List of practice Questions

A galvanometer having 30 divisions has a current sensitivity of \(0.0625 \, \frac{\text{div}}{\mu\text{A}}\). If it is converted into a voltmeter to read a maximum of 6 V, then the resistance of that voltmeter is:
The efficiency of a Carnot's heat engine is \( \frac{1}{3} \). If the temperature of the source is decreased by \(50^\circ \text{C}\) and the temperature of the sink is increased by \(25^\circ \text{C}\), the efficiency of the engine becomes \( \frac{3}{16} \). The initial temperature of the sink is
The change in internal energy of given mass of a gas, when its volume changes from \( V \) to \( 3V \) at constant pressure \( P \) is
(\( \gamma \) - Ratio of the specific heat capacities of the gas)
A monatomic gas at a pressure of 100 kPa expands adiabatically such that its final volume becomes 8 times its initial volume. If the work done during the process is 180 J, then the initial volume of the gas is
If a gaseous mixture consists of 3 moles of oxygen and 4 moles of argon at an absolute temperature \( T \), then the total internal energy of the mixture is
(Neglect vibrational modes and \( R \) is the universal gas constant)
A sound wave of frequency 500 Hz travels between two points X and Y separated by a distance of 600 m in a time of 2 s. The number of waves between the points X and Y are
A ray of light incidents at an angle of \(60^\circ\) on the first face of a prism. The angle of the prism is \(30^\circ\) and its second face is silvered. If the light ray inside the prism retraces its path after reflection from the second face, then the refractive index of the material of the prism is
In an experiment, two polaroids are arranged such that the intensity of the polarised light emerged from the second polaroid is 37.5% of the intensity of the unpolarised light incident on the first polaroid. Then the angle between the axes of the two polaroids is
The angular velocity of a body changes from \(6 \, \text{rad/s}\) to \(21 \, \text{rad/s}\) in a time of \(1.5 \, \text{s}\). If the moment of inertia of the body is \(100 \, \text{g m}^2\), then the rate of change of angular momentum of the body is
The amplitude of a damped harmonic oscillator becomes 50% of its initial value in a time of 12 s. If the amplitude of the oscillator at a time of 36 s is \(x%\) of its initial amplitude, then the value of \(x\) is
The escape velocity of a body from a planet of mass \(M\) and radius \(R\) is 14 km/s. The escape velocity of the body from another planet having same mass and diameter \(8R\) (in km/s) is
The stress-strain graph of two wires A and B is shown in the figure. If \(Y_A\) and \(Y_B\) are Young’s moduli of materials of wires A and B respectively, then
stress strain
If two soap bubbles each of radius \(2 \, \text{cm}\) combine in vacuum under isothermal conditions, then the radius of the new bubble formed is
A rectangular slab consists of two cubes of copper and brass of equal sides having thermal conductivities in the ratio \(4 : 1\). If the free face of brass is at \(0^\circ \text{C}\) and that of copper is at \(100^\circ \text{C}\), then the temperature of their interface is
If a force \( \vec{F} = (3\hat{i} + 2\hat{j} + 5\hat{k})~\text{N} \) acting on a body displaces it through \( \vec{d} = (2\hat{i} + 2\hat{j} + 1\hat{k})~\text{m} \), then the work done by the force on the body is
If two bodies A and B are projected with same velocity but with different angles \( \theta_1 \) and \( \theta_2 \) respectively with the horizontal such that both will have same range, then the ratio of times of flight of the bodies A and B is
A body falls freely on to a hard horizontal surface. If the coefficient of restitution between the surface and the body is \( 0.8 \), then the ratio of the maximum height to which the body rises after second impact and the initial height of the body is
Two bodies of masses \( M \) and \( 4M \) initially at rest, start moving towards each other due to their mutual attraction. The velocity of their centre of mass when the first body attains a velocity \( v_0 \) is
Evaluate the integral: \[ \int_0^1 x^{5/2} (1 - x)^{3/2} \, dx = \]
Evaluate the limit: \[ \lim_{n \to \infty} \left[ \frac{1}{n^2} \sec^2 \frac{1}{n^2} + \frac{2}{n^2} \sec^2 \frac{4}{n^2} + \frac{3}{n^2} \sec^2 \frac{9}{n^2} + .s + \frac{1}{n^2} \sec^2 1 \right] = \]
The general solution of the differential equation \( \left(x \sin \frac{y}{x} \right) dy = \left( y \sin \frac{y}{x} - x \right) dx \) is
The general solution of the differential equation \( \cos(x + y) \, dy = dx \) is
If \( Ax^3 + Bxy = 4 \) (A and B are arbitrary constants) is the general solution of the differential equation \[ F(x)\frac{d^2y}{dx^2} + G(x)\frac{dy}{dx} - 2y = 0, \] then \( F(1) + G(1) = \)
The physical quantity having the dimensions of the square root of the ratio of the kinetic energy and surface tension is
If the displacement \( s \) (in metre) of a moving particle in terms of time \( t \) (in second) is \( s = t^3 - 6t^2 + 18t + 9 \), then the minimum velocity attained by the particle is