### 12th Standard Business Maths Study material & Free Online Practice Tests - View and download Sample Question Papers with Solutions for Class 12 Session 2019 - 2020 TN Stateboard

#### 12th Standard Business Maths Chapter 3 Integral Calculus – II Two Marks Questions - by Sridevi - Sankarankoil Sep 16, 2019 - View & Download

• 1)

The marginal cost function is MC = 300 ${ x }^{ \frac { 2 }{ 5 } }$ and fixed cost is zero. Find out the total cost and average cost functions.

• 2)

If the marginal cost function of x units of output is $\frac { a }{ \sqrt { ax+b } }$ and if the cost of output is zero. Find the total cost as a function of x.

• 3)

If the marginal cost (MC) of a production of the company is directly proportional to the number of units (x) produced, then find the total cost function, when the fixed cost is Rs. 5,000 and the cost of producing 50 units is Rs. 5,625.

• 4)

The demand function p = 85 − 5x and supply function p = 3x − 35. Calculate the equilibrium price and quantity demanded .Also calculate consumer’s surplus.

• 5)

The demand and supply functions under perfect competition are p= 1600 − x2 and ps = 2x2 + 400 respectively. Find the producer’s surplus.

#### 12th Business Maths Unit 2 Integral Calculus – I Two Marks Questions - by Sridevi - Sankarankoil Sep 16, 2019 - View & Download

• 1)

Integrate the following with respect to x.

$\frac { 8x+13 }{ \sqrt { 4x+7 } }$

• 2)

Integrate the following with respect to x.

$\frac { 1 }{ \sqrt { x+1 } +\sqrt { x-1 } }$

• 3)

Integrate the following with respect to x.
$\frac { { x }^{ 3 } }{ x+2 }$

• 4)

$If\quad f' \prime x=\frac { 1 }{ x } andf(1)=\frac { \pi }{ 4 } ,\quad then\quad findf(x)$

• 5)

Integrate the following with respect to x.
$\frac { { e }^{ 3x }+{ e }^{ 5x } }{ { e }^{ x }+{ e }^{ -x } }$

#### 12th Business Maths - Applications of Matrices and Determinants Two Marks Questions - by Sridevi - Sankarankoil Sep 16, 2019 - View & Download

• 1)

Solve the following system of equations by rank method
x+y+z=9,2x+5y+7z=52,2x−y−z =0

• 2)

For what values of the parameterl , will the following equations fail to have unique
solution: 3x−y+lz=1,2x+y+z=2,x+2y−lz = −1 by rank method.

• 3)

An amount of 5,000/- is to be deposited in three different bonds bearing 6%, 7%
and 8% per year respectively. Total annual income is 358/-. If the income from
first two investments is `70/- more than the income from the third, then find the
amount of investment in each bond by rank method.

• 4)

Two types of soaps A and B are in the market. Their present 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 and when is the equilibrium reached?

• 5)

Find k if the equations 2x+3y−z=5,3x−y+4z=2,x+7y−6z=k are consistent.

#### 12th Business Maths - Term 1 Five Mark Model Question Paper - by Sridevi - Sankarankoil Sep 16, 2019 - View & Download

• 1)

Solve the equations 2x + 3y = 7, 3x + 5y = 9 by Cramer’s rule.

• 2)

The price of 3 Business Mathematics books, 2 Accountancy books and one
Commerce book is Rs840. 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.

• 3)

Evaluate $\int { \frac { 7x-1 }{ { x }^{ 2 }-5x+6 } dx }$

• 4)

A company produces 50,000 units per week with 200 workers. The rate of change of productions with respect to the change in the number of additional labour x is represented as 300 - 5x1/2 If 64 additional labours are employed, find out the additional number of units, the company can produce.

• 5)

Solve 3extan ydx +(1 + ex)sec2ydy = 0 given y(0) = $\frac { \pi }{ 4 }$

#### 12th Business Maths Quarterly Model Question Paper - by Sridevi - Sankarankoil Sep 13, 2019 - View & Download

• 1)

If A=(1 2 3), then the rank of AAT is

• 2)

if T= $_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.7 } & \overset { B }{ 0.3 } \\ 0.6 & x \end{matrix} \right)$ is a transition probability matrix, then the value of x is

• 3)

For what value of k, the matrix $A=\left( \begin{matrix} 2 & k \\ 3 & 5 \end{matrix} \right)$ has no inverse?

• 4)

If A, B are two n x n non-singular matrices, then

• 5)

$\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } }$ dx is

#### 12th Business Maths Unit 10 Operations Research Book Back Questions - by Sridevi - Sankarankoil Sep 05, 2019 - View & Download

• 1)

The transportation problem is said to be unbalanced if _________

• 2)

Solution for transportation problem using __________method is nearer to an optimal solution.

• 3)

In an assignment problem the value of decision variable xij is _________

• 4)

If number of sources is not equal to number of destinations, the assignment problem is called____________

• 5)

The solution for an assignment problem is optimal if

#### 12th Business Maths Chapter 9 Applied Statistics Book Back Questions - by Sridevi - Sankarankoil Sep 05, 2019 - View & Download

• 1)

A time series is a set of data recorded

• 2)

The value of ‘b’ in the trend line y=a+bx is

• 3)

The component of a time series attached to long term variation is trended as

• 4)

Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:

• 5)

Which of the following Index number satisfy the time reversal test?

#### 12th Business Maths - Sampling Techniques and Statistical Inference Book Back Questions - by Sridevi - Sankarankoil Sep 05, 2019 - View & Download

• 1)

A …………. may be finite or infinite according as the number of observations or items in it is finite or infinite.

• 2)

A finite subset of statistical individuals in a population is called __________

• 3)

Any statistical measure computed from sample data is known as ____________

• 4)

In simple random sampling from a population of units, the probability of drawing any unit at the first draw is

• 5)

In ___________ the heterogeneous groups are divided into homogeneous groups.

#### 12th Standard Business Maths Unit 7 Probability Distributions Book Back Questions - by Sridevi - Sankarankoil Sep 04, 2019 - View & Download

• 1)

Normal distribution was invented by

• 2)

If Z is a standard normal variate, the proportion of items lying between Z = –0.5 and Z = –3.0 is

• 3)

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

• 4)

If for a binomial distribution b(n,p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to :

• 5)

The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are:

#### 12th Standard Business Maths - Random Variable and Mathematical Expectation Book Back Questions - by Sridevi - Sankarankoil Sep 04, 2019 - View & Download

• 1)

Value which is obtained by multiplying possible values of random variable with probability of occurrence and is equal to weighted average is called

• 2)

Probability which explains x is equal to or less than particular value is classified as

• 3)

If X is a discrete random variable and p x ( ) is the probability of X , then the expected value of this random variable is equal to

• 4)

Which of the following is not possible in probability distribution?

• 5)

A discrete probability distribution may be represented by

#### 12th Standard Business Maths Differential Equations Book Back Questions - by Sridevi - Sankarankoil Sep 03, 2019 - View & Download

• 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 formed by eliminating a and b from y=ae+ be−x is

• 3)

The differential equation of y = mx + c is (m and c are arbitrary constants)

• 4)

The integrating factor of x $\frac { dy }{ dx }$ - y = x2 is

• 5)

The differential equation of x+ y= a2

#### 12th Standard Business Maths Unit 5 Numerical Methods Book Back Questions - by Sridevi - Sankarankoil Sep 03, 2019 - View & Download

• 1)

Δ2y0 =

• 2)

If ‘n’ is a positive integer Δn[ Δ-n​ ​​​​​​f(x)]

• 3)

∇ f(a) =

• 4)

Lagrange’s interpolation formula can be used for

• 5)

If f (x)=x+ 2x + 2 and the interval of differencing is unity then Δf (x)

#### 12th Standard Business Maths Unit 3 Integral Calculus – II Book Back Questions - by Sridevi - Sankarankoil Sep 03, 2019 - View & Download

• 1)

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

• 2)

Area bounded by the curve y = e−2x between the limits 0 ≤ x ≤ ∞ is

• 3)

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

• 4)

The profit of a function p(x) is maximum when

• 5)

When x0 = 5 and p0 = 3 the consumer’s surplus for the demand function pd = 28 − x2 is

#### 12th Standard Business Maths Unit 1 Integral Calculus – I Book Back Questions - by Sridevi - Sankarankoil Aug 31, 2019 - View & Download

• 1)

$\frac { 1 }{ { x }^{ 3 } }$dx is

• 2)

$\frac{logx}{x}$dx , x > 0 is

• 3)

$\left[ \frac { 9 }{ x-3 } -\frac { 1 }{ x+1 } \right]$dx is

• 4)

$\int _{ 0 }^{ 1 }{ (2x+1) } dx$ is

• 5)

$\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } }$ dx is

#### 12th Standard Business Maths Unit 1 Applications of Matrices and Determinants Book Back Questions - by Sridevi - Sankarankoil Aug 30, 2019 - View & Download

• 1)

The system of linear equations x+y+z=2,2x+y−z=3,3x+2y+k =4 has unique solution, if k is not equal to

• 2)

Cramer’s rule is applicable only to get an unique solution when

• 3)

if $\frac { { a }_{ 1 } }{ x } +\frac { { b }_{ 1 } }{ y } ={ c }_{ 1 },\frac { { a }_{ 2 } }{ x } +\frac { { b }_{ 2 } }{ y } ={ c }_{ 2 },{ \triangle }_{ 1= }\begin{vmatrix} { a }_{ 1 } & { b }_{ 1 } \\ { a }_{ 2 } & { b }_{ 2 } \end{vmatrix};\quad { \triangle }_{ 2 }=\begin{vmatrix} { b }_{ 1 } & { c }_{ 1 } \\ { b }_{ 2 } & { c }_{ 2 } \end{vmatrix}{ \triangle }_{ 3 }=\begin{vmatrix} { c }_{ 1 } & { a }_{ 1 } \\ { c }_{ 2 } & a_{ 2 } \end{vmatrix}$ then (x,y) is

• 4)

$\left| { A }_{ n\times n } \right|$=3 $\left| adjA \right|$ =243 then the value n is

• 5)

Rank of a null matrix is

#### 12th Standard Business Maths Unit 8 Applied Statistics One Mark Question with Answer Key - by Sridevi - Sankarankoil Aug 29, 2019 - View & Download

• 1)

A time series is a set of data recorded

• 2)

A time series consists of

• 3)

The components of a time series which is attached to short term fluctuation is

• 4)

Factors responsible for seasonal variations are

• 5)

The additive model of the time series with the components T, S, C and I is

#### 12th Standard Business Maths - Sampling Techniques and Statistical Inference One Mark Question and Answer - by Sridevi - Sankarankoil Aug 29, 2019 - View & Download

• 1)

A …………. may be finite or infinite according as the number of observations or items in it is finite or infinite.

• 2)

A __________ of statistical individuals in a population is called a sample.

• 3)

A finite subset of statistical individuals in a population is called __________

• 4)

Any statistical measure computed from sample data is known as ____________

• 5)

A_________is one where each item in the universe has an equal chance of known opportunity of being selected.

#### 12th Standard Business Maths - Probability Distributions One Mark Question and Answer - by Sridevi - Sankarankoil Aug 28, 2019 - View & Download

• 1)

Normal distribution was invented by

• 2)

If X ~N(9,81) the standard normal variate Z will be

• 3)

In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is

• 4)

The parameters of the normal distribution $f(x)=\left( \frac { 1 }{ \sqrt { 72\pi } } \right) \frac { { e }^{ -(x-10)^{ 2 } } }{ 72 } -\infty <X<\infty$

• 5)

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 :

#### 12th Business Maths Unit 6 Random Variable and Mathematical Expectation One Mark Question and Answer - by Sridevi - Sankarankoil Aug 27, 2019 - View & Download

• 1)

Value which is obtained by multiplying possible values of random variable with probability of occurrence and is equal to weighted average is called

• 2)

Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0⋅ 29, 0⋅ 40, 0⋅ 35. Pofit per unit is 0⋅ 50 paisa then expected profits for three days are

• 3)

Probability which explains x is equal to or less than particular value is classified as

• 4)

Given E(X) = 5 and E(Y) = -2, then E(X – Y) is

• 5)

A variable that can assume any possible value between two points is called

#### 12th Business Maths Chapter 5 Numerical Methods One Mark Question and Answer - by Sridevi - Sankarankoil Aug 27, 2019 - View & Download

• 1)

Δ2y0 =

• 2)

Δf(x) =

• 3)

∇ ≡

• 4)

∇ f(a) =

• 5)

For the given points (x0, y0) and (x1,y1) the Lagrange’s formula is

#### 12th Business Maths Unit 4 Differential Equations One Mark Question and Answer - by Sridevi - Sankarankoil Aug 27, 2019 - View & Download

• 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 formed by eliminating a and b from y=ae+ be−x is

• 3)

The complementary function of (D2+ 4)y = e2x is

• 4)

The differential equation of y = mx + c is (m and c are arbitrary constants)

• 5)

The differential equation satisfied by all the straight lines in xy plane is

#### 12th Business Maths Unit 3 Integral Calculus – II One Mark Question Paper with Answer Key - by Sridevi - Sankarankoil Aug 26, 2019 - View & Download

• 1)

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

• 2)

Area bounded by the curve y = e−2x between the limits 0 ≤ x ≤ ∞ is

• 3)

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

• 4)

If the marginal revenue MR = 35 + 7x − 3x2, then the average revenue AR is

• 5)

The profit of a function p(x) is maximum when

#### 12th Standard Business Maths Unit 2 Integral Calculus – I One Mark Question Paper - by Sridevi - Sankarankoil Aug 24, 2019 - View & Download

• 1)

$\frac { 1 }{ { x }^{ 3 } }$dx is

• 2)

$\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } }$dx is

• 3)

$\frac { { e }^{ x } }{ { e }^{ x }+1 }$ dx

• 4)

$\int _{ 2 }^{ 4 }{ \frac { dx }{ x } }$ is

• 5)

The value of $\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ cosx }$ dx is

#### 12th Business Maths Chapter 1 Applications of Matrices and Determinants One Mark Question Paper - by Sridevi - Sankarankoil Aug 23, 2019 - View & Download

• 1)

If A=(1 2 3), then the rank of AAT is

• 2)

The rank of the unit matrix of order n is

• 3)

Which of the following is not an elementary transformation?

• 4)

The system of equations 4x+6y=5, 6x+9y=7 has

• 5)

if $\left| A \right| \neq 0,$ then A is

#### 12th Business Maths Chpater 6 Random Variable and Mathematical Expectation Model Question Paper - by Sridevi - Sankarankoil Aug 20, 2019 - View & Download

• 1)

A variable that can assume any possible value between two points is called

• 2)

A discrete probability distribution may be represented by

• 3)

If we have f(x)=2x, 0$\le$x$\le$1, then f (x) is a

• 4)

A set of numerical values assigned to a sample space is called

• 5)

The distribution function F(x) is equal to

#### 12th Standard Business Maths Chapter 5 Numerical Methods Model Question Paper - by Sridevi - Sankarankoil Aug 05, 2019 - View & Download

• 1)

Δf(x) =

• 2)

If m and n are positive integers then ΔmΔnf(x) =

• 3)

∇ f(a) =

• 4)

Lagrange’s interpolation formula can be used for

• 5)

If f (x)=x+ 2x + 2 and the interval of differencing is unity then Δf (x)

#### 12th Standard Business Maths First Mid Term Model Question Paper - by Sridevi - Sankarankoil Aug 01, 2019 - View & Download

• 1)

The rank of m×n matrix whose elements are unity 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)

$\sqrt { { e }^{ x } }$ dx is

• 4)

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

• 5)

If MR = 15 - 8x, then the revenue function is

#### 12th Standard Business Maths Differential Equations Important Question Paper - by Sridevi - Sankarankoil Jul 30, 2019 - View & Download

• 1)

The differential equation ${ \left( \frac { dx }{ dy } \right) }^{ 3 }+2{ y }^{ \frac { 1 }{ 2 } }$ = x is

• 2)

The integrating factor of the differential equation $\frac{dx}{dy}+Px=Q$

• 3)

The complementary function of (D2+ 4)y = e2x is

• 4)

The particular integral of the differential equation is $\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -8\frac { dy }{ dx }$+16y = 2e4x

• 5)

Solution of $\frac { dy }{ dx }$ + Px = 0

#### 12th Standard Business Maths Chapter 3 Integral Calculus – II Important Question Paper - by Sridevi - Sankarankoil Jul 26, 2019 - View & Download

• 1)

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

• 2)

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

• 3)

The marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function is

• 4)

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

• 5)

The area unded by the curves y = 2x, x = 0 anx=2 is________sq.units.

#### Plus 2 Business Maths Unit 2 Integral Calculus – I Important Question Paper - by Sridevi - Sankarankoil Jul 24, 2019 - View & Download

• 1)

$\frac { 1 }{ { x }^{ 3 } }$dx is

• 2)

ഽ2xdx is

• 3)

$\frac { sin2x }{ 2sinx } dx$ is

• 4)

$\Gamma \left( \frac { 3 }{ 2 } \right)$

• 5)

$\int _{ 0 }^{ \infty }{ { x }^{ 4 }{ e }^{ -x } }$dx is

#### 12th Business Maths - Applications of Matrices and Determinants Important Question Paper - by Sridevi - Sankarankoil Jul 18, 2019 - View & Download

• 1)

If A=(1 2 3), then the rank of AAT is

• 2)

The rank of m×n matrix whose elements are unity is

• 3)

if T=$_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.4 } & \overset { B }{ 0.6 } \\ 0.2 & 0.8 \end{matrix} \right)$ is a transition probability matrix, then at equilibrium A is equal to

• 4)

if T= $_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.7 } & \overset { B }{ 0.3 } \\ 0.6 & x \end{matrix} \right)$ is a transition probability matrix, then the value of x is

• 5)

Which of the following is not an elementary transformation?

#### frequently asked questions in +2 state board english medium business maths first chapter - by Balamurugan Jun 29, 2019 - View & Download

• 1)

If A=(1 2 3), then the rank of AAT is

• 2)

The rank of m×n matrix whose elements are unity is

• 3)

The rank of the unit matrix of order n is

• 4)

Rank of a null matrix is

• 5)

For what value of k, the matrix $A=\left( \begin{matrix} 2 & k \\ 3 & 5 \end{matrix} \right)$ has no inverse?

#### twelfth standard business maths chapter one important two mark questions for state board english medium - by Balamurugan Jun 29, 2019 - View & Download

• 1)

Examine the consistency of the system of equations: x+y+z=7,x+2y+3z=18,y+2z=6 .

• 2)

Find k if the equations 2x+3y−z=5,3x−y+4z=2,x+7y−6z=k are consistent.

• 3)

Find k if the equations x+y+z=1,3x−y−z=4,x+5y+5z=k are inconsistent.

• 4)

Solve the equations x+2y+z=7,2x−y+2z=4,x+y−2z = −1 by using Cramer’s rule

• 5)

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.

#### important multiple choice questions in state board english medium business maths chapter one - by Balamurugan Jun 29, 2019 - View & Download

• 1)

If $\rho (A)$ =r then which of the following is correct?

• 2)

IfA =$\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right)$  then the rank of AAT is

• 3)

If the rank of the matrix  $\left( \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right)$  is 2. Then $\lambda$ is

• 4)

The rank of the diagonal matrix$\left( \begin{matrix} 1 & & \\ & 2 & \\ & & -3 \end{matrix}\\ \quad \quad \quad \quad \quad \quad \quad \begin{matrix} 0 & & \\ & 0 & \\ & & 0 \end{matrix} \right)$

• 5)

if T= $_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.7 } & \overset { B }{ 0.3 } \\ 0.6 & x \end{matrix} \right)$ is a transition probability matrix, then the value of x is