MHT CET 2025 Physics Paper: 22 Apr, Shift 1

When alternating current is passed through $L - R$ series circuit, the power factor is $\frac{\sqrt{3}}{2}$ and $R = 50\ \Omega$, then the value of L is

$\left[\cos\frac{\pi}{6} = \frac{\sqrt{3}}{2}, \sin\frac{\pi}{6} = \frac{1}{2}, \tan\frac{\pi}{6} = \frac{1}{\sqrt{3}}\right]$

An a.c. e.m.f. of peak value 230 V and frequency 50 Hz is connected to a circuit with $R = 11.5\ \Omega,\ L = 2.5\text{ H}$ and a capacitor all in series. The value of capacitance is ' $C$ ' for the current in the circuit to be maximum. The value of ' $C$ ' and maximum current are respectively ( $\pi^2 = 10$)

Out of the following transitions in hydrogen atom, identify the transition which emits photons of highest frequency.

The graph shows the variation of voltage (v) across the plates of two parallel plate capacitos $A$ and $B$ versus increase of charge $Q$ stored in them. Then

Three capacitors each of capacitance ' C ' and breakdown voltage ' $V$ ' are connected in series. The capacitance and breakdown voltage of the series combination will be respectively

A series combination of 10 capacitors, each of value ' $C_1$ ' is charged by a source of potential difference ' 4 V '. When another parallel combination of 8 capacitors, each of value ' $C_2$ ' is charged by a source of potential difference ' V ', it has the same total energy stored in it as in the first combination. The value of ' $C_2$ ' is

A vehicle is moving with a constant speed of $10\text{ m/s}$ in a circular horizontal track of radius 20 m. A bob is suspended from the roof of a vehicle by a massless string. The angle made by the string with the vertical will be (acceleration due to gravity, $g = 10\text{ m/s}^2$)

A vehicle is moving with uniform speed along 3 different shaped roads as horizontal, concave and convex. The surface of road on which, the normal reaction on vehicle is maximum is

A body of mass 100 gram is tied to a spring of spring constant $8\text{ N/m}$, while the other end of a spring is fixed. If the body moves in a circular path on smooth horizontal surface with constant angular speed $8\text{ rad/s}$ then the ratio of extension in the spring to its natured length will be

The voltmeter has range 10 V and its internal resistance is $50\ \Omega$. To increase the range of voltmeter to 15 V, the resistance which is to be connected is

In the given electrical network, the value of resistance ' $R$ ' when the current in the galvanometer will be zero, is

When a photosensitive metal surface is illuminated with radiation of wavelength ' $\lambda_1$ ', the stopping potential is ' $V_1$ '. If the same surface is illuminated with radiation of wavelength ' $3\lambda_1$ ', the stopping potential is $\frac{V_1}{6}$. The threshold wavelength for the photosensitive metal surface is

From photoelectric effect experiment, select the correct statement.

A copper ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet while it is passing through the ring is

A coil of resistance $400\,\Omega$ is placed in a magnetic field. If the magnetic flux ' $\phi$ ' ( Wb) linked with the coil varies with time ' $t$ ' ( $\text{s}$) is $\phi = 50t^{2} + 4$, the current in the coil at $t = 2\text{ s}$ will be

The total charge induced in a conducting loop when it is moved in a uniform magnetic field depends on

Four charges $2\ \mu\text{C},\ -3\ \mu\text{C},\ 4\ \mu\text{C},\ -4\ \mu\text{C}$ and $-1\ \mu\text{C}$ are enclosed by the Gaussian surface of radius 2 m. Net outward flux through the Gaussian surface is (in $\mu\text{V-m}$) [ $\varepsilon_0 =$ permittivity of free space]

There are two identical small holes on the opposite side of a tank containing full of a liquid. The tank is open at the top. The difference in height between the two holes is ' $h$ '. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to

Time period of a simple pendulum on earth's surface is ' T '. It time period becomes ' xT ' when taken to a height ' $2R$ ' above earth's surface. The value of $x$ will be $(R =$ radius of earth)

Two satellites P and Q go round a planet in circular orbits having radii ' $3R$ ' and ' $R$ ' respectively. If the speed of satellite $P$ is ' $2V$ ', the speed of the satellite $Q$ will be

If 120 J of thermal energy is incident on area $3\text{ m}^{2}$, the amount of heat transmitted is 12 J, coefficient of absorption is 0.6, then the amount of heat reflected is

For a gas at a particular temperature on an average, the quantity which remains same for all molecules is

The mean kinetic energy of the molecules of an ideal gas at $399^\circ\text{C}$ is ' E '. The temperature at which the mean kinetic energy of its molecules will be ' $E/2$ ', is

Susceptibility of a paramagnetic substance is

A circular coil of wire consisting of ' $n$ ' tums each of radius 8 cm carries a current of 0.4 A. The magnitude of the magnetic field at the centre of coil is $3.14 \times 10^{-4}\text{ T}$. The value of ' $n$ ' is [Take $\mu_0 = 12.56 \times 10^{-7}$ SI unit]

The wire loop PQRSP formed by joining two semicircular wire of radii $R_1$ and $R_2$ carries a current $I$ as shown. The magnitude of the magnetic field at the centre ' O ' is

${}_{88}\text{Ra}^{226}$ is converted into ${}_{82}\text{Pb}^{206}$ by emission of alpha ( $\alpha$) and beta ( $\beta$) particles. The number of alpha and beta particles emitted are respectively

For a particle performing S.H.M.; the total energy is ' $n$ ' times the kinetic energy, when the displacement of a particle from mean position is $\frac{\sqrt{3}}{2}A$, where A is the amplitude of S.H.M. The value of ' $n$ ' is

Two thin lenses having $R_1, R_2$ as the radii of curved surfaces are kept coaxially together. Their power is proportional to

A solid sphere and thin walled hollow sphere have same mass and same material. Which of them have greater moment of inertia about their diameter?

[ $I_h =$ moment of inertia of hollow sphere about an axis coinciding with its diameter, $I_s =$ moment of inertia of solid sphere about an axis coinciding with its diameter]

A solid sphere of mass ' $m$ ' and radius ' $R$ ' is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with angular speed twice that of sphere. The ratio of kinetic energy of sphere to kinetic energy of cylinder will be

If force $\vec{F} = -3\hat{i}+\hat{j}+5\hat{k}$ acts along $\vec{r} = 7\hat{i}+3\hat{j}+\hat{k}$ then the torque acting at that point is

In a pure silicon crystal electron-hole concentration is $10^{16}$ per $\text{m}^{3}$ at 301 K. Now $10^{21}$ atoms of phosphorus are added per cubic metre. The new hole concentration in silicon is (in per $\text{m}^{3}$)

In a common emitter transistor amplifier, the output voltage and input voltage have a phase difference of

If an alternating voltage is applied across a p-n junction diode in series with a load then

If a centre tap transformer is used with two p-n junction diodes for full wave rectification then output voltage of rectifier with respect to each diode is (secondary voltage of transformer $= \text{V}_\text{s}$)

A capillary tube is taken from earth's surface to moon's surface. The rise of liquid column on the moon's surface is (acceleration due to gravity on the earth's surface is six times that of moon's surface)

A rectangular film of liquid is expanded from $(5\text{ cm} \times 4\text{ cm})$ to $(7\text{ cm} \times 8\text{ cm})$. If the work done is $3 \times 10^{-4}\text{ J}$, the surface tension of the liquid is (nearly)

When an ideal gas $\left(\gamma = \frac{5}{3}\right)$ is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work?

A gas undergoes a change in which its pressure ' P ' and volume ' V ' are related as $PV^{n} =$ constant, where n is a constant. If the specific heat of the gas in this change is zero, then the value of $n$ is ( $\gamma =$ adiabatic ratio)

The temperature of a body on Kelvin scale is ' $x$ ' $K$. When it is measured by a Fahrenheit thermometer, it is found to be ' x ' $^\circ\text{F}$. The value of ' $x$ ' is (nearly)

The period of oscillating simple pendulum is $T = 2\pi\sqrt{\frac{l}{g}}$ where length ' $l$ ' is 100 cm with error 1 mm. Period is 2 second. The time of 100 oscillations is measured by a stopwatch of least count 0.1s. The percentage error in gravitational acceleration ' g ' is

An organ pipe has fundamental frequency 80 Hz. If its one end is closed, the frequencies produced will be (in Hz) (Neglect end correction)

The equation of wave is $y = 60\sin(1200t - 6x)$, where ' $y$ ' is in micron, ' $t$ ' is in second and ' $x$ ' is in metre. The ratio of maximum particle velocity to the wave velocity of wave propagation is

A person standing between two parallel cliffs fires a gun and hears two echoes, first echo after 1 second and the second echo after 3 second. The distance between the two cliffs is (Velocity of sound $= 340\text{ m/s}$)

Two waves of same frequency ( n) are approaching each other with same velocity $12\text{ m/s}$ along the same linear path and interfere. The distance between two consecutive nodes is

In a single slit diffraction pattern, identify the incorrect statement from the following.

Assuming human pupil to have radius of 0.25 cm and comfortable viewing distance of 25 cm, the minimum separation between the two objects that human eye can resolve at 500 nm wavelength is nearly

In a Young's double slit experiment wavelength of light used is $6000\ \text{Å}$. The first order maxima and tenth order maxima fall at 14.50 mm and 16.75 mm from the particular reference point in the interference pattern respectively. If the wavelength is changed to $5500\ \text{\AA}$ then the position of zero order and tenth order maxima are respectively

[The other arrangements remaining same]

A body of mass 1 kg begins to move under the action of a time dependent force $\vec{F} = \left(t\hat{i} + 2t^2\hat{j}\right)\text{ N}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ and $y$ axis. The power developed by above force at time $t = 3$ second will be