MHT CET 2025 Physics Paper: 25 Apr, Shift 1

The power factor of a CR circuit is $\frac{1}{\sqrt{2}}$, If the frequency of a.c. signal is halved, then the power factor of the circuit will become

An a. c. voltage is applied to pure inductor. The current in the inductor

The reactance of a capacitor is $X_C$. If the frequency and the capacitance are doubled, then the new reactance will be

In LCR series circuit, when ' $L$ ' is removed from the circuit, the phase difference between voltage and current in the circuit is $\frac{\pi}{3}$. If ' $C$ ' is removed from the circuit instead of $L$ then phase difference is again $\frac{\pi}{3}$. The power factor of the circuit is $\left(\tan 60^\circ = \sqrt{3}\right)$

Five capacitors, each of capacity ' $C$ ' are connected as shown in the figure. The resultant capacity between A and B is $14\ \mu\text{F}$. The capacity of each capacitor is

A point mass ' $m$ ' attached at one end of a massless, inextensible string of length ' $l$ ' performs a vertical circular motion and the string rotates in vertical plane, as shown in the diagram. The increase in the centripetal acceleration of the point mass when it moves from point A to point C is [ $g =$ acceleration due to gravity.]

The current (I) drawn from the battery in the given circuit is

The value of the shunt resistance that allows $10\%$ of the main current through the galvanometer of $99\ \Omega$ is

Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. The ratio of threshold wavelength of sodium to that of copper is nearest to

When a metal surface is illuminated by light of wavelength $\lambda_1$ and $\lambda_2$, the maximum velocities of photoelectrons ejected are V and 2 V respectively. The work function of the metal is ( $h =$ Planck's constant, $c =$ velocity of light, $\lambda_1 > \lambda_2$)

If the electron in hydrogen atom jumps from third Bohr orbit to ground state directly and the difference between energies of the two states is radiated in the form of photons. If the work function of the material is 4.1 eV, then stopping potential is nearly

[Energy of electron in $n$th orbit $= \frac{-13.6}{n^2}\text{ eV}$ ]

The equivalent inductance between A and B is equal to

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

' $n$ ' identical small spherical drops of water, each of radius ' $r$ ' and charged to the same potential ' v ' are combined to form a big drop. The potential of a big drop is

Three charges $Q, (-2q)$ and $(-2q)$ are placed at the vertices of an isosceles right angled triangle as shown in figure. The net electrostatic potential energy is zero if $Q$ is equal to

Two planets A and B have densities ' $\rho_1$ ', ' $\rho_2$ ' and have radii ' $r_1$ ', ' $r_2$ ', respectively. The ratio of acceleration due to gravity on $A$ to that of $B$ is

A body cools from $80^\circ\text{C}$ to $50^\circ\text{C}$ in 5 min. In the next time of ' t ' in, the body continues to cool from $50^\circ\text{C}$ to $30^\circ\text{C}$. The total time taken by the body to cool from $80^\circ\text{C}$ to $30^\circ\text{C}$ is [The temperature of the surroundings is $20^\circ\text{C}$.]

A rectangular black body of temperature $127^\circ\text{C}$ has surface area $4\text{ cm} \times 2\text{ cm}$ and rate of radiation is E. If its temperature is increased by $400^\circ\text{C}$ and surface area is reduced to half of the initial value then the rate of radiation is

The temperature of an ideal gas is increased from 100 K to 400 K. If ' $x$ ' is the root mean square velocity of its molecules at 100 K, r.m.s. velocity becomes

According to the kinetic theory of gases, when two molecules of a gas collide with each other then

A machine gun fires a bullet of mass 35 gram with a speed of $600\text{ m/s}$. The person holding the gun can extract a maximum force of 147 N on it. The number of bullets that can be fired from the gun per second 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 ( $\mu_0 =$ permeability of free space)

A long straight wire of radius ' $r$ ' carries a steady current ' $I$ '. The current is uniformly distributed over its cross-section. The ratio $\left(\frac{B}{B_1}\right)$ of the magnetic field ' B ' and ' $\mathrm{B}_1$ ' at radial distances ' $\frac{r}{2}$ ' and ' $3r$ ' respectively, from the axis of the wire is

Current $I$ is carried in a wire of length ' $L$ '. If wire is bent into a circular coil of single turn, the maximum torque in a given magnetic field $B$ is

A square of side ' $L$ ' metre lies in $x-y$ plane in a region where the magnetic field is$\vec{B}$and $\vec{B} = B_0(2\hat{i} + 3\hat{j} + 4\hat{k})$, where $B_0$ is constant. The magnitude of flux passing through the square (in weber) is

A radioactive element has rate of disintegration 9000 disintegration per minute at a particular instant. After two minutes it becomes 3000 disintegration per minute. The decay constant per minute is

A small sphere oscillates simple harmonically in a watch glass whose radius of curvature is 1.6 m. The period of oscillation of the sphere is (acceleration due to gravity $g = 10\text{ m/s}^2$)

The displacement of particle in S.H.M. is $x = A\cos(\omega t + \pi/6)$. Its speed will be maximum at time $(\sin 90^\circ = 1)$

Two particles ' $A$ ' and ' $B$ ' execute SHMs of periods ' $T$ ' and $\frac{3T}{2}$. If they start from the mean position then the phase difference between them, when the particle ' $A$ ' completes two oscillations will be

Two boys are standing at points A and B on ground, where distance $AB = x$. The boy at B stars running perpendicular to $AB$ with velocity $v_1$. The boy at A starts running simultaneously with velocity v and meets the other boy in time $t$. The value of $t$ is

The image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $\frac{25}{3}\text{ m}$ to $\frac{50}{7}\text{ m}$ in 30 second. The speed of the object in $\text{km/hr}$ is

Two discs of moment of inertia ' $I_1$ ' and ' $I_2$ ' and angular speeds ' $\omega_1$ ' and ' $\omega_2$ ' are rotating along the collinear axes passing through their centre of mass and perpendicular to their plane. If the two discs are made to rotate together along the same axis. The rotational kinetic energy of the system will be

Four particles each of mass M are placed at the corners of a square of side L. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

The logic gate for which the output goes 'HIGH' or ' 1 ' only when an odd number of 'HIGH' or ' 1 ' are at its input, is

To get output of the following logic circuit as ' 0 ' (zero), the inputs $A, B, C$ should NOT be, respectively,

In which of the following figures, the p.n. junction diode is reverse biased?

In a capillary tube of area of cross-section 'a' water rises to height ' $h$ '. To what height will water rise in a capillary tube of area of cross-section $4a$?

The volume of given mass of a gas is decreased by $7\%$ at constant temperature. The pressure should be increased by

During the isothermal expansion, a confined ideal gas does $(-150)\text{ J}$ of work against its surroundings. This means that

A monoatomic ideal gas is compressed adiabatically to $\left(\frac{1}{27}\right)$ of its initial volume. If initial temperature of the gas is ' T ' K and final temperature is ' xT ' K, the value of ' x ' is

A wire has a mass $0.3 \pm 0.003$ gram, radius $0.5 \pm 0.005\text{ mm}$ and length $6 \pm 0.06\text{ cm}$. The maximum percentage error in the measurement of its density is

Vector $\vec{A}$ of magnitude $5\sqrt{3}$ units, another vector $\vec{B}$ of magnitude of 10 units are inclined to each other at an angle of $30^\circ$. The magnitude of vector product of the two vectors is $\left[\sin 30^\circ = \frac{1}{2}\right]$

The velocity of small spherical ball of mass ' $m$ ' and density ' $\mathrm{d}_1$ ', when dropped in a container filled with glycerine becomes constant after some time. The viscous force acting on the ball if density of glycerine is ' $\mathrm{d}_2$ ' is

Two tuning forks of frequencies 256 Hz and 258 Hz are sounded together. The time interval between two consecutive maxima is

A sound source is moving towards a stationary observer with $\left(\frac{1}{10}\right)$th the speed of sound, The ratio of apparent to real frequency is

The fundamental frequency of a closed pipe is 400 Hz. If $\left(\frac{1}{3}\right)$rd length of the pipe is filled with water, the frequency of the $2$nd harmonic of the pipe will be (Neglect end correction)

At poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting, to produce resonance with same fork, the vibrating length of wire

In Fraunhofer diffraction pattern, slit width is 0.3 mm and screen is at 1.5 m away from the lens. If wavelength of light used is $4500\text{ \AA}$, then the distance between the first minimum on either side of the central maximum is [ $\theta$ is small and measured in radian.]

A single slit diffraction pattern is formed with light of wavelength $6384\text{ Å}$. The second secondary maximum for this wavelength coincides with the third secondary maximum in the pattern for light of wavelength ' $\lambda_0$ '. The value of ' $\lambda_0$ ' is

If the two sources of light emit waves of different amplitudes and interfere then