MHT CET 2025 Physics Paper: 21 Apr, Shift 2

An ideal inductor of $\left(\frac{1}{\pi}\right)\text{H}$ is connected in series with a $300\ \Omega$ resistor. If a $20\text{ V},\ 200\text{ Hz}$ alternating source is connected across the combination, the phase difference between the voltage and current is

An alternating e.m.f. having voltage $V = V_0 \sin\omega t$ is applied to a series L-C-R circuit. Given: $|X_L - X_C| = R$. The r.m.s. value of potential difference across capacitor will be

In an electrical circuit ' $R$ ', ' $L$ ', ' $C$ ' and an a.c. voltage source are all connected in series. When ' L ' is removed from the circuit, the phase difference between the voltage and the current in the circuit is $\frac{\pi}{3}$. If instead ' $C$ ' is removed from the circuit, the phase difference is again $\frac{\pi}{3}$. The power factor of the circuit is $\left(\tan\frac{\pi}{3} = \sqrt{3}\right)$

Using Bohr's quantization condition, the rotational kinetic energy in the third orbit for a diatomic molecule is ( $h =$ Planck's constant, $I =$ moment of inertia of diatomic molecule)

A parallel plate capacitor has plate area $50\text{ cm}^2$ and plate separation 3 mm. The space between the plates is filled with a dielectric medium of thickness 1 mm and dielectric constant 4. The capacitance becomes ( $\varepsilon_0 =$ permittivity of free space)

If the charge on the capacitor is increased by 3C, the energy stored in it increases by $21\%$. The original charge on the capacitor is

A parallel plate capacitor having plate area ' $A$ ' and separation ' $d$ ' is charged to a potential difference ' $V$ '. The charging battery is disconnected and the plates are pulled apart to four times the initial separation. The work required to increase the distance between the plates is ( $\varepsilon_0 =$ permittivity of free space)

A pendulum bob has a speed $4\text{ m/s}$ at its lowest position. The pendulum is 1 m long. When the length of the string makes an angle of $60^\circ$ with the vertical, the speed of the bob at that position is (acceleration due to gravity, $g = 10\text{ m/s}^2, \cos 60^\circ = 0.5$)

A simple pendulum oscillates with an angular amplitude $\theta$. If the maximum tension in the string is 4 times the minimum tension then the value of $\theta$ is

If an ammeter is to be used in place of a galvanometer then we must connect

In the circuit shown in the figure, $P \neq R$. The reading of the galvanometer remains the same with switch ' $S$ ' open or closed. Then

When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other, the maximum velocities of the photoelectrons emitted in the two cases are $V_1$ and $V_2$ respectively. The ratio $V_1 : V_2$ is

When a light of wavelength $\lambda$ falls on the emitter of a photocell, maximum speed of emitted photoelectrons is V. If the incident wavelength is changed to $\frac{2\lambda}{3}$, maximum speed of emitted photoelectrons will be:

A conducting ring of certain resistance is falling towards a current carrying straight long conductor. The ring and conductor are in the same plane. Then

What is the phase difference between the flux linked with a coil rotating in a uniform magnetic field and the induced e.m.f. produced in it?

A coil is wound on a core of rectangular cross-section. If all the linear dimensions of core are increased by a factor 3 and number of turns per unit length of coil remains same, the self- inductance increases by a factor

The electric field intensity on the surface of a solid charged sphere of radius $\mathbf{r}$ and volume charge density $\sigma$ is ( $\varepsilon_0 =$ permittivity of free space)

Water flows through a horizontal pipe of varying cross-section at the rate of $\pi \times 10^{-1}\text{ m}^3/\text{s}$. The velocity of water at a point where the radius of the pipe is 10 cm is $(\pi = 3.14)$

The radii of circular orbits of two satellites $A$ and $B$ of the earth are ' $4R$ ' and ' $R$ ' respectively, where $R$ is the radius of earth. If the speed of satellite $B$ is 6 V, then the speed of satellite $A$ will be

Hot water cools from $80^\circ\text{C}$ to $60^\circ\text{C}$ in 1 minutes. In cooling from $60^\circ\text{C}$ to $50^\circ\text{C}$ it will take (room temperature $= 30^\circ\text{C}$)

If a black body at 400 K surrounded by atmosphere at 300 K has rate of cooling ' $R_0$ ', the same body at 900 K, surrounded by same atmosphere, will have rate of cooling nearly

The r.m.s. speed of gas molecules at 800 K will be

The temperature of an ideal gas is increased from 100 K to 400 K. If ' $x$ ' is the R.M.S. velocity of its molecules at 100 K, it becomes

A conveyor belt is moving with constant velocity (V). Sand is being dropped on the belt at the rate of $M\text{ kg/s}$. The force necessary to keep the belt moving with a constant velocity $V\text{ m/s}$ will be

The space within the current carrying toroid is filled with aluminium of susceptibility ' $\chi$ '. The percentage increase in the magnetic field ' $B$ ' will be

A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered by the body in the $n$th second of its motion to the total distance travelled in n second is

A coil having 9 turns carrying current produces magnetic field $B_1$ at the centre. Now that coil is rewounded into 3 turns carrying same current. Then magnetic field at the centre $B_2$ is

An electron moves in Bohr orbit. The magnetic field at the centre is proportional to

Two long parallel wires carry currents $I_1$ and $I_2\ (I_1 > I_2)$. When currents are flowing in the same direction, the magnetic field at a point midway between the wires is $6 \times 10^{-6}\text{ T}$. If the direction of $I_2$ is reversed the field at midpoint becomes $3 \times 10^{-5}\text{ T}$. The ratio $I_1 : I_2$ is

The length of the simple pendulum is made 3 times the original length. If ' T ' is its original time period, then the new time period will be

A plano convex lens fits exactly in to a plano concave lens. Their plane surfaces are parallel to each other. Lenses are made up of different materials of refractive indices ' $n_1$ ' ' $n_2$ ' and ' R ' is the radius of curvature of the curved surface of lenses. Focal length of the combination is

A ray of light travelling through rarer medium is incident at a very small angle ' $i$ ' on a glass slab and after refraction its velocity is reduced by $20\%$. The angle of deviation is

The moment of inertia of a ring about an axis passing through its centre and perpendicular to its plane is I. It is rotating with angular velocity $\omega$. Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis then loss in kinetic energy is

Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is ' $I$ '. If the same rod is bent in the form of ring, its moment of inertia about the diameter is ' $I_1$ '. If $I_1 = xI$, then the value of ' x ' is

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 common emitter mode of a transistor, the current gain is 8. The input impedance is $25\text{ k}\Omega$ and load resistance is $75\text{ k}\Omega$. The power gain is

In the following combination of logic gates, the output $Y$ can be written in the terms of inputs $A$ and B as

If the internal resistance of cell is negligible then current flowing through the circuit is

Two capillary tubes of same diameter are kept vertically in two liquids whose densities are in the ratio $4 : 3$. If their surface tensions are in the ratio $6 : 5$, the ratio of heights $\left(\frac{h_1}{h_2}\right)$ of liquids in the two capillary tubes is (Their angle of contacts are same)

In air, a charged soap bubble of radius R breaks into 64 small soap bubbles of equal radius $r$. The ratio of mechanical force per unit area of big soap bubble to that of a small bubble is

A Carnot engine has efficiency $\frac{1}{6}$. It becomes $\frac{1}{3}$, when the temperature of $\text{sink}$ is lowered by 57 K. The temperature of the source is

Heat is given to an ideal gas in an isothermal process. Then

A. internal energy of the gas will decrease.

B. internal energy of the gas will increase.

C. internal energy of the gas will not change.

D. the gas will do negative work.

Error in the measurement of radius of the sphere is $2\%$. The error in the calculated value of its volume is

A unit vector in the direction of resultant vector of $\vec{A} = -2\hat{i} + 3\hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + 2\hat{j} - 4\hat{k}$ is

Two strings ' X ' and ' Y ' of a guitar produces a beat frequency of 6 Hz. When the tension of the string ' Y ' is increased, the beat frequency is found to be 4 Hz. If the frequency of string ' X ' is 300 Hz, then the original frequency of string ' Y ' is

A vehicle starts from rest and accelerates along straight path at $2\text{ m/s}^2$. At the starting point of the vehicle, there is a stationary electric siren. How far has the vehicle nearly gone when the driver hears the siren at $94\%$ of its value when the vehicle was at rest?

(speed of sound $= 330\text{ m/s}$)

The equation of a progressive wave is $Y = 3\sin\left[\pi\left(\frac{t}{3} - \frac{x}{5}\right) + \frac{\pi}{4}\right]$ where x and y are in meter and time in second. Which of the following is correct?

A transverse displacement of vibrating string is $y = 0.06\sin\left(\frac{2\pi}{3}x\right)\cos(120\pi t)$.

If the mass per unit length of a string is $4 \times 10^{-2}\text{ kg/m}$, then the tension in the string will be

The two coherent sources produce interference with intensity ratio ' $b$ '. In the interference pattern, the ratio $\frac{I_{max} + I_{min}}{I_{max} - I_{min}}$maxmaxminmin will be

According to Huygen's wave theory of light, which one of the following statements is not correct?