MHT CET 2026 Physics Paper: 16 Apr, Shift 2

Alternating current of peak value $\left(\frac{2}{\pi}\right)$ A flows through the primary coil of a transformer. The coefficient of mutual inductance between primary and secondary coils is 1H. The peak value of induced e.m.f. in the secondary coil is

(Frequency of a.c. = 50 Hz)

An inductor of inductance $2\ \mu$H is connected in series with a resistance, a variable capacitor and an a.c. source of 10 kHz. The value of capacitance for which maximum current is drawn in to the circuit is $\frac{1}{x}$ F, where the value of x is (Take $\pi^2 = 10$)

Series LCR circuit containing an a.c. source of 100V has a inductor and a capacitor of reactance $24\ \Omega$ and $16\ \Omega$ respectively. If a resistance of $6\ \Omega$ is connected in series, then the potential difference across the series combination of inductor and capacitor only is

An electron makes a transition from an excited state to the ground state of a hydrogen like atom. Out of the following statements which one is correct?

(A) K.E, P. E. and T.E. decreases

(B) K.E. increases but P. E. and T.E. decreases

(C) K.E. and T.E. decreases but P.E. increases

(D) K.E. decreases, P.E. increases but T.E. remains the same

A capacitor has capacity C when it's parallel plates are separated by air medium of thickness 'd'. A slab of material of dielectric constant K having area equal to that of plates but thickness $\frac{d}{2}$ is inserted between the plates. Capacitance of the capacitor in the presence of slab will be

If the potential difference between points B and D is zero in the given circuit, the value of x is $\frac{1}{n}\ \Omega$. The value n is

A photoemissive substance is illuminated with a radiation of wavelength $\lambda_i$ so that it releases electrons with de-Broglie wavelength $\lambda_e$. The longest wavelength of radiation that can emit photoelectron is $\lambda_0$. Expression for de-Broglie wavelength is (m = mass of electron, h = Planck's constant, C = Speed of light)

When a light of wavelength '$\lambda$' falls on the emitter of a photosensitive surface, maximum speed of emitted photoelectrons is 'V'. If the incident wavelength is changed to '$2\lambda/3$', maximum speed of emitted photoelectrons will be

In the given circuit, if $dI/dt = -1$ A/s then the value of $V_{AB}$ at this instant will be

A circular coil of radius 'r' is placed on another circular coil whose radius is 'R' and the current flowing through it is changing and their centers coincide. ($R \gg r$). If both the coils are coplanar, then the mutual inductance between them is proportional to

A graph of magnetic flux ($\Phi$) versus current (I) is shown for four inductors A, B, C, D. The smallest value of self inductance is for inductor.

Two spherical hollow spheres of radii '$R_1$' and '$R_2$' are charged with same charge. Let '$\sigma_1$' and '$\sigma_2$ ' are their respective charge densities, then the ratio $\sigma_1$ to $\sigma_2$ is

An electric dipole of length $0.5\,\mu$m is placed with its axis making an angle of $30^\circ$ with uniform electric field $10^{4}$ V/m. If it experiences a torque of $5 \times 10^{-9}$ Nm, the magnitude of the charge on the dipole is ($\sin 30^\circ = 0.5$)

Two charges $q_1$ and $q_2$ are separated by a distance of 30cm. A third charge $q_3$ initially at point C is shown in figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of $q_3$ from C to D is $q_3k/4\pi\varepsilon_0$, the value of K is ($\varepsilon_0$ = permittivity of free space)

A horizontal pipe carries water in a streamline flow. At point along the pipe, where the cross- sectional area is $A_1$, the velocity of water is $V_1$ and the pressure is $P_1$. What is the pressure of water at another point where the cross-sectional area is $A_2$?

The time taken by simple pendulum for one oscillation is T on earth's surface. Its time period becomes xT when taken to a height R (equal to earth's radius) above the earth's surface. The value of x is

A body of mass m is taken from earth surface to a height h equal to twice the radius of earth, the increase in potential energy will be ($g$ = acceleration due to gravity on earth's surface) (R - radius of earth)

A bowl filled with very hot water cools from $98^\circ$C to $86^\circ$C in 2 minutes when the room temperature is $22^\circ$C. How long it will take to cool from $75^\circ$C to $69^\circ$C?

The average transnational kinetic energy of a molecule in a gas is $E_1$. The kinetic energy of the electron (e) accelerated from rest through potential difference 'V' volt is $E_2$. The temperature at which $E_1 = E_2$ possible is (mass of molecule and electron is same) (N = number of molecules, V = Velocity, R = gas constant)

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 circular loop of radius R is carrying current I. The ratio of magnetic field at the center of circular loop and at a distance R from the center of the loop on its axis is

The magnitude of magnetic induction at mid point 'O' due to current arrangement as shown in figure will be ($\mu_0$ = permeability of free space)

A galvanometer has resistance G and range Vg. How much resistance is required to read voltage up to V volt?

The ratio of the density of oxygen nucleus $\left({}_{8}^{16}\text{O}\right)$ and helium nucleus $\left({}_{2}^{4}\text{He}\right)$ is

The maximum potential energy of a block executing S.H.M. is E and amplitude of oscillation is 'A'. The kinetic energy of the block at amplitude A/2 is

A mass $m_1$ performs S.H.M. with amplitude A which is connected to horizontal spring. While mass $m_1$ passing through mean position, another mass $m_2$ ($m_2 < m_1$) is placed on it so that both masses move together with amplitude $A_1$. The ratio of $A/A_1$ is

Two objects are projected with same velocity 'u' at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha + \beta = 90^\circ$, the ratio of horizontal range of the first object to the second object will be $[\sin(\pi - \theta) = \sin\theta]$

A ray of light passes from the vacuum into a medium of refractive index 'n'. If the angle of incidence is twice the angle of refraction, then the angle of incidence in terms of refractive index is

A convex lens having refractive index 1.6 has focal length 12 cm, when it is in air. The focal length of that lens when placed in water is (refractive index of water = 1.28)

A solid sphere of mass M and a disc of mass $\frac{M}{2}$ have the same radius. The ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be

Solid sphere is rotating about an axis as shown in figure. If the radius of the sphere is 5 cm, then radius of gyration about that axis will be $\sqrt{x}$ cm. The value of x is

A uniform solid cylinder with radius R and length L has moment of inertia $I_1$ about the axis of the cylinder. A concentric solid cylinder of radius $R/2$ and length $L/2$ is carved out of the original cylinder. If $I_2$ is the moment of inertia of the carved out portion of the cylinder then $I_1/I_2$ is (Both $I_1$ and $I_2$ are about the axis of the cylinder)

Electrical conductivity of insulators is

In which of the logic gate the following statement is true? "The output is high when either of the inputs is high but not if both inputs are high"

Which of the following statement is NOT correct in the case of LED?

(A) It is a heavily doped p-n junction diode.

(B) It emits light only when it is forward biased.

(C) It emits light only when it is reverse biased.

(D) The energy of the light emitted is equal to or slightly less than the energy gap of the semiconductor used.

Under isothermal condition, two soap bubbles of radii $r_1$ and $r_2$ combine to form a single soap bubble of radius R. The surface tension of the soap is (P = outside pressure)

One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is

A rigid diatomic gas having molar mass m is contained in an insulated container. The container is moving with velocity V. If it is stopped suddenly, the change in temperature is (R - gas constant)

A Carnot engine with efficiency 50% takes heat from a source at 600 K. To increase the efficiency by 20%, keeping temperature of the sink same, the new temperature of the source will be

One gram of a liquid is converted to vapour at $3 \times 10^{5}$ Pa pressure. If 10% of the heat supplied is used for increasing the volume by $1600$ cm$3$ during this phase change, then the increase in internal energy in the process will be

If a gas is compressed isothermally then the r.m.s. velocity of the molecules

The error in the measurement of length and mass of a cube is 3% and 4% respectively. The error in the measurement of its density will be

Vectors $a\hat{i} + b\hat{j} + \hat{k}$ and $2\hat{i} - 3\hat{j} + 4\hat{k}$ are perpendicular to each other when $3a + 2b = 7$, the ratio of a to b is $x/2$. The value of x is

Two waves $Y_1 = 0.25\sin 316t$ and $Y_2 = 0.25\sin 310t$ are propagating along the same direction. The number of beats produced per second are

A person observes two moving trains. 'A' reaching the station and 'B' leaving the station with equal speed of 30m/s. If both trains emit sounds with frequency 300 Hz, (speed of sound = 330 m/s) difference of frequencies heard by the person will be

An air column in a pipe which is closed at one end will be in resonance with a vibrating tuning fork of frequency 415 Hz for various vibrating air columns. Which one of the following lengths is not in resonance? (velocity of sound in air = 332 m/s) (Neglect end correction)

When open pipe is closed from one end then third overtone of closed pipe is higher in frequency by 150Hz than second overtone of open pipe. The fundamental frequency of open end pipe will be (Neglect end correction)

Three identical polaroids $P_1, P_2$ and $P_3$ are placed one after another. The pass axis of $P_2$ and $P_3$ are inclined at angle of $60^\circ$ and $90^\circ$ with respect to axis of $P_1$. The source has an intensity $I_0$. The intensity of light finally coming out is

In Young's double slit experiment, two slits are illuminated with a light of wavelength $\lambda$. The line joining $A_1 P$ is perpendicular to $A_1 A_2$ as shown in figure. If the first minimum is detected at P, the value of slits separation 'a' will be

(D = distance between source and screen)

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