List of practice Questions

The gases carbon monoxide (CO) and nitrogen at the same temperature have kinetic energies $ E_1 $ and $ E_2 $, respectively. Then,

A gas is taken through the cycle $ A \to B \to C \to A $, as shown in the figure. What is the net work done by the gas?

In the figure, pendulum bob on the left side is pulled aside to a height $ h $ from its initial position. After it is released, it collides with the right pendulum bob at rest, which is of the same mass. After the collision, the two bobs stick together and rise to a height

Two wires of the same material having radius in ratio 2 : 1 and lengths in ratio 1 : 2. If the same force is applied on them, then the ratio of their change in length will be
A thin circular ring of mass $ M $ and radius $ R $ rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity $ \omega $. Four small spheres each of mass $ m $ (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be
One end of the string of length $ l $ is connected to a particle of mass $ m $ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $ v $, the net force on the particle (directed towards the center) will be (T represents the tension in the string)
A transistor is connected in CE configuration. The collector supply is 10 V and the voltage drop across a resistor of 1000 $ \Omega $ in the collector circuit is 0.5 V. If the current gain factor is 0.96, then the base current is
A particle is projected at an angle $30^\circ$ with horizontal having kinetic energy $K$. The kinetic energy of the particle at the highest point is.
The ratio of amplitude of magnetic field to the amplitude of electric field of an electromagnetic wave propagating in vacuum is
A capacitor of capacity 2 $ \mu F $ is charged up to a potential 14 V and then connected in parallel to an uncharged capacitor of capacity 5 $ \mu F $. The final potential difference across each capacitor will be
The mass density of a nucleus varies with mass number $ A $ as
The mean energy per molecule for a diatomic gas is
If the galvanometer G does not show any deflection in the circuit shown, the value of R is given by:
galvanometer G does not show any deflection in the circuit
In a Young's double slit experiment, a student observes 8 fringes in a certain segment of screen when a monochromatic light of 600 nm wavelength is used. If the wavelength of light is changed to 400 nm, then the number of fringes he would observe in the same region of the screen is
An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 ms-1. The frictional force opposing the motion is 3000N. The minimum power delivered by the motor to the lift in watts is: (g =10 ms-2)
The peak voltage of the ac source is equal to:
A long solenoid of radius 1 mm has 100 turns per mm. If 1 A current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:
The solution x1 = 1, x2 = 1, x3 = 0 and z = 3 to the system of equations
x1+x2+x3=2
x1+x2-x3=2
x1,x2,x3≥0
which minimizes z = x1 + 2x2 + 3x3 is

A straight line parallel to the line y = √3 x passes through Q(2,3) and cuts the line 2x + 4y - 27 = 0 at P. Then the length of the line segment PQ is

Which of the following statements is correct?
If $2f(x^2) + 3f\left( \frac{1}{x^2} \right) = x^2 - 1$, for $x \in \mathbb{R} - \{0\}$, then $f(x^8)$ is equal to

The general solution of $ 2 \cos 4x + \sin^2 2x $= 0  is

The expression $ \frac{2 \tan A}{1 - \cot A} + \frac{2 \cot A}{1 - \tan A} $ can be written as

If $ \cos A = m \cos B $ and $ \cot \left( \frac{A+B}{2} \right) = \lambda \tan \left( \frac{B-A}{2} \right), $  then $ \lambda \text{ is equal to} $

In a trial, the probability of success is twice the probability of failure. In six trials, the probability of at most two failures will be