The value of \(\int _{ 2 }^{ 3 }{ f(5-x) } dx-\int _{ 2 }^{ 3 }{ f(x) } dx\) is _______.

(a)

1

(b)

0

(c)

-1

(d)

5

The marginal cost function is MC = 100 \(\sqrt x\). find AC given that TC  = 0 when the out put is zero is ________.

(a)

\(\frac { 200 }{ 3 } { x }^{ \frac { 1 }{ 2 } }\)

(b)

\(\frac { 200 }{ 3 } { x }^{ \frac { 3 }{ 2 } }\)

(c)

\(\frac { 200 }{ { 3x }^{ \frac { 3 }{ 2 } } } \)

(d)

\(\frac { 200 }{ { 3x }^{ \frac { 1 }{ 2 } } } \)

If sec² x is an integrating factor of the differential equation \(\frac { dy }{ dx } \) + Py Q then P = ______.

(a)

2 tan x

(b)

sec x

(c)

cos² x

(d)

tan² x

The solution of \(\frac { dy }{ dx } \) = e^x-y is _____________

(a)

e^ye^x = c

(b)

y=log ce^x

(c)

y=log(e^x+c)

(d)

e^x+y = c

Lagrange’s interpolation formula can be used for _______.

(a)

equal intervals only

(b)

unequal intervals only

(c)

both equal and unequal intervals

(d)

none of these.

E [f(x₀)] is ______________

(a)

f(x_o + h)

(b)

f(x_o - h)

(c)

f(x_o) + h

(d)

f(x_o) - h

The probability density function p(x) cannot exceed ________.

(a)

zero

(b)

one

(c)

mean

(d)

infinity

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)

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

Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be: ________.

(a)

1.00

(b)

-1.00

(c)

0.00

(d)

-0.41

If the mean of the binomial distribution is 25, then its standard deviation lies in the interval ___________

(a)

[0,5)

(b)

(0,5]

(c)

[0,25]

(d)

(0,25]