For what value of k, the matrix \(A=\left( \begin{matrix} 2 & k \\ 3 & 5 \end{matrix} \right) \) has no inverse?

(a)

\(\frac { 3 }{ 10 } \)

(b)

\(\frac { 10 }{ 3 } \)

(c)

3

(d)

10

\(\int { \left( x-1 \right) } { e }^{ -x }\) dx = __________ +c

(a)

-xe^x

(b)

xe^x

(c)

-xe^-x

(d)

xe^-x

The area bounded by y = 2x - x² and X-axis is _________ sq. units

(a)

\(\frac{2}{3}\)

(b)

\(\frac{4}{3}\)

(c)

2

(d)

4

The differential equation \(\left( \frac { dx }{ dy } \right) ^{ 2 }+5y^{ \frac { 1 }{ 3 } }\)= x is _____________

(a)

order 2 degree 

(b)

order 1 degree 2

(c)

order 1 degree 6

(d)

order 1 degree 3

E².f(x) = ______________

(a)

f(x + h)

(b)

f(x + 2h)

(c)

f(2h)

(d)

f(2x)

If \(f(x)=\left\{\begin{array}{lc} k x^{2} & 0  if a p.d.f. then the value of k is ___________

(a)

\(\frac{1}{3}\)

(b)

\(\frac{1}{6}\)

(c)

\(\frac{1}{9}\)

(d)

\(\frac{1}{12}\)

The area under the standard normal curve between Z=-∞ and z=∞ is

(a)

0

(b)

0.5

(c)

1

(d)

0.75

The central limit theorem states that the sampling distribution of the mean will approach normal distribution __________

(a)

as the size of the population increases

(b)

as the sample size increase and becomes larger

(c)

as the number of samples gets larger

(d)

as the sample size decreases

Variation due to assignable causes in the product occur due to, _____

(a)

faulty process

(b)

carelessness of operators

(c)

poor quality of raw material

(d)

all the above.

A set of non-negative values that satisfies the constants in a transportation problem is a ___________

(a)

Basic feasible solution

(b)

Feasible solution

(c)

Optimal solution

(d)

Non degenerate basic feasible solution