List of practice Questions

A sample was excited by 4358 Å line of mercury. A Raman line was observed at 4447 Å. Calculate Raman Shift in cm^-1

Let a circle $C_1$ be obtained on rolling the circle $x^2+y^2-4 x-6 y+11=0$ upwards 4 units on the tangent $T$ to it at the point $(3,2)$ Let $C_2$ be the image of $C_1$ in $T$ Let $A$ and $B$ be the centers of circles $C_1$ and $C_2$ respectively, and $M$ and $N$ be respectively the feet of perpendiculars drawn from $A$ and $B$ on the $x$-axis. Then the area of the trapezium AMNB is:

If $ \vec{a} = \hat{i} + \hat{j} + \hat{k} $, $ \vec{a} \cdot \vec{b} = 1 $ and $ \vec{a} \times \vec{b} = \hat{j} - \hat{k} $, then $ \vec{b} $ is:

Among the given halides, which one will give the same product in both S$_N1$ and S$_N2$ reactions?

Among the ligands $ {NH}_3, \, {en}, \, {CN}^-, \, {CO} $, the correct order of their increasing field strength is:

Evaluate the integral: \[ I = \int \frac{x + 3}{(x + 4)^2} e^x \,dx \]

If $ y = \sqrt{\frac{1 + \cos 2\theta}{1 - \cos 2\theta}} $, then $ \frac{dy}{d\theta} $ at $ \theta = \frac{3\pi}{4} $ is:

If \[ A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix} \] and \[ kA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}, \] then the values of $ k $, $ a $, and $ b $ respectively are:

If work done on a body is positive, then what will be the sign of kinetic energy?

If Today is Monday, After 62 it will be :

A circle touches both the y-axis and the line $ x + y = 0 $. Then the locus of its center is:

A particle executes Simple Harmonic Motion (SHM) with amplitude $ A $. The distance from the mean position when its kinetic energy becomes equal to its potential energy is:

Find the mean deviation about the mean for the data: $ 4, 7, 8, 9, 10, 12, 13, 17 $

Find out the figure that can be formed from the piece given below:

Find the value of \[ \tan^{-1}\left(\frac{1}{4}\right) + \tan^{-1}\left(\frac{2}{9}\right) \]

If the coordinates of the points A and B are (3, 3) and (7, 6), then the length of the portion of the line AB intercepted between the axes is:

A particle of mass $ m $ moving with velocity $ v $ collides with a stationary particle of mass $ 2m $. After the collision, they stick together and continue to move with velocity:

Five children Arun, Bhuvi, Charu, Deepak and Emmy are sitting along the corners of a pentagonal table facing the centre. Bhuvi is between Emmy and Charu. Deepak is to the right of Emmy. Who is to the left of Charu?

A proton ($ p $) and an electron ($ e $) will have the same de-Broglie wavelength when the ratio of their momenta is
(Assume $ m_p = 1849 m_e $):

In a reflecting telescope, a secondary mirror is used to:

For all $ n \in \mathbb{N} $, the sum of $ \frac{n^5}{5} + \frac{n^3}{3} + \frac{7n}{15} $ is:

For the separation of two immiscible liquids, which method is used?

A conducting loop of radius $ \frac{10}{\sqrt{\pi}} $ cm is placed perpendicular to a uniform magnetic field of 0.5T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25s is:

A charged particle is moving in a uniform magnetic field $ \mathbf{B} = 2\hat{i} + 3\hat{j} $ T. If it has an acceleration of $ \mathbf{a} = \alpha\hat{i} - 4\hat{j} $ m/s², then the value of $ \alpha $ will be:

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Clothes are not washed properly in hard water.
Reason (R): Hard water contains many minerals.
In the light of the above statements, choose the most appropriate answer from the options given below: