List of practice Questions

The variance of the first 50 even natural numbers is:

The sides of a triangle are $\sin\alpha$, $\cos\alpha$, and $\sqrt{1+\sin\alpha\cos\alpha}$ for some $0 < \alpha < \frac{\pi}{2}$. Then, the greatest angle of the triangle is:

If $ \mathbf{a} = \mathbf{i} + 2\mathbf{j} - 3\mathbf{k} $ and $ \mathbf{b} = 2\mathbf{i} - 3\mathbf{j} - 5\mathbf{k} $, then:

$ \int_{\pi/11}^{9\pi/22} \frac{dx}{1 + \sqrt{\tan x}} $ is equal to:

The equation of a circle with center $ (5, 4) $ and touching the $ Y $-axis is:

Let $ F(\alpha) = \begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix} $, where $ \alpha \in \mathbb{R} $. Then $ [F(\alpha)]^{-1} $ is equal to:

Switching current of $ (p \land q) \lor (p \land (q \lor p \lor r)) $?

The value of the integral $ \int_0^2 |2x - 3| \, dx $ is:

If the curve $y^2 = 6x$ and $9x^2 + by^2 = 16$ intersect each other at right angles, then the value of $b$ is:

Let $ p: $ I am brave, $ q: $ I will climb the Mount Everest. The symbolic form of a statement, 'I am neither brave nor I will climb the Mount Everest' is:

Evaluate $ i^2 + i^3 + \dots + i^{4000} $:

Evaluate the following limit: \[ \lim_{\theta \to -\frac{\pi}{4}} \frac{\cos\theta + \sin\theta}{\theta + \frac{\pi}{4}}. \]

If $ f(x) $ is differentiable at $ x = 1 $ and \[ \lim_{h \to 0} \frac{1}{h} f(1 + h) = 5, \] then $ f'(1) $ is equal to:

Which of the following are components of a time series?(A) Irregular component
(B) Cyclical component
(C) Chronological component
(D) Trend Component
Choose the correct answer from the options given below:

Mohan caught 100 frogs from a garden and measured their weights. The mean weight of these frogs is a :

Evaluate the role of Giuseppe Mazzini in the unification of the Italian Republic.

Which of the following is an example of actinomorphic flower?

Fill in the blank with the correct option:
The candidate assured the interviewers that the dip in her grades during her second semester was an ___________ since she had always been a top scorer in the first semester.

A certain sum becomes 2356 in 3 years and 2660 in 5 years on simple interest. What is the value of the sum?

Evaluate the integral $\int \frac{\pi}{x^n + 1 - x} , dx$:

The rate of change (in cm2/s) of the total surface area of a hemisphere with respect to the radius r at r = 3.

Match List-I with List-II:

Integrating factor of xdy − (y + 2x2)dx = 0

The integral of the function $ \frac{1}{9 - 4x^2} $ is:

For \[ f(x) = \int \frac{e^x}{\sqrt{4 - e^{2x}}} \, dx, \] if the point $\left(0, \frac{\pi}{2}\right)$ satisfies $y = f(x)$, then the constant of integration of the given integral is:

The function f(x) = |x| + |1 − x| is: