daily holding cost is Rs. 3.5
5)
The marginal cost function of a product is given by \(\frac { dC }{ dx } \) = 100 −10x + 0.1x²where x is the output. Obtain the total and the average cost function of the firm under the assumption, that its fixed cost is Rs. 500.

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The demand and supply function of a commodity are p_d = 18− 2x − x² and p_s = 2x − 3 . Find the consumer’s surplus and producer’s surplus at equilibrium price.
2)
The demand function for a commodity is p = e^−x. Find the consumer’s surplus when p = 0.5.
3)
If the supply function for a product is p = 3x + 5x². Find the producer’s surplus when x = 4.
4)
A company has determined that marginal cost function for x product of a particular commodity is given by MC = 125 +10x − \(\frac { { x }^{ 2 } }{ 9 } \). Where C is the cost of producing x units of the commodity. If the fixed cost is Rs. 250 what is cost of producing 15 units
5)
Find the area of the region bounded by the curve between the parabola y = 8x² − 4x + 6 the y-axis and the ordinate at x = 2.

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Evaluate \(\int { \frac { { x }^{ 3 } }{ { \left( { x }^{ 2 }+1 \right) }^{ 3 } } dx } \)
2)
Integrate the following with respect to x.
\(\frac { { e }^{ 3logx } }{ { x }^{ 4 }+1 } \)
3)
Evaluate ഽ\(\frac { dx }{ x^{ 2 }-3x+2 } \)
4)
Integrate the following with respect to x
\(\frac { 1 }{ \sqrt { { x }^{ 2 }-3x+2 } } \)
5)
Using second fundamental theorem, evaluate the following:
\(\int _{ 1 }^{ e }{ \frac { dx }{ x(1{ +logx) }^{ 3 } } } \)

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Evaluate \(\int \frac{a x^{2}+b x+c}{\sqrt{x}} d x\)
2)
Evaluate \(\int { \frac { 1 }{ \sqrt { x+2 } -\sqrt { x-2 } } } dx\)
3)
Integrate the following with respect to x.
\(\sqrt{x}\)(x³− 2x + 3)
4)
Evaluate \(\int { \frac { { x }^{ 2 }+2x+3 }{ x+1 } dx}\)
5)
Integrate the following with respect x.
\(\frac { { x }^{ 3 }+3x^{ 2 }-7x+11 }{ x+5 } \)

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 3 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 2 & -1 & 1 \\ 3 & 1 & -5 \\ 1 & 1 & 1 \end{matrix} \right) \)
2)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} -1 & 2 & -2 \\ 4 & -3 & 4 \\ -2 & 4 & -4 \end{matrix} \right) \)
3)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 1 & 2 & -1 \\ 2 & 4 & 1 \\ 3 & 6 & 3 \end{matrix}\begin{matrix} 3 \\ -2 \\ -7 \end{matrix} \right) \)
4)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 1 & -2 & 3 \\ -2 & 4 & -1 \\ -1 & 2 & 7 \end{matrix}\begin{matrix} 4 \\ -3 \\ 6 \end{matrix} \right) \)
5)
Solve the following equation by using Cramer’s rule
5x + 3y = 17; 3x + 7y = 31

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 3 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
If A=\(\left( \begin{matrix} 1 & 1 & -1 \\ 2 & -3 & 4 \\ 3 & -2 & 3 \end{matrix} \right) \) and B=\(\left( \begin{matrix} 1 & -2 & 3 \\ -2 & 4 & -6 \\ 5 & 1 & -1 \end{matrix} \right) \), then find the rank of AB and the rank of BA.
2)
Solve the equations 2x + 3y = 7, 3x + 5y = 9 by Cramer’s rule.
3)
The following table represents the number of shares of two companies A and B during the month of January and February and it also gives the amount in rupees invested by Ravi during these two months for the purchase of shares of two companies. Find the the price per share of A and B purchased during both the months

Months Number of Shares of
the company Amount invested by Ravi
(in Rs)

A B

January 10 5 125

February 9 12 150
4)
The total cost of 11 pencils and 3 erasers is Rs. 64 and the total cost of 8 pencils and 3 erasers is Rs. 49. Find the cost of each pencil and each eraser by Cramer’s rule.
5)
A total of Rs. 8,600 was invested in two accounts. One account earned \(4\frac { 3 }{ 4 } %\)% annual interest and the other earned \(6\frac { 1 }{ 2 } %\)% annual interest. If the total interest for one year was Rs. 431.25, how much was invested in each account? (Use determinant method).

12th Standard English Medium Business Maths Subject Operations Research Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
What is transportation problem?
2)
Write mathematical form of transportation problem.
3)
What do you mean by balanced transportation problem?
4)
Give mathematical form of assignment problem.
5)
What is the difference between Assignment Problem and Transportation Problem?

12th Standard English Medium Business Maths Subject Operations Research Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Write mathematical form of transportation problem.
2)
What is feasible solution and non degenerate solution in transportation problem?
3)
What do you mean by balanced transportation problem?
4)
What is the Assignment problem?
5)
What is the difference between Assignment Problem and Transportation Problem?

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
What do you mean by product control?
2)
Define a control chart.
3)
Define mean chart.
4)
What are the uses of statistical quality control?
5)
Write the control limits for the R chart.

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Define true value ratio.
2)
Define Family Budget Method.
3)
Define Statistical Quality Control.
4)
Define Chance Cause.
5)
What do you mean by product control?

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
What is interval estimation?
2)
What is null hypothesis? Give an example.
3)
Define critical region.
4)
Define level of significance.
5)
What is single tailed test.

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
What is population?
2)
What is statistic?
3)
What is sampling distribution of a statistic?
4)
State any two merits of simple random sampling.
5)
State any two merits for systematic random sampling.

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Verfy the following statement:
The mean of a Binomial distribution is 12 and its standard deviation is 4.
2)
In a book of 520 pages, 390 typo-graphical errors occur. Assuming Poisson law for the number of errors per page, find the probability that a random sample of 5 pages will contain no error.
3)
Define Bernoulli trials.
4)
If the probability of success is 0.09, how many trials are needed to have a probability of atleast one success as 1/3 or more ?
5)
The mean of a binomial distribution is 5 and standard deviation is 2. Determine the distribution.

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The mean of a binomial distribution is 5 and standard deviation is 2. Determine the distribution.
2)
Define Poisson distribution.
3)
Write the conditions for which the poisson distribution is a limiting case of binomial distribution.
4)
Define Normal distribution.
5)
Write down the conditions in which the Normal distribution is a limiting case of binomial distribution.

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
How do you define variance in terms of Mathematical expectation?
2)
State the definition of Mathematical expectation using continuous random variable.
3)
Let X be a random variable and Y = 2X + 1. What is the variance of Y if variance of X is 5 ?
4)
Prove that, V(aX) = a²V(X)
5)
The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function
\(f(x)= \begin{cases}2 e^{-2 x}, & x>0 \\ 0,& \text { otherwise }\end{cases}\)
Find the expected life of this piece of equipment.

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
What are the properties of Mathematical expectation?
2)
What do you understand by Mathematical expectation?
3)
How do you define variance in terms of Mathematical expectation?
4)
State the definition of Mathematical expectation using continuous random variable.
5)
Let X be a random variable and Y = 2X + 1. What is the variance of Y if variance of X is 5 ?

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Find (i) Δe^ax
(ii) Δ²e^x
(iii) Δ log x
2)
Evaluate \({ \Delta }^{ 2 }\left( \frac { 1 }{ x } \right) \) by taking ‘1’ as the interval of differencing.
3)
If f (x) = e^ax then show that f(0), Δf(0), Δ²f(0) are in G.P
4)
Prove that
(1 + Δ)(1 - ∇) = 1
5)
Prove that
∇Δ = Δ - ∇

12th Standard English Medium Business Maths Subject Differential Equations Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Solve \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -4\frac { dy }{ dx } +5y\) = 0
2)
Solve the following differential equations
\(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -4\frac { dy }{ dx } +4y=0\)
3)
Solve the following differential equations
\(\frac{d^2 y}{dx^2}-2k\frac{dy}{dx}+k^2y = 0\)
4)
A manufacturing company has found that the cost C of operating and maintaining the equipment is related to the length ‘m’ of intervals between overhauls by the equation m²\(\frac{dC}{dm}\) + 2mC = 2 and c = 4 and when m = 2. Find the relationship between C and m.
5)
Find the order and degree of the following differential equations.
\(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =0\)

12th Standard English Medium Business Maths Subject Differential Equations Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Solve: \(\frac { 1+{ x }^{ 2 } }{ 1+y } =xy\frac { dy }{ dx } \)
2)
Solve: log\(\left( \frac { dy }{ dx } \right) \) = ax + by
3)
Find the order and degree of the following differential equation
\(\frac { { d }^{ 2 }y }{ { dx }^{ 3 } } -3{ \left( \frac { dy }{ dx } \right) }^{ 6 }+2y={ x }^{ 2 }\)
4)
Find the order and degree of the following differential equation
y' + (y'')² = (x + y'')²
5)
Find the order and degree of the following differential equation
\(y=2{ \left( \frac { dy }{ dx } \right) }^{ 2 }\)+ 4x\(\frac { dx }{ dy } \)

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Find the rank of the matrix \(\begin{pmatrix} 1 & 5 \\ 3 & 9 \end{pmatrix}\)
2)
Find the rank of the matrix \(\begin{pmatrix} -5 & -7 \\ 5 & 7 \end{pmatrix}\)
3)
Find the rank of the matrix A = \(\left( \begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 5 & 7 \end{matrix} \right) \)
4)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix} \right) \)
5)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 1 & -1 \\ 3 & -6 \end{matrix} \right) \)

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Evaluate the following using properties of definite integrals:
\(\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ { x }^{ 3 }{ cos }^{ 3 }xdx } \)
2)
Evaluate the following integrals:
ഽ\(\sqrt { 2{ x }^{ 2 }-3 } \) dx
3)
Evaluate the following
\(\int _{ 0 }^{ \infty }{ { e }^{ -mx } } { x }^{ 6 }dx\)
4)
Evaluate
\(\Gamma(\frac{7}{2})\)
5)
Evaluate
\(\int _{ 0 }^{ \infty }{ { e }^{ -2x }{ x }^{ 5 }dx } \)

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Integrate the following with respect to x.
\(\frac { 8x+13 }{ \sqrt { 4x+7 } } \)
2)
Integrate the following with respect to x.
\({ \left( \sqrt { 2x } -\frac { 1 }{ \sqrt { 2x } } \right) }^{ 2 }\)
3)
Evaluate ∫(2sin x − 5cos x)dx
4)
Integrate the following with respect to x.
2cos x − 3sin x + 4sec² x − 5cosec²x
5)
Integrate the following with respect to x.
x⁸(1+x⁹)⁵

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Find the area of the region bounded by the parabola \(y=4{ - }x^{ 2 }\) , x −axis and the lines x = 0, x = 2.
2)
Find the area bounded by the lines y − 2x − 4 = 0, y = 1, y = 3 and the y-axis
3)
If MR = 20 − 5x + 3x², find total revenue function.
4)
If MR = 14 − 6x + 9x², find the demand function.
5)
For the marginal revenue function MR = 6 − 3x² − x³, Find the revenue function and demand function.

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Find the area of the region bounded by the line x − 2y − 12 = 0 , the y-axis and the lines y = 2, y = 5.
2)
Using Integration, find the area of the region bounded the line 2y + x = 8, the x axis and the lines x = 2, x = 4.
3)
Find the area bounded by the lines y − 2x − 4 = 0, y = 1, y = 3 and the y-axis
4)
If MR = 20 − 5x + 3x², find total revenue function.
5)
For the marginal revenue function MR = 6 − 3x² − x³, Find the revenue function and demand function.

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Find the rank of the matrix \(\begin{pmatrix} 1 & 5 \\ 3 & 9 \end{pmatrix}\)
2)
Find the rank of the matrix A = \(\left( \begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 5 & 7 \end{matrix} \right) \)
3)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix} \right) \)
4)
Find the rank of the matrix A =\(\left( \begin{matrix} 1 & -3 \\ 9 & 1 \end{matrix}\begin{matrix} 4 & 7 \\ 2 & 0 \end{matrix} \right) \)
5)
Find the rank of each of the following matrices.
\(\left( \begin{matrix} 1 & 4 \\ 2 & 8 \end{matrix} \right) \)

12th Standard English Medium Business Maths Subject Operations Research Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
North-West Corner refers to ________.
2)
Solution for transportation problem using ________method is nearer to an optimal solution.
3)
In an assignment problem the value of decision variable x_ij is ______.
4)
If number of sources is not equal to number of destinations, the assignment problem is called______.
5)
The purpose of a dummy row or column in an assignment problem is to _______.

12th Standard English Medium Business Maths Subject Operations Research Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The purpose of a dummy row or column in an assignment problem is to _______.
2)
The solution for an assignment problem is optimal if _______.
3)
In an assignment problem involving four workers and three jobs, total number of assignments possible are _______.
4)
Decision theory is concerned with _______.
5)
A type of decision –making environment is _______.

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The components of a time series which is attached to short term fluctuation is ________.
2)
Factors responsible for seasonal variations are ________.
3)
The additive model of the time series with the components T, S, C and I is ________.
4)
Least square method of fitting a trend is ________.
5)
The value of ‘b’ in the trend line y = a + bx is ________.

12th Standard English Medium Business Maths Subject Applied Statistics Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The quantities that can be numerically measured can be plotted on a ________.
2)
How many causes of variation will affect the quality of a product?
3)
Variations due to natural disorder is known as ________.
4)
The assignable causes can occur due to ________.
5)
A typical control charts consists of ________.

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
In simple random sampling from a population of N units, the probability of drawing any unit at the first draw is ______.
2)
In ________ the heterogeneous groups are divided into homogeneous groups.
3)
If probability \(P[|\hat{\theta}-\theta|<\varepsilon] \rightarrow 1\) as \(n \rightarrow \infty\), for any positive \(\varepsilon \) then \(\hat{\theta}\) is said to ________ estimator of \(\theta\).
4)
An estimator is said to be ________ if it contains all the information in the data about the parameter it estimates.
5)
An estimate of a population parameter given by two numbers between which the parameter would be expected to lie is called an………..interval estimate of the parameter.

12th Standard English Medium Business Maths Subject Sampling Techniques and Statistical Inference Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
A _______is one where each item in the universe has an equal chance of known opportunity of being selected.
2)
A random sample is a sample selected in such a way that every item in the population has an equal chance of being included ______.
3)
Which one of the following is probability sampling
4)
In ________ the heterogeneous groups are divided into homogeneous groups.
5)
Errors in sampling are of ______.

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
A manufacturer produces switches and experiences that 2 per cent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is ________.
2)
An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is ________.
3)
If for a binomial distribution b(n,p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to ________.
4)
Forty percent of the passengers who fly on a certain route do not check in any luggage. The planes on this route seat 15 passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?
5)
Which of the following statements is/are true regarding the normal distribution curve?

12th Standard English Medium Business Maths Subject Probability Distributions Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Using the standard normal table, the sum of the probabilities to the right of z = 2.18 and to the left of z = -1.75 is ________.
2)
The time until first failure of a brand of inkjet printers is normally distributed with a mean of 1,500 hours and a standard deviation of 200 hours. What proportion of printers fails before 1000 hours?
3)
Monthly expenditure on their credit cards, by credit card holders from a certain bank, follows a normal distribution with a mean of Rs. 1,295.00 and a standard deviation of Rs. 750.00. What proportion of credit card holders spend more than Rs. 1,500.00 on their credit cards per month?
4)
Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be: ________.
5)
If the area to the left of a value of z (z has a standard normal distribution) is 0.0793, what is the value of z?

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0.29, 0.40, 0.35. Profit per unit is 0.50 paisa then expected profits for three days are ________.
2)
Given E(X)=5 and E(Y)=−2, then E(X−Y) is ________.
3)
A formula or equation used to represent the probability distribution of a continuous random variable is called ________.
4)
Which of the following is not possible in probability distribution?
5)
A discrete probability distribution may be represented by ________.

12th Standard English Medium Business Maths Subject Random Variable and Mathematical Expectation Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
A variable which can assume finite or countably infinite number of values is known as ________.
2)
If p(x) =\(\frac{1}{10}\), c = 10, then E(X) is ________.
3)
In a discrete probability distribution the sum of all the probabilities is always equal to ________.
4)
A discrete probability function p(x) is always non-negative and always lies between ________.
5)
The height of persons in a country is a random variable of the type ________.

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
If c is a constant then Δc = _______.
2)
If ‘n’ is a positive integer Δⁿ[ Δ^-n f(x)] _______.
3)
∇ ≡ _______.
4)
For the given points (x₀, y₀) and (x₁, y₁) the Lagrange’s formula is _______.
5)
If f (x)=x²+ 2x + 2 and the interval of differencing is unity then Δf (x) _______.

12th Standard English Medium Business Maths Subject Numerical Methods Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
Δ²y₀ = _______.
2)
E ≡ _______.
3)
If c is a constant then Δc = _______.
4)
If ‘n’ is a positive integer Δⁿ[ Δ^-n f(x)] _______.
5)
∇ ≡ _______.

12th Standard English Medium Business Maths Subject Differential Equations Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The integrating factor of x \(\frac { dy }{ dx } \) - y = x² is ______.
2)
The particular integral of the differential equation f(D)y = e^ax where f(D) = (D−a)² ______.
3)
The P.I of (3D²+ D − 14)y = 13e^2x is ______.
4)
A homogeneous differential equation of the form \(\frac { dx }{ dy } \) = f\(\left( \frac { y }{ x } \right) \) can be solved by making substitution,______.
5)
The solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } +\frac { f\left( \frac { y }{ x } \right) }{ f'\left( \frac { y }{ x } \right) } \) is ______.

12th Standard English Medium Business Maths Subject Differential Equations Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The degree of the differential equation \(\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3\) ______.
2)
The differential equation \({ \left( \frac { dx }{ dy } \right) }^{ 3 }+2{ y }^{ \frac { 1 }{ 2 } }\) = x is ______.
3)
If y = cx + c− c³ then its differential equation is ______.
4)
The particular integral of the differential equation is \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -8\frac { dy }{ dx } \) + 16y = 2e^4x ______.
5)
The integrating factor of x \(\frac { dy }{ dx } \) - y = x² is ______.

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The marginal cost function is MC = 100 \(\sqrt x\). find AC given that TC = 0 when the out put is zero is ________.
2)
If MR and MC denote the marginal revenue and marginal cost and MR − MC = 36x − 3x² − 81 , then the maximum profit at x is equal to ________.
3)
If the marginal revenue of a firm is constant, then the demand function is ________.
4)
Area bounded by y = e^x between the limits 0 to 1 is ________.
5)
Area bounded by y = \(\left| x \right| \) between the limits 0 and 2 is ________.

12th Standard English Medium Business Maths Subject Integral Calculus – II Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The demand and supply functions are given by D(x)= 16 − x² and S(x) = 2x² + 4 are under perfect competition, then the equilibrium price x is ________.
2)
The given demand and supply function are given by D(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is ________.
3)
The profit of a function p(x) is maximum when ________.
4)
The demand function for the marginal function MR = 100 − 9x² is ________.
5)
When x₀ = 2 and P₀ = 12 the producer’s surplus for the supply function P_s = 2x² + 4 is ________.

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The value of \(\int _{ -\frac{\pi}{2}}^{ \frac{\pi}{2}}\) cos x dx is _______.
2)
The value of \(\int _{ 2 }^{ 3 }{ f(5-x) } dx-\int _{ 2 }^{ 3 }{ f(x) } dx\) is _______.
3)
Using the factorial representation of the gamma function, which of the following is the solution for the gamma function \(\Gamma \)(n) when n = 8 _______.
4)
If n > 0, then \(\Gamma \)(n) is _______.
5)
\(\int _{ 0 }^{ \infty }{ { x }^{ 4 }{ e }^{ -x } } \)dx is _______.

12th Standard English Medium Business Maths Subject Integral Calculus – I Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
ഽ\(\frac { sin2x }{ 2sinx } dx\) is _______.
2)
ഽ\(\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } } \) dx is _______.
3)
ഽ\(\frac { { e }^{ x } }{ { e }^{ x }+1 } \) dx is _______.
4)
ഽ\(\frac { dx }{ \sqrt { { x }^{ 2 }-{ 36 } } } \) is _______.
5)
\(\int _{ 2 }^{ 4 }{ \frac { dx }{ x } } \) is _______.

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 04, 2021 - View & Read

1)
The rank of m x n matrix whose elements are unity is ________.
2)
The rank of the matrix \(\left( \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 4 & 9 \end{matrix} \right) \) is ________.
3)
If A =\(\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right) \) then the rank of AA^Tis ________.
4)
If \(T=\begin{array}{l} A \\ B \end{array}\left(\begin{array}{ll} 0.7 & 0.3 \\ 0.6 & x \end{array}\right)\) is a transition probability matrix, then the value of x is ________.
5)
If \(\rho (A)=\rho (A,B)\) the number of unknowns, then the system is______.

12th Standard English Medium Business Maths Subject Applications of Matrices and Determinants Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 04, 2021 - View & Read

1)
If \(\rho (A)=\rho (A,B)\) the number of unknowns, then the system is______.
2)
If the number of variables in a non-homogeneous system AX = B is n, then the system possesses a unique solution only when _______.
3)
If \(\left| A \right| \neq 0,\) then A is _______.
4)
Cramer’s rule is applicable only to get an unique solution when _______.
5)
Rank of a null matrix is _______.

Months	Number of Shares of the company		Amount invested by Ravi (in Rs)
Months	A	B	Amount invested by Ravi (in Rs)
January	10	5	125
February	9	12	150

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13

Commodity	2002		2012
Commodity	Price	Quantity	Price	Quantity
A	10	20	16	10
B	12	34	18	42
C	15	30	20	26

Year	1990	1991	1992	199	1994	1995	1996	1997	1998
Sales	506	620	1036	673	588	696	1116	738	663

Strategy	States-of-nature
	E₁	E₂
S₁	40	60
S₂	10	-20
S₃	-40	150

Types of Steel	Types of Car			Total Steel available
Types of Steel	C₁	C₂	C₃	Total Steel available
S₁	3	2	4	28
S₂	1	1	2	13
S₃	2	2	2	14

Weight in lbs	0-40	40-60	60-80	80-100	100-120
No.of.students	250	120	100	70	50

X = x	1	2	3	4	5	6
F_x(x)	\(\frac{1}{6}\)	\(\frac{2}{6}\)	\(\frac{3}{6}\)	\(\frac{4}{6}\)	\(\frac{5}{6}\)	1

Year	I quarter	II quarter	III quarter	IV quarter
1985	68	62	61	63
1986	65	58	66	61
1987	68	63	63	67

year (x)	1961	1971	1981	1991	2001
population in thousands (y)	46	66	81	93	101

x	40	50	60	70
y	6.2	7.2	9.1	12

X=x	0	1	2	3
p(x)	0.2	0.1	0.4	0.3

x	3	4	5
P(x)	0.1	0.1	0.2

Year	2001	2002	2003	2004	2005	2006	2007	2008	2009
Sales	124	120	135	140	145	158	162	170	175

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13

X	-1	0	1	2
P(X=x)	\(\frac{1}{3}\)	\(\frac{1}{6}\)	\(\frac{1}{6}\)	\(\frac{1}{3}\)

Alternative	States of Nature
	Good	Fair	Bad
A	100	60	+50
B	80	50	+10
C	40	20	+5

year	1961	1962	1963	1964	1965	1966	1967
Production in tonnes	200	-	260	306	-	390	430

Height in cm (x)	40-60	60-80	80 - 100	100-120	120-140
No. of. students (y)	250	120	100	70	50

X	0	1	2	3
P(X)	\(\frac{1}{5}\)	\(\frac{2}{5}\)	\(\frac{1}{5}\)	\(\frac{1}{5}\)

Y	0	1	2	3
P(Y)	\(\frac{1}{5}\)	\(\frac{3}{10}\)	\(\frac{2}{5}\)	\(\frac{1}{10}\)

X	1	2	4	2A	3A	5A
P(X)	\(\frac{1}{2}\)	\(\frac{1}{5}\)	\(\frac{3}{25}\)	\(\frac{1}{10}\)	\(\frac{1}{25}\)	\(\frac{1}{25}\)

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13

12th Standard stateboard question papers & Study material

தமிழ் Subjects

உயிரியல்

கணினி பயன்பாடுகள்

கணினி அறிவியல்

வணிகக் கணிதம் மற்றும் புள்ளியியல்

வணிகவியல்

பொருளியல்

கணிதவியல்

வேதியியல்

இயற்பியல்

கணினி தொழில்நுட்பம்

வரலாறு

கணக்குப்பதிவியல்

தமிழ்

English Subjects

Maths

Chemistry

Physics

Biology

Computer Science

Business Maths and Statistics

Economics

Commerce

Accountancy

History

Computer Applications

Computer Technology

English

11th Standard stateboard question papers & Study material

தமிழ் Subjects

கணிதம்

உயிரியல்

பொருளியல்

இயற்பியல்

வேதியியல்

வரலாறு

வணிகக் கணிதம் மற்றும் புள்ளியியல்

கணினி அறிவியல்

கணக்குப்பதிவியல்

வணிகவியல்

கணினி பயன்பாடுகள்

கணினி தொழில்நுட்பம்

தமிழ்

English Subjects

Maths

Commerce

Economics

Biology

Business Maths and Statistics

Accountancy

Computer Science

Physics

Chemistry

Computer Applications

History

Computer Technology

தமிழ்

English

9th Standard stateboard question papers & Study material

தமிழ் Subjects

English Subjects

Maths

Science

Social Science

கணிதம்

அறிவியல்

சமூக அறிவியல்

6th Standard stateboard question papers & Study material

தமிழ் Subjects

கணிதம்

அறிவியல்

சமூக அறிவியல்

English Subjects

Maths

Science

Social Science

10th Standard stateboard question papers & Study material

தமிழ் Subjects

கணிதம்

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13