MHT CET 2026 Physics Paper: 13 Apr, Shift 2

In a series LR circuit with $X_L = R$. Power factor is $P_1$. If a capacitor of capacitance $C$ with $X_c = X_L$ is added to the circuit the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be:

An inductor of $0.5$ mH, a capacitor of $20\ \mu$F and resistance $20\ \Omega$ are connected in series with a $220$ V ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $[x]^{1/2}$ A. The value of $x$ is

In the circuit shown, the ratio of the quality factor and the band width is

(Given: band width = R/L)

The wavelength of the radiation emitted is $\lambda_{0}$ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be $(20\lambda_{0}/x)$. The value of $x$ is

For hydrogen atom, $\lambda_{1}$ and $\lambda_{2}$ are the wavelengths corresponding to the transitions $1$ and $2$ respectively as shown in figure. The ratio of $\lambda_{1}$ and $\lambda_{2}$ is $x/32$. The value of $x$ is

A parallel plate capacitor with air between the plate has a capacitance of $15$ pF. The separation between the plates becomes twice and the space between them is filled with a medium of dielectric constant $3.5$. Then the capacitance becomes $x/4$ pF.

The value of $x$ is

In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf $1.5$ V is found to be $60$ cm. If this cell is replaced by another cell of emf $E$, the length of null point increases by $40$ cm. The value of $E$ is $x/10$ V.

The value of $x$ is

Resistances are joint as shown in the figure. In the balanced condition, the current $I$ drawn from the battery is

An electron accelerated through a potential difference $V_1$ has a de-Broglie wavelength of $\lambda$. When the potential is changed to $V_2$, its de-Broglie wavelength increases to $2\lambda$. The value of $(V_1/V_2)$ is equal to

The threshold frequency of metal is $f_0$. When the light of frequency $2f_0$ is incident on the metal plate, the maximum velocity of photoelectron is $v_1$. When the frequency of incident radiation is increased to $5f_0$ the maximum velocity of photoelectrons emitted is $v_2$. The ratio $v_1$ to $v_2$ is

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following {Assume negligible air friction}

A conducting loop of radius $10/[\pi]^{1/2}$ cm is placed perpendicular to a uniform magnetic field $0.5$ T. The magnetic field is decreased to zero in $0.5$ s at a steady rate. The induced emf in the circular loop at $0.25$ s is

If two charges $q_1$ and $q_2$ are separated with distance 'd' and placed in a medium of dielectric constant $K$. What will be the equivalent distance between charges in air for the same electrostatic force?

The electric potential at the center of two concentric half rings of radii $R_1$ and $R_2$, having same linear charge density $\lambda$ is ($\epsilon_0$ = permittivity of free space)

Two isolated metallic spheres of radii $R$ and $2R$ are charged such that both have the same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the larger sphere is $\sigma_1$. The ratio $\sigma_1$ to $\sigma$ is

The surface of water in a water tank of cross-section area $750$ cm$^{2}$ on the top of a house is $h$ m above the tap level. The speed of water coming out through the tap of cross-section area $500$ mm$^{2}$ is $30$ cm/s. At that instant, $dh/dt$ is $y \times 10^{-3}$ m/s. The value of $y$ will be

If earth has a mass nine times and radius twice to the planet P. Then $\frac{v_e}{3}\sqrt{x}$ ms$-1$ will be the minimum velocity required by a rocket to pull out of gravitational force of P, where $v_e$ is escape velocity on earth. The value of $x$ is

The coefficient of thermal conductivity of a metal rod depends on its

What will be the ratio of rate of radiation of metal sphere at two different temperatures $T_1 = 527^\circ$C and $T_2 = 127^\circ$C

Energy of a gas/litre is $600$ joule, then what will be its pressure?

$100$ balls each of mass $m$ moving with speed $v$ simultaneously strike a wall normally and reflected back with same speed, in time $t$ s. The total magnitude of force exerted by the balls on the wall is

A rod with a circular cross-section area $2$ cm${}^{2}$ and length $40$ cm is wound uniformly with $400$ turns of an insulated wire. If a current $0.4$ A flows in the wire winding, the total magnetic flux produced inside the winding is $4\pi \times 10^{-6}$ Wb. The relative permeability of the rod is

(Given permeability of vacuum $\mu_0 = 4\pi \times 10^{-7}$ N m A${}^{-2}$)

The velocity time graph of a body moving in a straight line is shown in a figure. The ratio of displacement to distance travelled by the body in time $0$ to $10$ s is

The magnetic moments associated with two closely wound circular coils a and b of radius $r$ and $2r$ respectively are equal if (where $N_a, I_a$ and $N_b, I_b$ are number of turns and current in A and B respectively)

Two long straight wires are arranged parallel to each other and are kept $20$ cm apart in vacuum. They carry currents of $2$ A and $4$ A respectively in the same direction. What will be the magnetic force on a length of $10$ cm of either wire?

($\mu_0 = 4\pi \times 10^{-7}$ SI units)

A charged particle $q$ is accelerated by a potential difference of $V$ enters a region of uniform magnetic field of induction $B$ at right angles to the direction of the field. The charged particle completes semi circle of the radius $r$ inside the magnetic field. The mass of the charged particle is (all quantities are in SI units)

The amplitude of a particle executing SHM is $3$ cm. The displacement at which its kinetic energy will be $25\%$ more than the potential energy is (in cm)

A block is fastened to a horizontal spring. The block is pulled to a distance $x = 10$ cm from its equilibrium position (at $x = 0$) on a frictionless surface from rest. The kinetic energy of the block at $x = 5$ cm is $0.25$ J. The spring constant of the spring is nearly (in Nm$-1$)

The velocity of a particle executing SHM varies with displacement ($x$) as $4v^2 = 50 - x^2$. The time period of oscillations is $x/7$ s.

The value of $x$ is (Take $\pi = 22/7$)

When a beam of white light is allowed to pass through convex lens parallel to principle axis, the different colors of light converge at different point on the principle axis after refraction. This is called

Moment of inertia of a disc of mass $M$ and radius 'R' about any of its diameter is $MR^2/4$. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, $(x/2)MR^2$. The value of $x$ is

A thin uniform rod of length $2$ m cross-sectional area 'A' and density 'd' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$. If the value of $\omega$ in terms of its rotational kinetic energy $E$ is $(\alpha E/Ad)^{1/2}$, then the value of $\alpha$ is

A solid sphere of mass $1$ kg rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{-3}$ J. The speed of the center of mass of the sphere in cm s$^{-1}$ is

A pure silicon crystal at temperature $300$ K has electron and hole concentration ($n_i$) $10^{16}$ per m${}^{3}$ each and $10^{21}$ phosphorus atoms ($n_e$) are added per cubic metre. The new hole concentration in silicon crystal is

If transistor having $\alpha = 0.9$, is used in CE configuration, then for a change of $0.4$ mA in base current, what will be the change in collector current?

Choose the correct statement about Zener diode:

A spherical drop of liquid splits into $1000$ identical spherical drops. If $u_i$ is the surface energy of the original drop and $u_f$ is the total surface energy of the resulting drops, the (ignoring evaporation). $u_f/u_i = (10/x)$. Then value of $x$ is

Determine the ratio of surface energy of $1$ large drop to $1$ small drop, if $1000$ small drops combined to form $1$ large drop.

According to law of equipartition of energy the molar specific heat of a non rigid diatomic gas at constant volume is

Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a mono-atomic gas and $\gamma_2$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, $\gamma_1/\gamma_2$ is

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is (given, $\gamma = \frac{3}{2}$ ):

The length of a cylinder is measured with a meter rod having least count $0.1$ cm. Its diameter is measured with vernier calipers having least count $0.01$ cm. Length of cylinder is $8.0$ cm and radius is $4.0$ cm. Find the percentage error in the calculated value of the volume.

Calculate the values of $a$ and $b$ if vectors $a\hat{i} + b\hat{j} = \hat{n}$ and $(\hat{i} + \hat{j})$ are perpendicular to each other

A traveling wave is described by the equation $y(x, t) = [0.05\sin(8x - 4t)]$ m

The velocity of the wave is [All the quantities are in SI unit]

Two waves are represented by the equations, $y_1 = a\sin(\omega t + kx + 0.57)$ m and $y_2 = a\cos(\omega t + kx)$ m, where $x$ is in metre and $t$ is in second. What is the phase difference between them? ($\pi = 3.14$)

The distance between two consecutive points with phase difference of $60^\circ$ in a wave of frequency $n$ is $x$ meter. The velocity with which wave is traveling is

Sound waves travel at $350$ m/s through a warm air and at $3500$ m/s through brass. Which of the following is correct about the wavelength of a $700$ Hz accoustic wave as it enters brass from warm air?

'n' polarizing sheets are arranged such that each makes an angle $45^\circ$ with the preceding sheet. An unpolarized light of intensity $I$ is incident into this arrangement. The output intensity is found to be $I/64$. The value of $n$ will be

In Young's double slit experiment, two slits $S_1$ and $S_2$ are 'd' distance apart and the separation from slits to screen is $D$. Now if two transparent slabs of equal thickness $0.1$ mm but refractive index $1.51$ and $1.55$ are introduced in the path of beam ($\lambda = 4000$ Å) from $S_1$ and $S_2$ respectively. The central bright fringe spot will shift by ___ number of fringes.

In Young's double slit experiment, following figure shows that $Q$ is the position of second bright fringe on the right side of point $O.\ P$ is the eleventh bright fringe on the other side measured from point $Q$. If the wavelength of light used is $6000$ Å, then what will be the value of $S_1B$?