The rank of the matrix  \(\left( \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 4 & 9 \end{matrix} \right) \) is ________.

(a)

0

(b)

1

(c)

2

(d)

3

If the number of variables in a non-homogeneous system AX = B is n, then the system possesses a unique solution only when _______.

(a)

\(\rho (A)=\rho (A,B)>n\)

(b)

\(\rho(A)=\rho(A, B)=n\)

(c)

\(\rho (A)=\rho (A,B) < n\)

(d)

none of these

ഽ\(\frac { sin2x }{ 2sinx } dx\) is _______.

(a)

sin x + c

(b)

\(\frac12\)sin x + c

(c)

cos x + c

(d)

\(\frac12\)cos x + c

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)

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

Using the factorial representation of the gamma function, which of the following is the solution for the gamma function \(\Gamma \)(n) when n = 8 _______.

(a)

5040

(b)

5400

(c)

4500

(d)

5540

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 ________.

(a)

2

(b)

3

(c)

4

(d)

5

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)

3

(b)

6

(c)

9

(d)

5

The differential equation formed by eliminating a and b from \(y=a e^{x}+b e^{-x}\) is ______.

(a)

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

(b)

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

(c)

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

(d)

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

The differential equation formed by eliminating A and B from y = e^−2x(A cos x + B sin x) is ______.

(a)

y₂ − 4y₁ + 5 = 0

(b)

y₂+ 4y – 5 = 0

(c)

y₂−4y₁−5= 0

(d)

y₂ + 4y₁ + 5 = 0

Which of the following is the homogeneous differential equation?

(a)

(3x−5)dx = (4y−1)dy

(b)

xy dx−(x³+y³)dy = 0

(c)

y²dx+(x² − xy  − y²)dy = 0

(d)

(x²+y)dx = (y²+x)dy

E f (x)= _______.

(a)

f(x− h)

(b)

f (x)

(c)

f(x+ h)

(d)

f(x+ 2h)

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 ________.

(a)

21, 19, 22

(b)

21.5, 19.5, 22.5

(c)

0.29, 0.40, 0.35

(d)

3.045, 3.8, 3.85

E[X-E(X)] is equal to ________.

(a)

E(X)

(b)

V(X)

(c)

0

(d)

E(X)-X

The probability function of a random variable is defined as

X=x	-1	-2	0	1	2
P(x)	K	2K	3K	4K	5K

Then k is equal to ________.

(a)

zero

(b)

\(\frac{1}{4}\)

(c)

\(\frac{1}{15}\)

(d)

one

If X ~ N(μ, σ²), the maximum probability at the point of inflexion of normal distribution is ________.

(a)

\({ \left( \frac { 1 }{ \sqrt { 2\pi } } \right) }^{ { e }^{ \frac { 1 }{ 2 } } }\)

(b)

\({ \left( \frac { 1 }{ \sqrt { 2\pi } } \right) }^{ { e }^{ \left( -\frac { 1 }{ 2 } \right) } }\)

(c)

\({ \left( \frac { 1 }{ \sigma \sqrt { 2\pi } } \right) }^{ { e }^{ \left( \frac { 1 }{ 2 } \right) } }\)

(d)

\({ \left( \frac { 1 }{ \sqrt { 2\pi } } \right) }\)

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

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?

(a)

0.487

(b)

0.392

(c)

0.500

(d)

0.791

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

(a)

Parameter

(b)

random sample

(c)

statistic

(d)

entire data

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.

(a)

point estimate

(b)

interval estimation

(c)

standard error

(d)

confidence

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

(a)

Always positive

(b)

Always negative

(c)

Either positive or negative

(d)

Zero

While computing a weighted index, the current period quantities are used in the: ________.

(a)

Laspeyre’s method

(b)

Paasche’s method

(c)

Marshall Edgeworth method

(d)

Fisher’s ideal method

Cyclic variations in a time series are caused by __________

(a)

Lock out in a factor

(b)

war

(c)

floods

(d)

none of above

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

(a)

NWCM

(b)

LCM

(c)

VAM

(d)

Row Minima

A type of decision –making environment is _______.

(a)

certainty

(b)

uncertainty

(c)

risk

(d)

all of the above