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.
2cos x − 3sin x + 4sec² x − 5cosec²x

Evaluate ഽ\(\frac { dx }{ \sqrt { { 4x }^{ 2 }-9 } } \)

If \(\int _{ 1 }^{ a }{ { 3 }x^{ 2 } } \) dx = -1, then find the value of a ( a ∈ R ).

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

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

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

Find the order and degree of the following differential equation
\(\frac { { d }^{ 2 }y }{ { dx }^{ 3 } } -3{ \left( \frac { dy }{ dx } \right) }^{ 6 }+2y={ x }^{ 2 }\)

Prove that 
(1 + Δ)(1 - ∇) = 1

Two coins are tossed simultaneously. Getting a head is termed as success. Find the probability distribution of the number of successes.

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.

Define Bernoulli trials.

Define Normal distribution.

What is population?

What is confidence interval?

State the uses of time series.

Write note on Fisher’s price index number.

Define a control chart.

What is the Assignment problem?