If A is a singular matrix, then Adj A is ___________

(a)

non-singular

(b)

singular

(c)

symmetric

(d)

not defined

\(\int { \frac { 2 }{ { \left( { e }^{ x }+{ e }^{ -x } \right) }^{ 2 } } } \) dx = ____________ +c 

(a)

\(\frac { { -e }^{ -x } }{ { e }^{ x }+{ e }^{ -x } } \)

(b)

\(-\frac { { -e }^{ -x } }{ { e }^{ x }+{ e }^{ -x } } \)

(c)

\(\frac { 1 }{ { \left( { e }^{ x }+1 \right) }^{ 2 } } \)

(d)

\(\frac { 1 }{ { e }^{ x }-{ e }^{ -x } } \)

The area enclosed by the curve y = cos²x in [0,\(\pi\)] the lines x=0, x = \(\pi\) and the X-axis is ________sq.units.

(a)

2\(\pi\)

(b)

2\(\pi\)

(c)

\(\frac{2}{\pi}\)

(d)

\(\frac{\pi}{2}\)

If y = k.e^λx then its differential equation where k is arbitrary constant is _____________

(a)

\(\frac { dy }{ dx } \)= λy

(b)

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

(c)

\(\frac { dy }{ dx } \)+ky = 0

(d)

\(\frac { dy }{ dx } \)= e^λx

If c is a constant, then Δc = ______________

(a)

c.∆

(b)

c.∇

(c)

0

(d)

1

Given E(X + c) = 8 and E(X - c) = 12, then the value of c is ___________

(a)

-2

(b)

4

(c)

-4

(d)

2

If Z is a standard normal variate, then p(0

(a)

0.5

(b)

1

(c)

0.25

(d)

0.75

Which of the following statements is true?

(a)

point estimate gives a range of value

(b)

sampling is done only to estimate a statistic

(c)

sampling is done to estimate the population parameter

(d)

sampling is not possible for an infinite population

The normal equations for estimating a and b so that the line y = ax + b may be the line of best fit are __________

(a)

aΣx² + bΣx = Σxy, aΣx + nb = Σy

(b)

aΣx + bΣx² = Σxy, aΣx² + nb = Σy

(c)

aΣx + nb = Σxy, aΣx² + bΣx = Σy

(d)

aΣx² + nb = Σxy, aΣx + bΣx = Σy

To assign different jobs to the different machines to minimize the overall cost is ___________

(a)

transportation problem

(b)

assignment problem

(c)

minimax principle

(d)

maximin principle