List of practice Questions

Composition of Total Cultivable Land

Categories of Reporting Area	As a percentage of total cultivable land (1950-51)	As a percentage of total cultivable land (2014-15)	Area (1950-51)	Area (2014-15)
Culturable waste land	8.0	4.0	13.4	6.8
Fallow other than current fallow	6.1	3.6	10.2	6.2
Current fallow	3.7	4.9	6.2	8.4
Net area sown	41.7	45.5	70.0	78.4
Total Cultivable Land	59.5	58.0	100.00	100.00

‘World Beneath His Feet’ is a biography of

Let \( z \) be a complex variable and \( C : |z| = 3 \) be a circle in the complex plane. Then,

\[ \oint_C \frac{z^2}{(z - 1)^2(z + 2)} \, dz = \]

For a stable closed loop system, the gain at phase crossover frequency should always be:

If the matrix \[ A = \begin{pmatrix} 3 & -1 & 1 \\ -1 & 5 & -1 \\ 1 & -1 & 3 \end{pmatrix} \] has three distinct eigenvalues, and one of its eigenvectors is \[ \begin{pmatrix} 1 \\ 0 \\ -1 \end{pmatrix}, \] then which of the following can be another eigenvector of \( A \)?

Which of the options correctly represents the Laplace inverse of \( \dfrac{2}{s^3} \)?

For a first order reaction, the starting material reduces to \( \dfrac{1}{4} \) of its initial value after 20 min.
The rate constant of the reaction will be: (Given \( \ln 4 = 1.38 \))

If the Laplace transform of a function \( f(t) \) is given by \[ \frac{2s + 1}{(s + 1)(s + 2)} \] then \( f(0) \) is equal to ______

The probability of a component being defective is 0.01. There are 100 such components in a machine. Then the probability of two or more defective components in the machine is ...........

The value of the integral \( \int_1^3 \frac{2}{x} \, dx \), when evaluated by using Simpson’s \( \frac{1}{3} \) rule on two equal subintervals each of length 1, is ...........

If $\vec{F} = x(x^2 + y^2 + z^2)\hat{i} + 2y(x^2 + y^2 + z^2)\hat{j} + 3z(x^2 + y^2 + z^2)\hat{k}$, then $\text{div} \, \vec{F}$ at $(1,1,1)$ is equal to ______

Consider the ordinary differential equation \[ x^2 \frac{d^2y}{dx^2} - 2x \frac{dy}{dx} + 2y = 0 \] with \( y(x) \) as a general solution. Given the values of \( y(1) = 1 \), \( y(2) = 5 \), the value of \( y(3) \) is equal to ______