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 _______.

(a)

4

(b)

0

(c)

-4

(d)

1

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 function of a commodity are P(x) = (x − 5)² and S(x)= x² + x + 3 then the equilibrium quantity x₀ is ________.

(a)

5

(b)

2

(c)

3

(d)

19

The P.I. of \(\frac { d^{ 2 }y }{ { dx }^{ 2 } } -6\frac { dy }{ dx } +9y\)=e^3x is ______

(a)

\(\frac { { e }^{ 3x } }{ 2! } \)

(b)

\(\frac { { x }^{ 2 }e^{ 3x } }{ 2! } \)

(c)

\(\frac { xe^{ 3x } }{ 2! } \)

(d)

9e^3x

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

(a)

probability distribution

(b)

probability density function

(c)

distribution function

(d)

continuous random variable

If F(x) is the probability distribution function, then F(∞) is ________.

(a)

1

(b)

2

(c)

∞

(d)

0

In a Poisson distribution mean is 25, then S.D is ___________

(a)

5

(b)

625

(c)

125

(d)

\(\sqrt{5}\)

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

Variations due to natural disorder is known as ________.

(a)

random cause

(b)

non-random cause

(c)

human cause

(d)

all of them

In an assignment problem involving four workers and three jobs, total number of assignments possible are _______.

(a)

4

(b)

3

(c)

7

(d)

12