Find the rank of the matrix A =\(\left( \begin{matrix} 1 & -3 \\ 9 & 1 \end{matrix}\begin{matrix} 4 & 7 \\ 2 & 0 \end{matrix} \right) \)

If f '(x) = 8x³ − 2x and f(2) = 8, then find f(x)

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

Evaluate \(\int _{ \frac { \pi }{ 6 } }^{ \frac { \pi }{ 3 } }{ \sin x } \) dx

Evaluate the following
\(\Gamma \) \(\left( \frac { 9 }{ 2 } \right) \)

If MR = 20 − 5x + 3x², find total revenue function.

Solve the following differential equations
\(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -4\frac { dy }{ dx } +4y=0\)

Solve: \(\frac { dy }{ dx } \) + e^x+ye^x = 0

Prove that 
(1 + Δ)(1 - ∇) = 1

Define 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.

In a book of 520 pages, 390 typo-graphical errors occur. Assuming Poisson law for the number of errors per page, find the probability that a random sample of 5 pages will contain no error.

Mention the properties of poisson distribution.

What is sample?

Define critical value.

A machine drills hole in a pipe with a mean diameter of 0.532 cm and a standard deviation of 0.002 cm. Calculate the control limits for mean of samples 5.

State the uses of Index Number.

What do you mean by process control?

What do you mean by balanced transportation problem?