MHT CET 2025 Physics Paper: 20 Apr, Shift 1

A $20\ \Omega$ resistance, 10 mH inductance coil and $15\ \mu\text{F}$ capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance is made $\frac{1}{3}\text{rd}$, the resonant frequency

A resistance of $200\ \Omega$ and an inductor of $\frac{1}{2\pi}\text{ H}$ are connected in series to a.c. voltage of 40 V and 100 Hz frequency. The phase angle between the voltage and current is

A coil of self-inductance $L$ is connected in series with a bulb and an a. c. source. Brightness of the bulb decreases when

In hydrogen spectrum, the ratio of wavelengths of the last line of Lyman series and that of the last line of Balmer series is

For a particle moving in a circle with constant angular speed, which of the following statements is 'false'?

The potential difference $(V_A - V_B)$ between the points A and B in the given figure is

A null point is obtained at 200 cm on potentiometer wire when cell in secondary circuit is shunted by $5\ \Omega$. When a resistance of $15\ \Omega$ is used for shunting, null point moves to 300 cm. The internal resistance of the cell is

Light of wavelength ' $\lambda$ ' falls on a metal having work function $\frac{hc}{\lambda_0}$. Photoelectric effect will take place only if ( $\lambda_0$ is the threshold wavelength)

A parallel beam of light is incident normally on a plane surface absorbing $50\%$ of the light and reflecting the rest. If the incident beam carries 90 W of power, the force exerted by it on the surface is ( $C =$ velocity of light in air $= 3 \times 10^{8}\text{ m/s}$)

The coefficient of mutual induction is 2 H and induced e.m.f. across secondary is 2 kV. Current in the primary is reduced from 6 A to 3 A. The time required for the change of current is

Two planar concentric rings of metal wire having radii $r_1$ and $r_2 \ (r_1 > r_2)$ are placed in air. The current I is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( $\mu_0 =$ permeability of free space)

The current flowing through an inductor of selfinductance L is continuously increasing at constant rate. The variation of induced e.m.f. (e) verses $dI/dt$ is shown graphically by figure

A hollow cylinder has a charge of ' $q$ ' $C$ within it. If $\phi$ is the electric flux associated with the curved surface B, the flux linked with the plane surface A will be

A conducting sphere of radius ' R ' is given a charge ' $Q$ ' uniformly. The electric field and the electric potential at the centre of the sphere are respectively [ $\varepsilon_0 =$ permittivity of free space]

' n ' small spherical drops of same size which are charged to ' $V$ ' volt each coalesce to form a single big drop. The potential of the big drop is

Three point charges $+Q, +2Q$ and $q$ are placed at the vertices of an equilateral triangle. The value of charge $q$ in terms of $Q$, so that electrical potential energy of the system is zero, is given by

A body is projected vertically from earth's surface with $\left(\frac{1}{3}\right)^{\text{rd}}$ of escape velocity. The maximum height reached by the body is ( $R =$ radius of earth)

A body cools from $60^\circ\text{C}$ to $40^\circ\text{C}$ in 6 minutes. After next 6 minutes its temperature will be (Temperature of the surroundings is $10^\circ\text{C}$)

For a perfectly black body, coefficient of emission is

The average force applied on the walls of a closed container depends as $T^{x}$ where T is the temperature of an ideal gas. The value of $x$ is

Which one of the following person is in an inertial frame of reference?

The magnetic susceptibility of iron is 5499. The relative permeability of iron will be

A long wire carrying a steady current is bent into a circle of single turn. The magnetic field at the centre of the coil is ' B '. If it is bent into a circular loop of radius ' $r_1$ ' having ' n ' turns, the magnetic field at the centre of the coil for same current is

A wire has three different sections as shown in figure. The magnitude of the magnetic field produced at the centre ' $O$ ' of the semicircle by three sections together is ( $\mu_0 =$ permeability of free space)

For the following reaction, the particle ' X ' is

${}_{6}\text{C}^{11} \longrightarrow {}_{5}\text{B}^{11} + \beta + \text{X}$

The period of S. H.M. of a particle is 16 second. The phase difference between the positions at $t = 2\text{ s}$ and $t = 4\text{ s}$ will be

A particle oscillates in straight line simple harmonically with period 8 second and amplitude $4\sqrt{2}\text{ m}$. Particle starts from mean position. The ratio of the distance travelled by it in $1$st second of its motion to that in $2$nd second is $\left(\sin 45^\circ = 1/\sqrt{2}, \sin\frac{\pi}{2} = 1\right)$

If the period of a oscillation of mass ' m ' suspended from a spring is 2 s, then the period of suspended mass ' 4 m ' with the same spring will be

The length of the compound microscope is 15 cm. The magnifying power for relaxed eye is 25. If the focal length of eye lens is 6 cm then the object distance for objective lens will be

Two spheres each of mass $M$ and radius $R$ are connected with a massless rod of length 4 R. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod will be

Two discs A and B of same material and thickness have radii $R$ and $3R$ respectively. Their moments of inertia about their axis will be in the ratio

An inclined plane makes an angle $30^\circ$ with the horizontal. A solid sphere rolling down an inclined plane from rest without slipping has linear acceleration ( $g =$ acceleration due gravity) ( $\sin 30^\circ = 0.5$)

When an n-p-n junction transistor is used as an amplifier in common emitter mode,

In a transistor (common emitter configuration) the ratio of power gain to voltage gain is ( $\alpha$ and $\beta$ are current ratios)

For an ideal diode, in forward and reverse biased condition the resistance is respectively

A water drop of $0.01\text{ cm}^{3}$ is squeezed between two glass plates and spreads in to area of $10\text{ cm}^{2}$. If surface tension of water is 70 dyne $/\text{cm}$ then the normal force required to separate glass plates from each other will be

The surface energy of a liquid drop is ' $V$ '. It is sprayed into 1000 equal droplets. The surface energy of all the droplets is

A liquid drop having surface energy $E$ is spread into 729 droplets of same size. The final surface energy of the droplets is

A tyre of a vehicle is filled with air having pressure 270 kPa at $27^\circ\text{C}$. The air pressure in the tyre when the temperature increases to $37^\circ\text{C}$ is

The work done by a gas as it is taken in a cyclic process (shown in graph) is

A diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{V_0}{32}$, where $V_0$ is its initial volume. The initial temperature of the gas is $T_i$ in kelvin and the final temperature is $xT_i$ in kelvin. The value of $x$ is

A student measures time for 20 oscillations of a simple pendulum as $30\text{ s}, 32\text{ s}, 35\text{ s}$ and 35 s. If the minimum division in the measuring clock is 1 s, then correct mean time (in second) is

If $\vec{A} = \hat{i} + \hat{j} + 3\hat{k}, \ \vec{B} = -\hat{i} + \hat{j} + 4\hat{k}$ and $\vec{C} = 2\hat{i} - 2\hat{j} - 8\hat{k}$, then the angle between the vectors $\vec{P} = \vec{A} + \vec{B} + \vec{C}$ and $\vec{Q} = (\vec{A} \times \vec{B})$ is (in degree)

When an observer moves towards a stationary source with velocity ' $V_1$ ', the apparent frequency of emitted note is ' $F_1$ '. When observer moves away from stationary source with velocity ' $V_1$ ' the apparent frequency is ' $F_2$ '. If ' v ' is velocity of sound in air and $\frac{F_1}{F_2} = 2$, then $\frac{V}{V_1}$ is equal to

In fundamental mode, the time required for the sound wave to reach up to closed end of a pipe filled with air is ' $t$ ' second. The frequency of vibration of air column is (Neglect end correction)

Two pipes of lengths $L_1$ and $L_2$, open at both ends are joined in series. If ' $f_1$ ' and ' $f_2$ ' are the fundamental frequencies of two pipes, then the fundamental frequency of series combination will be (neglect end correction)

A wire of length L, diameter ' d ' density of material ' e ' is under tension ' T ', having fundamental frequency of vibration $n_A$. Another wire of length 2 L, tension 2 T, density 2 e and diameter 3 d has fundamental frequency of vibration $n_B$. The ratio $n_B : n_A$ is

In Young's double slit experiment, for the $n$th dark fringe ( $n = 1, 2, 3 \ldots$) the phase difference of the interfering waves in radian will be

In Young's double slit experiment, the distance between screen and aperture is 1 m. The slit width is 2 mm. Light of $6000\ \text{\AA}$ is used. If a thin glass plate ( $\mu = 1.5$) of thickness 0.04 mm is placed over one of the slits, then there will be a lateral displacement of the fringes by

In Young's double slit experiment, when light of wavelength 600 nm is used, 18 fringes are observed on the screen. If the wavelength of light is changed to 400 nm, the number of fringes observed on the screen is