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TN 12th Computer Applications மின் - வணிக பாதுகாப்பு அமைப்புகள் Sample Question Papers Study Material - QB365 Set A

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12th Standard Business Mathamatics English Medium All Chapter Book Back and Creative One Marks Questions 2020

Published on: 09/03/2020

Download Tamil Nadu 12th Standard Business Maths and Statistics question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

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Std: 12th Standard - Business Maths and Statistics

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Questions:

Multiple Choice Question

40 x 1 = 40

Choose the odd one out

(a)

Secular trend

(b)

seasonal variation

(c)

Simple averages

(d)

cyclic variations

The causes leading to vast variation in the specification of a product are usually due to _____

(a)

random process

(b)

assignable causes

(c)

non-traceable causes

(d)

all the above

The point estimate variance of 6.33, 6.37, 6.36, 6.32, 6.37 is

(a)

0.0022

(b)

0.00055

(c)

0.0055

(d)

0.055

The point estimate variance of 21, 25, 20, 16, 12, 10, 17, 18, 13 and 11 is _______

(a)

23.5

(b)

2.35

(c)

4.85

(d)

48.5

If the mean and variance of a binomial variate are 2 and 1 respectively, the probability that X takes a value greater than one is equal to ________

(a)

\(\frac{5}{16}\)

(b)

\(\frac{11}{16}\)

(c)

\(\frac{10}{16}\)

(d)

\(\frac{1}{2}\)

The variance of a binomial distribution is ___________

(a)

equal to its mean

(b)

less than its mean

(c)

greater than its mean

(d)

none

If X is a discrete random variable. then P(X≥a)=________.

(a)

P(X

(b)

1-P(X≤a)

(c)

1-P(X

(d)

If the p.d.f of a continuous random variable. X is \(f(x)=\left\{\begin{array}{l} \frac{x}{2}, 0 then E(3X²-2X) = _________

(a)

\(\frac{2}{3}\)

(b)

\(\frac{4}{3}\)

(c)

\(\frac{10}{3}\)

(d)

\(\frac{7}{3}\)

The least cost method is more economical than North West Corner Rule, since it starts with the ___________

(a)

least cost

(b)

minimum cost

(c)

maximum cost

(d)

lower beginning cost

10.

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.

(a)

transportation

(b)

assignment

(c)

unique

(d)

optimal

11.

The differential equation of the family of lines y=mx is ______

(a)

\(\frac { dy }{ dx } \)=m

(b)

y dx - x dx

(c)

\(\frac { d^{ 2 }y }{ dx^{ 2 } } \)=0

(d)

y dx + x dy=0

12.

Solution of \(\frac { dx }{ dy } \)+mx = 0 where m<0 is _______

(a)

x = ce^my

(b)

x = ce^-my

(c)

x = my + c

(d)

x = c

13.

\(\int { \left( \frac { x }{ m } +\frac { m }{ x } \right) } \) dx = __________ +c

(a)

\(\frac { { x }^{ 2 } }{ 2m } +m\log { \left| x \right| } \)

(b)

\(\frac { x }{ { m }^{ 2 } } +m\log { \left| x \right| } \)

(c)

\(-\frac { 1 }{ { mx }^{ 2 } } +m\log { \left| x \right| } \)

(d)

\(\frac { 1 }{ m } -\frac { m }{ { x }^{ 2 } } \)

14.

\(\int { { e }^{ x } } \) (1-cot x +cot² x) dx = _______________ +c

(a)

e^x cot x

(b)

- e^x cot x

(c)

e^x cosec x

(d)

-e^x cosec x

15.

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

(a)

AB is non-singular

(b)

AB is singular

(c)

(AB)^-1 = A^-1 B^-1

(d)

(AB)^-1 does not exit

16.

If \(\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right| \) then x =

(a)

(b)

± 3

(c)

± 6

(d)

17.

If y is to be estimated for the values of x which lies unside the given set of the values of it is called __________

(a)

Interpolation

(b)

extrapolation

(c)

Forward Interpolation

(d)

backward Interpolation

18.

∆f(x + 3h) ______________

(a)

f(x + 3h) - f(x + 4h)

(b)

f(x + 4h) - f(x + 3h)

(c)

f(x + h) - f(x)

(d)

f(x + 2h) - f(x + 3h)

19.

The area bounded by the curve y = 4ax and the lines y² = 2a and Y-axis is _______ sq. units.

(a)

\(\frac{2a}{3}\)

(b)

2a²

(c)

\(\frac{a^2}{3}\)

(d)

\(\frac{2a^2}{3}\)

20.

The area lying above the X-axis and under the parabola y = 4x - x² is ______ sq. units

(a)

\(\frac{16}{3}\)

(b)

\(\frac{8}{3}\)

(c)

\(\frac{32}{3}\)

(d)

\(\frac{64}{3}\)

21.

If f (x)=x²+ 2x + 2 and the interval of differencing is unity then Δf (x) _______.

(a)

2x −3

(b)

2x +3

(c)

x + 3

(d)

x − 3

22.

Δf(x) = _______.

(a)

f(x+ h)

(b)

f(x) − f(x+h)

(c)

f(x + h) − f(x)

(d)

f (x) − f(x−h)

23.

In a non – degenerate solution number of allocations is _______.

(a)

Equal to m+n–1

(b)

Equal to m+n+1

(c)

Not equal to m+n–1

(d)

Not equal to m+n+1

24.

The transportation problem is said to be unbalanced if _______.

(a)

Total supply ≠ Total demand

(b)

Total supply = Total demand

(c)

m = n

(d)

m+n–1

25.

A homogeneous differential equation of the form \(\frac { dx }{ dy } \) = f\(\left( \frac { y }{ x } \right) \) can be solved by making substitution,______.

(a)

x = v y

(b)

y = v x

(c)

y = v

(d)

x = v

26.

The order and degree of the differential equation \(\sqrt { \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } } =\sqrt { \frac { dy }{ dx } +5 } \) are respectively ______.

(a)

2 and 3

(b)

3 and 2

(c)

2 and 1

(d)

2 and 2

27.

A typical control charts consists of ________.

(a)

CL, UCL

(b)

CL, LCL

(c)

CL, LCL, UCL

(d)

UCL, LCL

28.

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

(a)

Secular trend

(b)

Seasonal variations

(c)

Cyclic variation

(d)

Irregular variation

29.

The standard error of sample mean is ______.

(a)

\(\frac { \sigma }{ \sqrt { 2n } } \)

(b)

\(\frac { \sigma }{ { n } } \)

(c)

\(\frac { \sigma }{ \sqrt { n } } \)

(d)

\(\frac { { \sigma }^{ 2 } }{ \sqrt { n } } \)

30.

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

(a)

Infinite set

(b)

finite subset

(c)

finite set

(d)

entire set

31.

\(\Gamma (n)\) is _______.

(a)

(n −1)!

(b)

(c)

\(n\Gamma (n)\)

(d)

(n −1)\(\Gamma \)(n)

32.

ഽ\(\frac { dx }{ \sqrt { { x }^{ 2 }-{ 36 } } } \) is _______.

(a)

\(\sqrt { { x }^{ 2 }-{ 36 } } +c\)

(b)

log\(\left| x+\sqrt { { x }^{ 2 }-36 } \right| +c\)

(c)

log\(\left| x-\sqrt { { x }^{ 2 }-36 } \right| +c\)

(d)

\(log\left| { x }^{ 2 }+\sqrt { { x }^{ 2 }-36 } \right| +c\)

33.

Which of the following cannot generate a Poisson distribution?

(a)

The number of telephone calls received in a ten-minute interval

(b)

The number of customers arriving at a petrol station

(c)

The number of bacteria found in a cubic feet of soil

(d)

The number of misprints per page

34.

In a parametric distribution the mean is equal to variance is ________.

(a)

binomial

(b)

normal

(c)

poisson

(d)

all the above

35.

Which one is not an example of random experiment?

(a)

A coin is tossed and the outcome is either a head or a tail

(b)

A six-sided die is rolled

(c)

Some number of persons will be admitted to a hospital emergency room during any hour

(d)

All medical insurance claims received by a company in a given year

36.

A probability density function may be represented by ________.

(a)

table

(b)

graph

(c)

mathematical equation

(d)

both (b) and (c)

37.

Area bounded by y = \(\left| x \right| \) between the limits 0 and 2 is ________.

(a)

1sq.units

(b)

3 sq.units

(c)

2 sq.units

(d)

4 sq.units

38.

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 ________.

(a)

(b)

(c)

(d)

39.

For the system of equations x + 2y + 3z = 1, 2x + y + 3z = 2, 5x + 5y + 9z = 4 _______.

(a)

there is only one solution

(b)

there exists infinitely many solutions

(c)

there is no solution

(d)

None of these

40.

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

(a)

(b)

(c)

(d)

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Answers Key:

Multiple Choice Question

40 x 1 = 40

(b)
assignable causes

(b)
0.00055

(a)
23.5

(b)
\(\frac{11}{16}\)

(b)
less than its mean

10.

(b)
assignment

11.

(b)
y dx - x dx

12.

(b)
x = ce^-my

13.

(a)
\(\frac { { x }^{ 2 } }{ 2m } +m\log { \left| x \right| } \)

14.

(b)
- e^x cot x

15.

The non-homogeneous equation are
2x - y + z = 7, 3x + y - 5z = 13, x + y + z = 5

Augmented matrix [A,B]	Elementary Transformation
\(\left( \begin{matrix} 2 & -1 & 1 \\ 3 & 1 & -5 \\ 1 & 1 & 1 \end{matrix}\begin{matrix} 7 \\ 13 \\ 5 \end{matrix} \right) \)
\(-\left( \begin{matrix} 1 & 1 & 1 \\ 3 & 1 & -5 \\ 2 & -1 & 1 \end{matrix}\begin{matrix} 5 \\ 13 \\ 7 \end{matrix} \right) \)	\({ R }_{ 1 }\leftrightarrow { R }_{ 3 }\)
\(\sim \left( \begin{matrix} 1 & 1 & 1 \\ 0 & -2 & -8 \\ 0 & -3 & -1 \end{matrix}\begin{matrix} 5 \\ -2 \\ -3 \end{matrix} \right) \)	\({ R }_{ 2 }\rightarrow { R }_{ 2 }-3{ R }_{ 1 }\) \({ R }_{ 3 }\rightarrow { R }_{ 3 }-2{ R }_{ 1 }\)
\(\sim \left( \begin{matrix} 1 & 1 & 1 \\ 0 & -2 & -8 \\ 0 & 0 & 11 \end{matrix}\begin{matrix} 5 \\ -2 \\ 0 \end{matrix} \right) \)	\({ R }_{ 3 }\rightarrow { R }_{ 3 }-\cfrac { 3 }{ 2 } { R }_{ 2 }\)