Find the rank of the matrix A = \(\left( \begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 5 & 7 \end{matrix} \right) \)

Evaluate \(\int { \left( { x }^{ 3 }+7 \right) \left( x-4 \right) dx } \)

Evaluate \(\int { \sqrt { 1+\sin2x \ dx } } \)

Evaluate ഽ\(\frac { dx }{ \sqrt { { x }^{ 2 }+25 } } \)

Using second fundamental theorem, evaluate the following:
\(\int _{ 0 }^{ 1 }{ { e }^{ 2x } } dx\)

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

Solve (D²−3D−4)y = 0

Find the order and degree of the following differential equations.
(2 - y'')² = y''² + 2y'

Find (i) Δe^ax
(ii) Δ²e^x
(iii) Δ log x

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.

What do you understand by continuous random variable?

Define Mathematical expectation in terms of discrete random variable.

In a family of 3 children, what is the probability that there will be exactly 2 girls?

Define Normal distribution.

What is population?

What is point estimation?

Define Time series.

Define Index Number.

Name the control charts for variables.

What is the Assignment problem?