MHT CET 2026 Physics Paper: 14 May, Shift 1

A resistance of $20\ \Omega$ is connected to a source of alternating potential $V = 220 \sin(100\pi t)$. The time taken by current to change from its peak value to r.m.s. value is $\left(\sin \frac{\pi}{4} = \frac{1}{\sqrt{2}}\right)$

In an a.c. circuit, if the frequency is doubled, what happens to the capacitive reactance ($X_c$) and the current ($I$)?

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

Bohr model is applied to a particle of mass $m$ and charge $q$ is moving in a plane under the influence of a transverse magnetic field $B$. The energy of the charged particle in $n^{th}$ level will be ($h$ = Planck's constant)

A parallel plate capacitor having capacity $12$ pF is charged by a battery of $10$ V between its plates. The battery is now disconnected and a slab of dielectric constant $6$ is kept between the plates. The work done by the capacitor on the slab is

A parallel plate air capacitor has capacity $C$ and plate area $A$. Now the space between its plates is filled by two slabs of thickness $\frac{d}{2}$ each, having dielectric constants $K_1$ and $K_2$. Distance of separation between plates is $d$. The capacity of the capacitor is ($\varepsilon_0$ = permittivity of free space)

A potentiometer wire has length $L$. For a given cell of e.m.f. $E$, the balancing length is $\frac{L}{3}$ from the positive end of the wire. If the length of potentiometer wire is increased by $50\%$ then for the same cell the balance point is obtained at length (from positive end)

Two particles A and B of masses $m_1$ and $m_2$ ($m_1 > m_2$) have the same de-Broglie wavelength, then

The de-Broglie wavelength $\lambda$ of a particle

A current $i = 10\sin(100\pi t)$ A is passed in first coil, which induces a maximum e.m.f. $5\pi$ V in second coil. The mutual inductance between the coils is

A conductor of length $1$ m rotates vertically about one of its ends at angular velocity $5$ rad/s. If the horizontal component of earth's magnetic field is $0.2 \times 10^{-4}$ T, then the e.m.f. developed between the ends of the conductor is

What is the self inductance of a solenoid of length $10\pi$ cm, area of cross-section $10^{-3}$ m${}^{2}$ and total number of turns $10^{3}$? ($\mu_0 = 4\pi \times 10^{-7}$ SI unit)

When a dielectric is placed in an electric field, the electric field inside the dielectric

The electric flux entering and leaving an enclosed surface are $\Phi_1$ and $\Phi_2$ respectively. The electric charge inside the surface will be ($\varepsilon_0$ = permittivity of vacuum)

Two particles of masses $m$ and $M$ are placed a distance $d$ apart. The gravitational potential at the position where the gravitational field due to them is zero is $V$. Then

At $273^\circ$C, the emissive power of a perfectly black body is $R$. The value at $0^\circ$C is

The wavelength of maximum intensity of radiation emitted by a star is $289.8$ nm. The radiation intensity of the star is (Stefan's constant = $5.67 \times 10^{-8}$ SI unit, Wein's constant $2898\,\mu$mk)

A bullet is fired from a gun. The force on the bullet is $F = (600 - 2 \times 10^{5} t)$ N where $t$ is in second. The force on the bullet becomes zero as soon as it leaves the barrel. The average impulse imparted to the bullet is

The angle made by electron's orbital angular momentum ($L$) with the direction of the orbital magnetic moment ($M$) is

The magnitude of magnetic induction at a point on the axis at a large distance $r$ from a centre of a circular coil of $n$ turns and area $A$ carrying current $i$ is ($\mu_0$ = permeability of free space)

Three long straight parallel wires carrying currents are arranged as shown. The wire C carries a current $50$ A is so placed that it experiences no force. The distance of wire C from wire A in cm is

When a resistance of $100\ \Omega$ is connected in series with galvanometer of resistance $R$, its range is $V$. To double its range, another additional resistance of $1000\ \Omega$ is connected in series. Find the value of $R$.

Activity of a radioactive sample decreases to $\left(\frac{1}{3}\right)^{rd}$ of its original value in $3$ days. Then in $9$ days its activity will become

Maximum kinetic energy of a particle of mass $1$ kg in S.H.M. is $8$ J and the time period is $4$ s. Maximum potential energy during the motion is $10$ J. Then

The path length of oscillation of simple pendulum of $1$ m is $8$ cm. Its maximum velocity is (Take $g = \pi^2$ m/s$^{2}$)

A mass is suspended from a vertical spring which is executing S.H.M. of frequency $10$ Hz. The spring is unstretched at the highest point of oscillation. Maximum speed of the mass is ($g = 10$ m/s$^{2}$)

A stone is thrown at an angle $\theta$ with the horizontal reaches a maximum height $H$, then the time of flight of stone will be ($g$ = acceleration due to gravity)

The combined focal length is $F$ when a convex lens of focal length $F_1$ and concave lens of focal length $F_2$ is combined. The combination of these lenses will behave like a concave lens, if

A particle of mass $m$ is projected with speed $v$ at $45^\circ$ with the horizontal. The magnitude of angular momentum of the particle about the point of projection when the particle is at its maximum height $h$ is $\left(\cos 45^\circ = \frac{1}{\sqrt{2}}\right)$

A disc of moment of inertia $I_1$ is rotating in horizontal plane about an axis passing through centre and perpendicular to its plane with constant angular speed $\omega_1$. Another disc of moment of inertia $I_2$ having zero angular speed is placed co-axially on a rotating disc. Now, both the discs are rotating with constant angular speed $\omega_2$. The energy lost by the entire system is $\frac{x\omega_1^2}{2}$ where the value of $x$ is

The moment of inertia of a solid sphere about an axis passing through centre of gravity is $\frac{2MR^2}{5}$ where M is the mass and R is the radius. The radius of gyration about a parallel axis at a distance $2R$ from first axis is

For a transistor, the current ratio $\alpha_{DC} = \frac{69}{70}$. The current gain $\beta_{DC}$ is

$\beta, R_L$ and $r$ are the a.c. current gain, load resistance and the input resistance of a transistor respectively in common emitter configuration, the voltage gain and the power gain are respectively

In the middle of the depletion region of reversed biased p-n junction the

Water rises up to a height $h$ in a capillary tube on the surface of the earth. The value of $h$ will increase, if the experimental set up is kept in ($g$ = acceleration due to gravity)

A drop of some liquid of volume $0.04$ cm$3$ is placed on the surface of the glass plate. Then another glass plate is placed on it such that the liquid forms a thin layer of area $20$ cm$2$ between the surfaces. To separate the plates a force of $16 \times 10^{5}$ dyne has to be applied normal to the surfaces. The surface tension of the liquid in dyne/cm is

At $10^\circ$C, the value of density of a fixed mass of a gas (ideal) divided by its pressure is $x$. At $110^\circ$C this ratio is

The temperature of an ideal gas increases $2$ times when compressed adiabatically to half the volume. Its equation of state is

$1$ g of water of volume $1$ cm$^{3}$ at $100^{\circ}$C is converted into steam of same temperature under normal atmospheric pressure ($10^{5}$ Pa). The volume of steam formed equals $1671$ cm$^{3}$. If the latent heat of vaporisation of water is $2256$ J/g, the change in internal energy is

The coefficient of volume expansion of mercury is $18 \times 10^{-5}/^\circ$C. A thermometer bulb has volume $10^{-6}$ m$^3$ and cross-section of stem is $0.004$ cm$^2$. Assuming bulb is filled with mercury at $0^\circ$C then the mercury column at $100^\circ$C is

If the error in the measurement of volume of the sphere is $6\%$ then the error in the measurement of its surface area will be

A vector $\vec{A}$ has magnitude $6$ units is added to vector $\vec{B}$ which is along $x$-axis. The resultant of $\vec{A}$ and $\vec{B}$ is along $y$-axis. If the magnitude of the resultant of $\vec{A}$ and $\vec{B}$ is $3$ times that of $\vec{B}$ then the magnitude of $\vec{B}$ is

Two spherical rain drops reach the surface of the earth with terminal velocities having ratio $16 : 9$. The ratio of their surface area is

An observer moves towards a stationary source of sound with a velocity $\left(\frac{1}{5}\right)^{th}$ of the velocity of sound. The percentage increase in the apparent frequency is

$n_1$ is the fundamental frequency of the pipe closed at one end and $n_2$ is the fundamental frequency of the pipe open at both ends. If both are joined end to end, the fundamental frequency of closed pipe so formed is

A wave travelling in the positive $x$-direction having displacement along $y$-direction as $1$ m, wavelength $2\pi$ m and frequency Hz is represented by

$\frac{1}{\pi}$

Two uniform strings A and B made of steel are vibrating under the same tension. If the first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the lengths of the strings is

A parallel beam of light of intensity $I_0$ is incident on a glass plate, $25\%$ of light is reflected by upper surface ($I_1$) and $50\%$ of light is reflected from lower surface ($I_2$). The ratio $I_2$ to $I_1$ is

The thickness of a plate (refractive index $\mu$) which will produce a change in optical path equal to half the wavelength $\lambda$ of the light passing through it normally, is

If fringe width is $0.4$ mm, the distance between fifth bright and third dark band on the same side in interference pattern of Young's double slit experiment is (in mm)