List of practice Questions

If the rms speeds of helium and oxygen are equal, then the ratio of the temperatures of helium and oxygen is:
The ratio of radii of two wires is 1:2 and the density of their materials are in the ratio 1:4. If same tension is applied to both the wires then the ratio of the speed of transverse waves produced in them is:
The frequency of a light ray is \( 6 \times 10^{14} \) Hz. Its frequency when it propagates in a medium of refractive index 1.5, will be:
Two charges \( Q \) and \( 4Q \) are separated by a distance of 6 cm. The distance of the point from \( 4Q \) at which the net electric field is zero is:
Inside a charged hollow sphere, at any point the electric field \( E \) and potential \( V \) are:
The equivalent capacitance between A and B in the given figure is:
equivalent capacitance between A and B
A uniform solid sphere of mass \( M \) and radius \( a \) is surrounded by a concentric uniform thin spherical shell of mass 0.5M and radius 1.5a. The gravitational potential energy of a unit mass kept at a distance of 2.5a from the center is:
A cylindrical rod made of aluminum has length 1 meter and diameter of 10 cm. The rod is subjected to a tensile force of 100 kN. The elongation in the rod is:
A large open top water tank is completely filled with water. A small hole of diameter 4 mm is made 10 m below the water level. The flow rate of water through the hole is:
The phenomena of lowering freezing point of water by the application of pressure is known as:
A steel ball of mass 200 g falls freely from a height of 20 m and bounces to a height of 10.8 m from the ground. If the energy lost in this process is absorbed by the ball, the rise in its temperature is:
A work of 166.28 J is done to adiabatically compress one mole of a gas. If the increase in the temperature of the gas is \( 8^\circ C \), the gas is:
In a Carnot’s engine, as the gas absorbs heat energy from the source, then the temperature of the source:
A ball of mass 10 g is allowed to fall down from 10 m height. After collision with the ground, if 50\% of its energy is lost, then the height reached by the ball is:
A bomb at rest explodes into three pieces of equal masses. If two pieces move perpendicular to each other, each with a speed \( v \), then the speed of the third piece is:
The mechanical energy of a damped oscillator becomes half of its initial energy in 4 seconds. In another \( t \) seconds its mechanical energy becomes 12.5\% of its initial mechanical energy. Then \( t = \):
When an external force with angular frequency \( \omega_0 \) acts on a system of natural angular frequency \( \omega \), the system oscillates with angular frequency \( \omega_d \). The condition for the amplitude of oscillations to be maximum is:
Which one of the following is a homogeneous differential equation?
The number of significant figures in 4.870 m is:
The resultant of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is perpendicular to vector \( \mathbf{A} \), and the resultant magnitude is equal to half of the magnitude of \( \mathbf{B} \). The angle between \( \mathbf{A} \) and \( \mathbf{B} \) is:
A lorry is moving on a smooth circular path of radius 50 m with a velocity of 20 m/s. Then the banking angle of the road is:
Evaluate the following integral: \[ \int (x^3 + x^2 m + x^m) (2x^{2m} + 3x^m + 6x^m) \, dx \]
If \( a \in \mathbb{Z}^+ \), \([x]\) is the greatest integer not more than \( x \) and \[ \int_0^a \left\lfloor x \right\rfloor \, dx = 127, \text{ then } a = ? \]
Evaluate the integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin x \cdot \sin^2 x \cdot \cos x \, dx \]
The positive value of \( x \) satisfying the equation \[ \int_0^x (1 - t) \, dt = \frac{1}{2} \] is: