List of practice Questions

A particle of mass $ 2 $ kg is on a smooth horizontal table and moves in a circular path of radius $ 0.6 $ m. The height of the table from the ground is $ 0.8 $ m. If the angular speed of the particle is $ 12 $ rad/s, the magnitude of its angular momentum about a point on the ground right under the center of the circle is:

The minimum deviation produced by a hollow prism filled with a certain liquid is found to be 30$^\circ$. The light ray is also found to be refracted at an angle of 30$^\circ$. Then the refractive index of the liquid is

What is the minimum age required to become a member of the Legislative Assembly (Vidhan Sabha) in India?

There are 2 bags each containing 3 white and 5 black balls and 4 bags each containing 6 white and 4 black balls. If a ball drawn randomly from a bag is found to be black, then the probability that this ball is from the first set of bags is:

A solid cylinder rolls down an inclined plane without slipping. If the translational kinetic energy of the cylinder is 140 J, the total kinetic energy of the cylinder is

When I look at my past, I often regret of my past decisions?

Find the sum of the first 10 terms of the sequence $ 2.5 + 5.9 + 8.13 + 11.17 + \cdots \ to \ 10 \ terms =$:

If \[ \cos \alpha + 4 \cos \beta + 9 \cos \gamma = 0 \quad \text{and} \quad \sin \alpha + 4 \sin \beta + 9 \sin \gamma = 0, \] then \[ 81 \cos (2\gamma - 2\alpha) - 16 \cos (2\beta - 2\alpha) = ? \]

If the position of the electron was measured with an accuracy of $ \pm 0.002 $ nm, the uncertainty in the momentum of it would be (in kg ms$^{-1}$) ($ h = 6.626 \times 10^{-34} $ Js):

“The French Revolution created a sense of collective identity amongst the French people.” Explain the statement with suitable arguments.

The determinant of the matrix $$ \begin{bmatrix} a & b & c \\ a^2 & b^2 & c^2 \\ 1 & 1 & 1 \end{bmatrix} $$ is not equal to:

A solid cylinder of mass 2 kg and radius 0.2 m is rotating about its own axis without friction with angular velocity 5 rad/s. A particle of mass 1 kg moving with a velocity of 5 m/s strikes the cylinder and sticks to it as shown in figure.

The angular velocity of the system after the particle sticks to it will be:

If the solution of the system of simultaneous linear equations: $$ x + y - z = 6, $$ $$ 3x + 2y - z = 5, $$ $$ 2x - y - 2z + 3 = 0 $$ is $ x = \alpha, y = \beta, z = \gamma $, then $ \alpha + \beta = ?$

If $ A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix} $ and $ \alpha^2 + \beta A = 21 $ for some $ \alpha, \beta \in \mathbb{R} $, then find $ \alpha + \beta $:

If $ Z $ is a complex number such that $ |Z| \leq 3 $ and $ -\frac{\pi}{2} \leq \text{arg } Z \leq \frac{\pi}{2} $, then the area of the region formed by the locus of $ Z $ is:

The independent term in the expansion of $ (1 + x + 2x^2) \left( \frac{3x^2}{2} - \frac{1}{3x} \right)^9 $ is:

The number of ways of selecting 3 numbers that are in GP from the set $ \{1, 2, 3, \dots, 100\} $ is:

Among [Co(CN)₄]⁴⁻, [Co(CO)₃(NO)], XeF₄, [PCl₄ ]⁺, [PdCl₄ ]²⁻ , [ICl₄ ]⁻ , [Cu(CN)₄]³⁻ and P₄ the total number of species with tetrahedral geometry is _____.

It is given that in a random experiment, events A and B are such that $ P(A) = \frac{1}{4} ,P(A|B) = \frac{1}{2} $ and $ P(B|A) = \frac{2}{3} $. Then $ P(B) $ is:

Numerically greatest term in the expansion of $ (5 + 3x)^6 $, when $ x = 1 $, is:

When two dice are thrown, the probability of getting the sum of the values on them as 10 or 11 is:

A unit vector perpendicular to the vectors $ \bar{a} = 2\bar{i} + 3\bar{j} + 4\bar{k} $ and $ \bar{b} = 3\bar{j} + 2\bar{k} $ is:

A shaft has diameter $20^{+0.05}_{-0.15}$ mm and a hole diameter $20^{+0.20}_{-0.10}$ mm. When these are assembled, then what is the nature of fit yield?

In critical path method, critical path moves along with the activities having total float of:

Hungarian method is generally used to solve the following type of problem: