MHT CET 2026 Physics Paper: 20 Apr, Shift 1

Which graph shows the correct variation of r.m.s. current '$i$' with frequency '$f$' of a.c. in case of series resonant circuit?

In a series LCR circuit, the voltage across R is $100$ V, $R = 1$ K $\Omega$ and $C = 2\ \mu$F. The angular frequency $\omega$ is $200$ rad s${}^{-1}$. At resonance, the voltage across '$L$' is

When an inductance '$L$' and resistor '$R$' are connected in series to $25$V, $50$ Hz supply, a current of $0.5$ A flows in the circuit. The current lags behind in phase from applied voltage by $\left(\frac{\pi}{3}\right)$ radian. The value of R is $\left(\cos 60^\circ = \frac{1}{2}\right)$

The angular momentum of an electron in Bohr's hydrogen atom having energy $(-0.544)$ eV is ($h$ = Planck's constant)

An electron in the hydrogen atom jumps from $n^{th}$ energy state to the ground state. The wavelength so emitted illuminates a photosensitive material having work function $2.65$ eV. If the maximum kinetic energy of the emitted photoelectrons is $10.1$ eV, then the value of '$n$' is

In a parallel plate air capacitor of plate separation '$d$', a dielectric slab of thickness '$t$' is introduced between the plates. The capacitance becomes one-third of the original value. The dielectric constant of the slab will be

A parallel plate air capacitor having area of each plate '$A$' and the distance between the plates '$d$' has uniform electric field E in the space between the plates. The energy stored in the capacitor is ($\epsilon_0$ = permittivity of free space.)

In the circuit shown charge q varies with time t as $q = t^{2} - 5$, where q is in coulomb and t is in second. At time $t = 3$ second, voltage $V_{AB}$ in volt will be

Two cells of e.m.f. $E_1$ and $E_2$ ($E_1 > E_2$) are connected as shown in figure.

When a potentiometer is connected between points A and B the balancing length of potentiometer wire is $412$ cm. When same potentiometer wire is connected between points A and C the balancing length is $103$ cm. The ratio $E_1 : E_2$ is

In meter bridge experiment, two resistances X and Y in the two gaps give a null point dividing the wire in the ratio $2:3$. When each resistance is increased by $30\ \Omega$, the null point divides the wire in the ratio $5:6$. The resistance X and Y are respectively

The proton and $\alpha$ - particle are accelerated through same potential difference. Then the ratio of the de-Broglie wavelength of proton and $\alpha$ - particle is (mass of $\alpha$-particle is $4$ times mass of proton, charge of $\alpha$-particle is $2$ times charge of proton)

Two identical photocathodes receive light of frequencies $n_1$ and $n_2$. If the velocities of the emitted photoelectrons of mass m are $V_1$ and $V_2$ respectively, then ($h$ = Planck's constant)

A coil of effective area $3$ m$^{2}$ is placed at right angles to a magnetic field of induction $0.05$ Wb/m$^{2}$. If the field is decreased to $20\%$ of its original value in $10$ second, the e.m.f. induced in the coil will be

The self inductance of an air-core inductor (solenoid) is $0.03$ mH. By introducing an iron core into inductor the self-inductance increases to $30$ mH. The relative permeability of the core used is

Two point charges $q_1$ and $q_2$ are '$l$' distance apart. If one of the charges is doubled and the distance between them is halved. The magnitude of the force becomes 'n' times, where 'n' is

Four electric charges $+q, +q, -q$, and $-q$ are placed in order at the corners of a square of side '$2r$'. The electric potential at a point midway between the two negative charges is

In case of liquid, if Reynold's number '$R_n$' is $1450$, then the flow of liquid will

The percentage decrease in the weight of a body when taken to a height of $48$ km above the surface of the earth is (Radius of the earth is $6400$ km)

Two rods of same length, radius and material transfer a given amount of heat in 't' second when they are joined as shown in fig (1). But when they are joined as shown in fig (2) then they will transfer same heat in same condition in time

A sphere is at temperature $600$ K. In an external environment of $200$ K, its cooling rate is R. When the temperature of the sphere falls to $400$ K then cooling rate R' will become

The weight of man in lift moving in upward direction with an acceleration 'a' is $660$ N. When the lift moves in the downward direction with the same acceleration, his weight is found to be $380$ N. The real weight of the man when the lift is at rest is

The periodic time of a magnet in vibration magnetometer is $T_0$. If a magnet is replaced by another magnet whose moment of inertia is three times and magnetic moment is one-third of the original magnet, then time period of new magnet will be

A long solenoid carrying a current produces a magnetic field '$B$' along its axis. If the current is tripled and the number of turns per cm is halved then new value of magnetic field will be

A square loop ABCD of side L carrying a current $I_1$ is placed at a distance $(L/3)$ from a conductor coplaner with a straight conductor XY carrying current $I_2$ as shown in figure. The net force on the loop will be ($\mu_0$ = magnetic permeability)

A simple pendulum of length $l_1$ has periodic time $2.4$ s. Another simple pendulum of length $l_2 < l_1$, has periodic time $1.8$ s. The periodic time of simple pendulum of length $(l_1 - l_2)$ is nearly

Two oscillating simple pendulums with time periods $T$ and $\frac{4T}{3}$ are in phase at a given time. They will be again in phase after an elapse of time

Two springs of force constants '$2k$' and '$k$' are connected to a mass '$m$' as shown. Mass is displaced slightly to one side and released. The frequency of oscillation of the two springs-mass system is

A boat crosses a river from one bank A to another bank B which is opposite. The distance between them is D. The speed of water is $V_W$ and that of boat relative to water is $V_B$. If $V_B = 2V_W$, the time taken by the boat to cross the river directly along AB is $\left(\sin 30^\circ = \frac{1}{2}\right) \cdot \left(\cos 30^\circ = \frac{\sqrt{3}}{2}\right)$

The prism has refracting angle A. The second refracting surface of the prism is silvered. Light ray falling on first refracting surface with angle of incidence $2A$, reaches the second surface and returns back through same path due to reflection at the silvered surface. The refractive index of the material of prism is

Two identical rings A and B of same mass and radius are revolving, ring A arounds its own diameter and ring B about tangential axis in its own plane. Both the rings A and B have same rotational kinetic energy. The ratio of the angular velocity of ring B to that of ring A is

A solid sphere rolls down from the top of an inclined plane. On reaching the bottom of the plane, its velocity is '$V_1$'. When the same sphere slides down from the top of the same plane of same height, its velocity on reaching the bottom is '$V_2$'. The ratio $V_1 : V_2$ is (neglect friction)

A body is rotating about its own axis. Its rotational kinetic energy is '$x$' and its angular momentum is '$y$'. Hence its moment of inertia about its own axis is

In the band structure of n-type semiconductor, the free electrons donated by impurity atoms occupy energy levels in

In a common emitter transistor amplifier, AC current gain is $65$, the load resistance is $5400\,\Omega$ and input resistance of the transistor is $450\,\Omega$. The voltage gain is

The output Y of the following digital logic circuit will be '1' (one) for the inputs

The excess pressure inside a soap bubble of radius $2.5$ cm is $48$ dyne/cm${}^{2}$. The surface tension of soap in dyne /cm is

If $450$ erg of work is done in blowing a soap bubble of radius '$r$', the additional work required to be done to blow it to a radius equal to $3r$ is

Gas at pressure P, temperature T, and volume V is filled in jar A. Another jar B is filled with gas having parameters $2P, \frac{V}{4}, 2T$. The ratio of number of molecules of jar B to those of jar A is

A rigid diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to volume $\left(\frac{V_i}{32}\right)$, where $V_i$ is the initial volume. The initial temperature of the gas is '$T_i$ ' K and the final temperature is '$xT_i$ ' K. The value of $x$ is

An ideal rigid diatomic gas $\left(\gamma = \frac{7}{5}\right)$ undergoes an adiabatic change. If the relation between temperature and volume is $TV^{x} =$ constant then the value of x is

The percentage error in the measurement of mass of a body and its speed are $0.73\%$ and $1.84\%$ respectively. The percentage error in the measurement of its momentum and kinetic energy are respectively

The area of parallelogram formed by vectors $\vec{P} = 2\hat{i} - \hat{j} + 5\hat{k}$ and $\vec{Q} = 3\hat{i} - 2\hat{j} + 4\hat{k}$ is

A train is moving towards a stationary observer with speed $34$ m/s. A train sounds a whistle of frequency $450$ Hz. If the speed of sound is $340$ m/s, the frequency heard by the observer in Hz is

A tuning fork of frequency '$n$' is held near the open end of a tube which is dipped in water and length of the tube is adjusted until resonance occurs. If the two shortest lengths that produce resonance are $l_1$ and $l_2$, the speed of sound in air is (neglect end correction)

The ratio of the speed of sound in helium gas to that in nitrogen gas at $295$ K is ( Ratio of specific heats $\gamma$ for helium is $\frac{5}{3}$ and that for nitrogen is $\frac{7}{5}$. Molecular weight for helium and nitrogen are $4$ and $28$ respectively.)

A wire of length '$L$', diameter '$d$', density of material '$\rho$' is under tension '$T$' has fundamental frequency of vibration '$n_A$'. Another wire of length '$2L$', diameter '$3d$', density of material '$2\rho$' is vibrated under tension '$2T$', the fundamental frequency of vibration becomes '$n_B$'. The ratio $n_B : n_A$ is

The 'Loudness' and 'Pitch' of sound respectively are the human perception to

In a biprism experiment, the distance between $4^{th}$ and $13^{th}$ bright band on the same side is '$y$' when light of wavelength $6000$ Å is used. For a light of wavelength '$\lambda$' the distance between $6^{th}$ and $16^{th}$ bright band on the same side is again '$y$'. The value of '$\lambda$' in Å units is

Light of wavelength $580$ nm is incident normally on a slit of width '$a$'. The distance between slit and screen is $2.5$ m and the distance of the second order maximum from the centre of the screen is $14.5$ mm in a diffraction pattern. The value of '$a$' is

In an interference experiment, the $m^{th}$ bright fringe for light of wavelength $\lambda_1$ coincides with the $n^{th}$ dark fringe for light of wavelength $\lambda_2$. The ratio $\frac{\lambda_2}{\lambda_1}$ is