Find the rank of each of the following matrices.
\(\left( \begin{matrix} 1 & -1 \\ 3 & -6 \end{matrix} \right) \)

Integrate the following with respect to x.
\({ \left( \sqrt { 2x } -\frac { 1 }{ \sqrt { 2x } } \right) }^{ 2 }\)

Evaluate the following using properties of definite integrals:
\(\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ { x }^{ 3 }{ cos }^{ 3 }xdx } \)

Find the order and degree of the following differential equation
\({ \left[ 1+\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right] }^{ \frac { 3 }{ 2 } }=a\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } }\)

Describe what is meant by a random variable.

Write any 2 examples for Poisson distribution.

What is sampling distribution of a statistic?

The following table gives the number of small-scale units registered with the Directorate of Industries between 1985 and 1991. Show the growth on a trend line by the free hand method.

Years	1985	1986	1987	1988	1989	1990	1991	1992
No. of units (in‘000)	10	22	36	62	55	40	34	50

Write the control limits for the mean chart. 

Give mathematical form of assignment problem.