MHT CET 2026 Physics Paper: 12 May, Shift 1

An e.m.f. $e = E_0 \cos\omega t$ is applied to a circuit containing L, C and R in series where $X_L = 4R$ and $X_C = R$. The average power dissipated in the circuit is

In a series LCR circuit, the inductance $L = 20$ mH, capacitor $C = 2\ \mu$F and resistance $R = 100$ ohm. The frequency at which resonance occurs is

Which of the following transition in hydrogen atom emits photon of highest frequency?

A parallel plate air capacitor consists of two metal plates of area $A$ and separation $d$. A slab of thickness $t$ and dielectric constant $2k$ is inserted between the plates with its faces parallel to the plates. The effective capacitance of the system is ($\epsilon_0 =$ permittivity of free space)

Two particles A and B are moving in uniform circular motion in concentric circles of radii $r_A$ and $r_B$ with speeds $v_A$ and $v_B$ respectively. $T_A$ and $T_B$ are the time periods of rotation of the particles respectively and their relation is $T_A = 3T_B$. The ratio of angular speed of B to that of A will be

Two cells of e.m.f.s approximately $5$ V and $10$ V are to be compared using a potentiometer (sum and difference method) of length $400$ cm, then,

An electron is moving with initial velocity $\vec{v} = a\hat{k}$ in a magnetic field $\vec{B} = b\hat{j}$. Its de-Broglie wavelength will

A photon of energy $10$ units ejects a photo-electron from a metal surface whose work function is $\Phi_0$. If an electron(e) having maximum kinetic energy enters into a uniform magnetic field of induction(B) in a direction perpendicular to the field and describes a circular path of radius R, then radius R is {$m =$mass of electron}

By combining three inductances, $2$ H, $4$ H and $6$ H, the minimum value of effective inductance that can be obtained is (in H)

Two inductors, $L_1$ and $L_2$, are connected in parallel and time-varying current flows the combination. If $I_1$ and $I_2$ are the currents passing through the inductor $L_1$ and $L_2$ respectively, the ratio $\frac{I_2}{I_1}$ is

Two conducting circular loops of radii $r$ and $2r$ are placed in the same plane with their centres coinciding. The mutual inductance $M$ between them is {same current is passing through both the coils} ($\mu_0 =$ permeability of free space)

A conducting rod AB of length $l$ is rotated about point O which lies between point A and B in a uniform magnetic field $\vec{B}$ directed into the paper. If length $AO = \frac{l}{3}$, then $(V_A - V_B)$ is $\{\omega =$ angular velocity$\}$

A charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium if $q$ is equal to

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

The equal charges (say 'q') are placed at a distance of $4r$ and a third charge $(-2q)$ is placed at a mid-point. The potential energy of the system is ($\epsilon_0 =$ permittivity of free space)

A vessel contains oil (density$= 0.6$ g/cm$^{3}$) over mercury (density$= 13.6$ g/cm$^{3}$). A homogeneous sphere floats with half its volume immersed in mercury and the remaining half in oil. The density of the material of the sphere in g/cm$^{3}$ is

In a hydraulic press, the small cylinder has a diameter of $d_1$ cm, while the large cylinder has a diameter of $d_2$ cm. If a force $F_1$ is applied to a piston of small cylinder, then the force on the piston of large cylinder $F_2$ is

Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their gravitational attraction, the speed of each particle is

$\{\sin(45)^\circ = \cos(45)^\circ$ $= 1/(2)^{0.5}\}$

Three rods made of the same material and the same cross-sectional areas have been joined as shown in the figure. Each rod is of the same length. The temperature of the junction is

Three spheres, P, Q and R, having radii $4$ m, $5$ m and $6$ m respectively, are coated with lamp black on their outer surfaces. The wavelengths corresponding to maximum intensity (radiated) are $400$ nm, $500$ nm and $600$ nm respectively. If the powers radiated by them are $P_P, P_Q$ and $P_R$ respectively, then $P_P : P_Q : P_R$ is

A charge $q$ is circulating at a constant speed $v$ with a semicircular loop of radius $r$. The magnetic moment of this loop is

Two long straight parallel wires are separated by a distance of $20$ cm. Each wire carries current $5$ mA in the same direction. The magnetic field at a point P midway between them is $\{\mu_0 =$ permeability of free space$\}$

A charged particle of mass $m$ and charge $q$ travels on a circular path, (of radius $5$ unit) is perpendicular to a magnetic field $B$. The time taken by a particle to complete $10$ revolutions is

The value of shunt resistance that allows $5\%$ of the main current through the galvanometer of $100\ \Omega$ is nearly

In transition 'a', three $\alpha$ particles and two $\beta$ particles are emitted in succession from the element ${}_{86}X^{226}$. In transition 'b', two gamma rays, one $\beta$ particle and two $\alpha$ particles are emitted in succession from element ${}_{96}Y^{236}$. The atomic number and the mass number of the new elements formed respectively are

A particle performing S.H.M., has a period of $12$ s. The particle starts from a mean position. The ratio of distances travelled by the particle in the first and second second is $\left\{\cos(\pi/6) = \frac{\sqrt{3}}{2}\right\}$

A simple harmonic oscillator having four identical springs (as shown in figure) has a time period $T_1$. Another similar simple harmonic oscillator of the same mass $m$ but the four identical springs with spring constants $2k$ has a time period $T_2$, then $\frac{T_1}{T_2}$ is

Two particles performing simple harmonic motions of maximum accelerations, $1$ m/s$2$ and $100$ m/s$2$, have the same amplitudes. The ratio of their angular frequencies is

Airplanes A and B are flying with constant velocity in the same vertical plane at angles $30^\circ$ and $60^\circ$ with respect to the horizontal as shown in the figure. The speed of A is $100\sqrt{3}$ m/s. At time $t = 0$ s, an observer in A finds B at a distance of $500$ m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at $t = t_0$, A just escapes being hit by B, $t_0$ in second is

$\{\sin(30^\circ) = 0.5, \cos(30^\circ) = 3^{0.5}/2\}$

A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index of the first lens is $1.5$ and that of second is $1.2$. Both the curved surfaces are of the same radius of curvature $R = 14$ cm. For an object distance of $40$ cm, the image distance will be

Four solid spheres, each of diameter $\sqrt{5}$ cm and mass $0.5$ kg are placed with their centres at the corners of a square of side $4$ cm. The M.I. of the system about the diagonal of the square is $N \times 10^{-4}$ kg-m$2$, then $N$ is

In the case of rotational dynamics, which of the following statements is correct? {$S$ = linear displacement, $\alpha$ = angular acceleration, $r$ = radius vector, $a$ = linear acceleration, $L$ = angular momentum, $p$ = linear momentum, $\theta$ = angular displacement}

1. $S = r \times \theta, a = r \times \alpha, L = p \times r$

2. $S = \theta \times r, a = \alpha \times r, L = r \times p$

3. $S = r \cdot \theta, a = r \cdot \alpha, L = p \cdot r$

4. $S = \omega \times r, a = r \times p, L = r \times f$

Which of the following sentence is true?

a. Moment of a couple is independent of the axis of rotation or the points of application of forces. b. Moment of a couple produces translational acceleration.

c. Moment of a couple can be balanced by single force.

d. Moment of a couple depends upon the axis of rotation or the points of application of forces.

The truth table for the system of four NAND gates as shown in the figure is

In one branch, $40\ \Omega$ resistance and a p-n junction diode are connected in series and in another branch, $40\ \Omega$ resistance is connected. Both the branches are connected in parallel to each other. The total resistance of the circuit when a) diode is forward biased and when b) diode is reverse biased respectively are {consider the p-n junction diode as an ideal diode}

A LED emits visible light when its

A rectangular film of liquid is expanded from ($6$ cm $\times 5$ cm) to ($8$ cm $\times 9$ cm). If the work done is $4 \times 10^{-4}$ J, the surface tension of the liquid is

The pressure of a given mass of a gas is decreased by $20\%$ at constant temperature, then its volume will

For any thermodynamic process, the work done by the system depends

One mole of a mono-atomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram, then

The difference between two molar specific heats of a gas is $7000$ J-kg$-1$-K $-1$. If the ratio of two specific heats of gas is $7/5$, the molar specific heat of the gas at constant pressure in J-kg $-1$-K $-1$ is

A particular physical quantity is given by $X = 2\pi\sqrt{\frac{a}{b}}$ and the measured value of 'a' is $40$ unit with $0.01$ unit accuracy. The value of 'b' is $\frac{98}{10}$ unit with $1$ unit accuracy. The % error in $X$ is nearly

If $\vec{A} = 5\hat{i} + 2\hat{j}$ and $\vec{B} = a\hat{i} + 3\hat{j}$ are perpendicular to each other, the value of 'a' is

A whistle giving out $400$ Hz approaches a stationary observer at a speed of $34$ m/s. The frequency heard by the observer (in Hz) is nearly (speed of sound$= 340$ m/s)

A pipe closed at one end vibrating in the sixth overtone is in unison with the open pipe vibrating in its sixth overtone. The ratio $l_c : l_o$ is $\{l_c =$ vibrating length of pipe closed at one end, $l_o =$ vibrating length of pipe open at both ends$\}$

Two simple harmonic progressive waves have displacements $y_1 = 5\sin\left(\frac{2\pi x}{\lambda} - \omega t\right)$ and $y_2 = 5\cos\left(\frac{2\pi x}{\lambda} - \omega t + \frac{\pi}{6}\right)$. The phase difference between the two waves is

A simple harmonic progressive wave is given by the equation $y = a\sin 2\pi\left(nt - \frac{x}{\lambda}\right)$. If the wave velocity is equal to $\frac{1}{6} \times$ (maximum particle velocity), then the wavelength $\lambda$ is $\{a =$ amplitude, $n =$ frequency, $t =$ time, $y =$ displacement, $x =$ distance$\}$

Unpolarized light with intensity $I_0$ passes through three polaroids such that the transmission axis of the last polaroid is crossed with the first. If the intensity of emerging light is $I_1\left(I_1 = \frac{3}{32}I_0\right)$. The angle between the first two polaroids and the angle for which the transmitted intensity is maximum are respectively $\{$given, $\cos(90) = 0\}$

Resolving power of a telescope can be increased by

In Young's double slit experiment, the fringe width is $2.4$ mm with light of wavelength $9000$ A.U. If the light of wavelength $5400$ A.U. is used, with no other change in the experimental set up. The change in fringe width is