if T = \(_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.4 } & \overset { B }{ 0.6 } \\ 0.2 & 0.8 \end{matrix} \right) \) is a transition probability matrix, then at equilibrium A is equal to ________.

(a)

\(\frac { 1 }{ 4 } \)

(b)

\(\frac { 1 }{ 5 } \)

(c)

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

(d)

\(\frac { 1 }{ 8 } \)

ഽ\(\frac { sin2x }{ 2sinx } dx\) is _______.

(a)

sin x + c

(b)

\(\frac12\)sin x + c

(c)

cos x + c

(d)

\(\frac12\)cos x + c

Area bounded by the curve y = \(\frac{1}{x}\) between the limits 1 and 2 is ________.

(a)

log 2 sq.units

(b)

log 5 sq.units

(c)

log 3 sq.units

(d)

log 4 sq.units

The order and degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{\frac{3}{2}}-\sqrt{\left(\frac{d y}{d x}\right)}-4=0\) are respectively ______.

(a)

2 and 6

(b)

3 and 6

(c)

1 and 4

(d)

2 and 4

E ≡ _______.

(a)

1 + Δ

(b)

1 - Δ

(c)

1 + ∇

(d)

1 - ∇

Probability which explains x is equal to or less than particular value is classified as ________.

(a)

discrete probability

(b)

cumulative probability

(c)

marginal probability

(d)

continuous probability

If Z is a standard normal variate, the proportion of items lying between Z = –0.5 and Z = –3.0 is ________.

(a)

0.4987

(b)

0.1915

(c)

0.3072

(d)

0.3098

A finite subset of statistical individuals in a population is called ________.

(a)

a sample

(b)

a population

(c)

universe

(d)

census

The components of a time series which is attached to short term fluctuation is ________.

(a)

Secular trend

(b)

Seasonal variations

(c)

Cyclic variation

(d)

Irregular variation

In a degenerate solution number of allocations is _______.

(a)

equal to m+n–1

(b)

not equal to m+n–1

(c)

less than m+n–1

(d)

greather than m+n–1