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 profit of a function p(x) is maximum when ________.

(a)

MC − MR = 0

(b)

MC = 0

(c)

MR = 0

(d)

MC + MR = 0

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

The integrating factor of (1+x²)\(\frac { dy }{ dx } \)+xy = (1+x²)³ is _____________

(a)

\(\sqrt { 1+{ x }^{ 2 } } \)

(b)

log(1+x²)

(c)

e^tan-1x

(d)

log(tan^-1x)

The particular integral of the differential equation \(\frac { d^{ 2 }y }{ { dx }^{ 2 } } -5\frac { dy }{ dx } \)+6y=e^5x is _______

(a)

\(\frac { e^{ 5x } }{ 6 } \)

(b)

\(\frac { xe^{ 5x } }{ 21 } \)

(c)

6e^5x

(d)

\(\frac { { e }^{ 5x } }{ 25 } \)

A discrete probability function p(x) is always non-negative and always lies between ________.

(a)

0 and \(\infty \)

(b)

0 and 1

(c)

–1 and +1

(d)

–∞ and +∞

V(4X + 3) is _________

(a)

7

(b)

16V(X)

(c)

4V(X)

(d)

19

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

(a)

1

(b)

2

(c)

∞

(d)

0

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?

(a)

-1.41

(b)

1.41

(c)

-2.25

(d)

2.25