List of practice Questions

If the angle of minimum deviation produced by an equilateral prism is equal to the angle of the prism, then the refractive index of the material of the prism is nearly
When two light waves of equal intensity superimpose, the maximum intensity obtained is I. If the intensity of one of the waves is quadrupled, then the maximum intensity obtained is
The electric field due to an infinitely long thin straight wire with uniform linear charge density of \(2.5 \times 10^{-7}\) Cm\(^{-1}\) at a radial distance of x from the wire is \(7.5 \times 10^4\) NC\(^{-1}\). Then x =
A parallel plate capacitor of capacitance 10 \(\mu\)F is charged by a 220 V supply. The capacitor is then disconnected from the supply and is connected to another uncharged parallel plate capacitor of capacitance 12 \(\mu\)F. The loss of electrostatic energy in this process is
The temperature of a body shown by a faulty Celsius thermometer is 49 °C and by a correct Fahrenheit thermometer is 122 °F. The correction to be applied to the faulty thermometer is
If the radiation emitted by a perfect radiator has maximum intensity at a wavelength of 2900 Å, the intensity of radiation emitted by it is (Stefan-Boltzmann's constant = \(5.67 \times 10^{-8}\) Wm\(^{-2}\)K\(^{-4}\) and Wein's constant = \(2.9 \times 10^{-3}\) mK)
The ratio of the work done, change in internal energy and heat absorbed when a diatomic gas expands at constant pressure is
If the temperature of a gas is increased from 127 °C to 527 °C, then the rms speed of the gas molecules
An air column in a tube of length 50 cm, closed at one end is vibrating in its fifth harmonic. The phase difference between a particle at the open end and a particle at 42 cm from the open end is
A solid sphere and a thin uniform circular disc of same radius are rolling down an inclined plane without slipping. If the acceleration of the sphere is 3 ms\(^{-2}\), then the acceleration of the disc is
If the amplitudes of a damped harmonic oscillator at times t=0, \(t_1\) and \(t_2\) are \(A_0\), \(A_1\) and \(A_2\) respectively, then the amplitude of the oscillator at a time of \((t_1+t_2)\) is
A meteor of mass 'm' having a speed 'v' at infinity reaches the surface of the earth with a speed of (\(v_e\) is escape speed from the earth's surface)
The work to be done to produce a strain of \(10^{-3}\) in a steel wire of mass 2.96 kg and density 7.4 gcm\(^{-3}\) is (Young's modulus of steel = \(2 \times 10^{11}\) Nm\(^{-2}\))
A wooden block of outer volume 1 litre and specific gravity \(\frac{3}{4}\) having a cavity floats with half of its volume immersed in water. Then the volume of the cavity is
When 'n' identical mercury drops combine to form a single big drop
The relation between the displacement 'x' (in metre) and the time 't' (in second) of a particle is \( t = 2x^2+3x \). If the displacement of the particle is 25 cm from the origin (x=0), then the acceleration of the particle is
A body projected at certain angle (\(\neq 90^\circ\)) from the ground crosses a point in its path at a time of 2.3 s and from there it reaches the ground after a time of 5.7 s. The maximum height reached by the body is (Acceleration due to gravity = 10 ms\(^{-2}\))
A circular path of radius 75 m is banked at an angle of \(\tan^{-1}(0.2)\). If the coefficient of static friction between the tyres of the car and the circular path is 0.1, then the maximum permissible speed of the car to avoid slipping is
A horizontal force of 10 N is applied on a block of mass 1.5 kg which is initially at rest on a rough horizontal surface. The work done by the applied force in a time of 6 s from the beginning of the motion is (Acceleration due to gravity = 10 ms\(^{-2}\); the coefficient of kinetic friction between the block and the surface is 0.2)
A ball is allowed to fall freely from a height of 42 m from the ground. If the coefficient of restitution between the ball and the ground is 0.4, then the total distance travelled by the ball before it comes to rest is
A thin uniform wire of mass 'm' and linear density '\(\rho\)' is bent in the form of a circular ring. The moment of inertia of the ring about a tangent parallel to its diameter is
\( \int_{0}^{\pi/2} \frac{dx}{\cos x - \sqrt{3}\sin x} = \)
\( \int_0^{\pi/2} \sqrt{\tan x} \, dx = \)
If y=f(x) is the solution of the differential equation \( (1+\cos^2 x)f'(x) - 4\sin(2x) - f(x)\sin(2x) = 0 \) when f(0)=0, then \( f(\pi/3) = \)
The differential equation corresponding to the family of ellipses \( \frac{x^2}{a^2} + \frac{y^2}{4} = 1 \), where 'a' is an arbitrary constant is