MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions

The displacements of two particles executing simple harmonic motion are represented as y₁ = 2 sin (10t + θ) and y₂ = 3 cos 10t. The phase difference between the velocities of these waves is ______.

A body perform linear simple harmonic motion of amplitude 'A'. At what displacement from the mean position, the potential energy of the body is one fourth of its total energy?

A wire of length 50 cm moves with a velocity of 300 m/min, perpendicular to a magnetic field. If the e.m.f. induced in the wire is 2 V, the magnitude of the field in tesla is ______.

A pure semiconductor has equal electron and hole concentration of 10¹⁶ m^-3. Doping by indium increases nh to 5 × 10²² m^-3. Then, the value of n_e in the doped semiconductor is ______.

A long straight wire in the horizontal plane carries a current of 75 A in north of south direction, magnitude and direction of field B at a point 3 m east of the wire is ______.

A transverse wave is represented by y = A sin (ωt - kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

If `vec"A"=3hat"i"-2hat"j"+hat"k",vec"B"=hat"i"-3hat"j"+5hat"k" and vec"C"=2hat"i"+hat"j"-4hat"k"` form a right angled triangle then out of the following which one is satisfied?

Magnetic susceptibility for a paramagnetic and diamagnetic materials is respectively ______.

A bomb at rest explodes into 3 parts of the same mass. The momentum of the two parts is `-3"P"hat"i"` and `2"P"hat"J"` respectively. The magnitude of the momentum of the third part is ______.

A particle is performing SHM starting extreme position, graphical representation shows that between displacement and acceleration there is a phase difference of ______.

A particle performs linear SHM at a particular instant, velocity of the particle is 'u' and acceleration is a while at another instant velocity is 'v' and acceleration is 'β (0 < α < β). The distance between the two position is ______.

An ammeter of resistance R gives a full-scale deflection when a current of 2 A passes through it. If it is measured with a maximum current of 10 A, the required shunt is ______.

A simple pendulum with a bob of mass m and conducting wire of length L swings under gravity through an angle θ. The component of the earth's magnetic field in the direction perpendicular to the swing is B. Maximum emf induced across the pendulum is ______.

(g = acceleration due to gravity)

The increase in internal energy of 1 kg of water at 100°c when it is converted into steam at the same temperature and at 1 atmospheric pressure will be ______.

(density of steam is 0.6 kg m^-3, latent heat of vaporisation of water = 2.25 × 10⁶ J kg^-1).

In figure, a particle is placed at the highest point A of a smooth sphere of radius r. It is given slight push and it leaves the sphere at B, at a depth h vertically below A, such that h is equal to ______.

A spring of force constant of 400 N/m is loaded with a mass of 0.25 kg. The amplitude of oscillations is 4 cm. When mass comes to the equilibrium position. Its velocity is ______.

A particle of mass 5 kg moves in a circle of radius 20 cm. Its linear speed at a time t is given by v = 4t, t is in the second and v is in ms^-1. Find the net force acting on the particle at t = 0.5 s.

The displacement of a particle of mass 3 g executing simple harmonic motion is given by Y = 3 sin (0.2 t) in SI units. The kinetic energy of the particle at a point which is at a distance equal to `1/3`​ of its amplitude from its mean position is ______.

A body of mass 0.5 kg travels in a straight line with velocity v = ax^3/2 where a = 5 m^–1/2s^–1. The change in kinetic energy during its displacement from x = 0 to x = 2 m is ______.

If a gas is compressed adiabatically: