Find the rank of each of the following matrices.
\(\left( \begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix} \right) \)

Evaluate \(\int \sqrt{2 x+1} \ d x\)

Integrate the following with respect to x.
(3 + x)(2 − 5x)

Integrate the following with respect to x.
(4x + 2) \(\sqrt { { x }^{ 2 }+x+1 } \)

Evaluate the following
\(\int _{ 0 }^{ \infty }{ { e }^{ -mx } } { x }^{ 6 }dx\)

Find the area of the region bounded by the line x − 2y − 12 = 0 , the y-axis and the lines y = 2, y = 5.

Find the area bounded by the lines y − 2x − 4 = 0, y = 1, y = 3 and the y-axis

If MR = 14 − 6x + 9x², find the demand function.

For the marginal revenue function MR = 6 − 3x² − x³, Find the revenue function and demand function.

Solve: (x² + x + 1)dx + (y²− y + 3)dy = 0

A manufacturing company has found that the cost C of operating and maintaining the equipment is related to the length ‘m’ of intervals between overhauls by the equation m²\(\frac{dC}{dm}\) + 2mC = 2 and c = 4 and when m = 2. Find the relationship between C and m.

Find the order and degree of the following differential equation
\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -2\frac { dy }{ dx } +3y=0\)

Suppose, the life in hours of a radio tube has the following p.d.f
\(f(x)=\left\{\begin{array}{l} \frac{100}{x^{2}}, \text { when } x \geq 100 \\ 0, \text { when } x<100 \end{array}\right.\)
Find the distribution function.

The discrete random variable X has the probability function

X	1	2	3	4
P(X=x)	k	2k	3k	4k

Show that k = 0.1.

Define random variable.

What do you understand by continuous random variable?

Explain the distribution function of a random variable.

In an investment, a man can make a profit of Rs. 5,000 with a probability of 0.62 or a loss of Rs. 8,000 with a probability of 0.38. Find the expected gain.

How do you define variance in terms of Mathematical expectation?

A fair coin is tossed 6 times. Find the probability that exactly 2 heads occurs.

In tossing of a five fair coin, find the chance of getting exactly 3 heads.

Write down the conditions for which the binomial distribution can be used.

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes.

Write any 2 examples for Poisson distribution.

Define Standard normal variate.

What is sample?

Define parameter.

What is standard error?

State any two demerits of systematic random sampling.

What is point estimation?

What is confidence interval?

Define critical value.

Define level of significance.

Define Time series.

State the uses of time series.

Mention the components of the time series.

Define seasonal index.

Mention the classification of Index Number.

Define Laspeyre’s price index number.

Write note on Fisher’s price index number.

State the test of adequacy of index number.

Define Time Reversal Test.

Define true value ratio.

Define Family Budget Method.

Name the control charts for variables.

Define R Chart.

What are the uses of statistical quality control?

What is feasible solution and non degenerate solution in transportation problem?

Give mathematical form of assignment problem.

What is the difference between Assignment Problem and Transportation Problem?