MHT CET 2021 Physics Paper: 20 Sep, Shift 1

An inductor coil wound uniformly has self inductance 'L' and resistance 'R'. The coil is broken into two identical parts. The two parts are then connected in parallel across a battery of 'E' volt of negligible internal resistance. The current through battery at steady state is

When a d.c. voltage of $200\text{ V}$ is applied to a coil of self-inductance $\left(\frac{2\sqrt{3}}{\pi}\right)\text{ H}$, a current of $1\text{ A}$ flows through it. But by replacing d.c. source with a.c. source of $200\text{ V}$, the current in the coil is reduced to $0.5\text{ A}$. Then the frequency of a.c. supply is

An inductor coil takes current 8A when connected to an 100 V and 50 Hz a.c. source. A pure resistor under the same condition takes current of 10A. If inductor coil and resistor are connected in series to an 100V and 40 Hz a.c. supply, then the current in the series combination of above resistor and inductor is

If the electron in a hydrogen atom moves from ground state orbit to 5th orbit, then the potential energy of the electron

The electron in hydrogen atom is initially in the third excited state. When it finally moves to ground state, the maximum number of spectral lines emitted are

A parallel plate capacitor filled with oil of a dielectric constant 3 between the plates has capacitance 'C'. If the oil is removed, then the capacitance of the capacitor will be

A galvanometer of resistance $50\ \Omega$ is converted to an ammeter. After shunting, the effective resistance of ammeter is $2.5\ \Omega$. The value of shunt is

Consider the circuit shown in the figure. The value of current 'I' is

When a photosensitive surface is irradiated by light of wavelengths '$\lambda_1$' and '$\lambda_2$', kinetic energies of emitted photoelectrons are 'E$_1$ ' and 'E$_2$ ' respectively. The work function of photosensitive surface is

When light of wavelength '$\lambda$' is incident on a photosensitive surface, photons of power 'P' are emitted. The number of photon 'n' emitted in time 't' is [h = Planck's constant, c = velocity of light in vacuum]

Two conducting wire loops are concentric and lie in the same plane. The current in the outer loop is clockwise and increasing with time. The induced current in the inner loop is

A straight conductor of length 0.6 M is moved with a speed of 10 ms$^{-1}$ perpendicular to magnetic field of induction 1.2 weber m $^{-2}$. The induced e.m.f. across the conductor is

An electric dipole having dipole moment $\mathrm{P} = \mathrm{q} \times 2\ell$ is placed in a uniform electric field '$\mathrm{E}$'. The dipole moment is along the direction of the field. The force acting on it and its potential energy are respectively

A spherical conducting shell of inner radius 'r ${}_{1}$' and outer radius 'r${}_{2}$ ' has a charge 'Q'. A charge $-$q is placed at the centre of the shell. The surface charge density on the inner and outer surface of the shell will be

A uniformly charged half ring of a radius ' $R$ ' has linear charge density '$\sigma$'. The electric potential at the centre of the half ring is ( $\epsilon_0 =$ permittivity of free space)

A charge of magnitude '2e' and mass '4m' is moving in an electric field $\vec{E}$. The acceleration imparted to the above charge is

The depth 'd' below the surface of the earth where the value of acceleration due to gravity becomes $\left(\frac{1}{n}\right)$ times the value at the surface of the earth is $(R =$ radius of the earth)

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is 'V'. For the satellite orbiting at an altitude of half the earth's radius, the orbital velocity is

A perfectly black body emits a radiation at temperature 'T $_{1}$' K. If it is to radiate at 16 times this power, its temperature 'T$_{2}$' K should be

The weight of a man in a lift moving upwards with an acceleration 'a' is 620 N. When the lift moves downwards with the same acceleration, his weight is found to be 340 N. The real weight of the man is

Two bodies '$A$' and '$B$' start from the same point at the same instant and move along a straight line. 'A' moves with uniform acceleration (a) and 'B' moves with uniform velocity (V). They meet after time 't'. The value of 't' is

The magnetic field intensity 'H' at the centre of a long solenoid having 'n' turns per unit length and carrying a current 'I', when no material is kept in it, is

An electron (e) moves in circular orbit of radius 'r' with uniform speed 'V'. It produces magnetic field 'B' at the centre of circle. The magnetic field B is $(\mu_0 =$ permeability of free space)

If the charge to mass ratio of an electron is 'A' C/kg, then the gyromagnetic ratio of an orbital electron in C/kg is

Two particles $P$ and $Q$ performs S.H.M. of same amplitude and frequency along the same straight line. At a particular instant, maximum distance between two particles is $\sqrt{2}$ a. The initial phase difference between them is

$\left[\sin^{-1}\left(\frac{1}{\sqrt{2}}\right) = \cos^{-1}\left(\frac{1}{\sqrt{2}}\right) = \frac{\pi}{4}\right]$

A mass '$m_1$ ' is suspended from a spring of negligible mass. A spring is pulled slightly in downward direction and released, mass performs S.H.M. of period '$T_1$ '. If the mass is increased by '$m_2$', the time period becomes '$T_2$'. The ratio $\frac{m_2}{m_1}$ is

A particle of mass 5 g is executing S.H.M. with an amplitude 0.3 m and time period $\frac{\pi}{5}$ s. The maximum value of the force acting on the particle is

A ray of light travels from a denser medium to a rarer medium. The reflected and the refracted rays are perpendicular to each other. If '$r$' and '$r_1$ ' are the angle of reflection and refraction respectively and '$C$' is the critical angle, then the angle of incidence is

A convex lens of focal length 'F' produces a real image 'n' times the size of the object. The image distance is

A solid sphere of mass $M$, radius $R$ has moment of inertia '$I$' about its diameter. It is recast into a disc of thickness 't' whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains 'I'. Radius of the disc will be

A disc of radius 0.4 m and mass one kg rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration of the disc is 10 rad/s$2$. The tangential force applied to the rim of the disc is

Two bodies rotate with kinetic energies 'E$1$' and 'E$2$'. Moments of inertia about their axis of rotation are 'I $1$' and 'I$2$'. If $I_1 = \frac{I_2}{3}$ and E $1$ = 27 E$2$, then the ratio of angular momenta 'L $1$' to 'L$2$' is

Silicon and copper are cooled from 300 K to 100 K, the specific resistance (resistivity)

Two different logic gates moving output '0' for the inputs (0, 1) and then for (1, 0) are

The frequency of a given a.c. signal is 'N' Hz. When it is connected to a half wave rectifier, the number of output pulses given by the rectifier in 1 second is

Air is pushed in a soap bubble to increase its radius from 'R' to '2R'. In this case, the pressure inside the bubble

Let '$R_1$' and '$R_2$' are radii of two mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is

The force required to take away a flat circular plate of radius $2\text{ cm}$ from the surface of water is $[$Surface tension of water $= 70 \times 10^{-3}\text{ N m}^{-1}, \pi = \frac{22}{7}]$

Specific heats of an ideal gas at constant pressure and volume are denoted by $C_p$ and $C_v$ respectively. If $\gamma = \frac{C_p}{C_v}$ and $R$ it's the universal gas constant then $C_v$ is equal to

For a monoatomic gas, work done at constant pressure is W. The heat supplied at constant volume for the same rise in temperature of the gas is

One mole of an ideal gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{\sqrt{V}}$. The value of $\gamma$ for the gas is ($\gamma = \frac{C_p}{C_v}\ , V =$ Volume of the gas)

On an imaginary linear scale of temperature (called 'W' scale) the freezing and boiling points of water are 39$^\circ$ W and 239$^\circ$ W respectively. The temperature on the new scale corresponding to 39 $^\circ$C temperature on Celsius scale will be

The frequencies of three tuning forks $A, B$ and $C$ are related as $n_A > n_B > n_C$. When the forks $A$ and $B$ are sounded together, the number of beats produced per second is '$n_1$'. When forks $A$ and $C$ are sounded together the number of beats produced per second is '$n_2$'. How may beats are produced per second when forks $B$ and $C$ are sounded together?

The equation of wave is given by $y = 10\sin\left(\frac{2\pi t}{30} + \alpha\right)$. If the displacement is $5\text{ cm}$ at $t = 0$, then the total phase at $t = 7.5\text{ s}$ will be

$\left[\sin 30^\circ = \cos 60^\circ = \frac{1}{2}, \cos 30^\circ = \sin 60^\circ = \frac{\sqrt{3}}{2}\right]$

A sonometer wire resonates with 4 antinodes between two bridges for a given tuning fork, when 1 kg mass is suspended from the wire. Using same fork, when mass M is suspended, the wire resonates producing 2 antinodes between the two bridges (distance between two bridges is as before). The value of M is

Two wires of same material of radius 'r' and '2r' respectively are welded together end to end. The combination is then used as a sonometer wire under tension 'T'. The joint is kept midway between the two bridges. The ratio of the number of loops formed in the wires such that the joint is a node is

The frequency of a tuning fork is 'n' Hz and velocity of sound in air is 'V' m/s. When the tuning fork completes 'x' vibrations, the distance travelled by the wave is

In Fraunhofer diffraction pattern, slit width is 0.2 mm and screen is at 2m away from the lens. If wavelength of light used is 5000$\text{\AA}$ then the distance between the first minimum on either side of the central maximum is ($\theta$ is small and measured in radian)

Light of wavelength '$\lambda$' is incident on a single slit of width 'a' and the distance between slit and screen is 'D'. In diffraction pattern, if slit width is equal to the width of the central maximum then $D =$

In Young's double slit experiment, the '$n^{\text{th}}$' maximum of wavelength '$\lambda_1$ ' is at a distance '$y_1$' from the central maximum. When the wavelength of the source is changed to '$\lambda_2$', $\left(\frac{n}{2}\right)$th maximum is at a distance of '$y_2$' from its central maximum. The ratio $\frac{y_1}{y_2}$ is