MHT CET 2026 Physics Paper: 17 Apr, Shift 2

In a series LCR circuit alternating e.m.f. and current are given by the equations $V = V_0\sin(\omega t)$ and $I = I_0\sin\left(\omega t + \frac{\pi}{3}\right)$ respectively. The average power dissipated in the circuit over one cycle of a.c. is $(\cos 60^\circ = 0.5)$

In an a.c. circuit with pure capacitance 'C' and a.c. source $E = E_0 \sin \omega t$, the equation of instantaneous current is given by

In LCR circuit, at a particular angular frequency the capacitive reactance and inductive reactance is same. If the angular frequency is doubled, the ratio of the reactance of the capacitor to that of the inductor will be

In Bohr's atomic model, the energy of the electron is 'E' in the second orbit of hydrogen atom. So the energy of the electron in the third orbit of helium atom $(Z = 2)$ will be

If the equivalent capacitance between points A and B of the combination of capacitors shown in figure, is 6C, the capacitor $C'$ is

Two indentical metal plates are given charges $q_1$ and $q_2\ (q_2 < q_1)$ respectively. They are brought close together to form a parallel plate capacitor with capacitance 'C'. The potential difference 'V' between the plates is

A current of 9A enters point P of an equilateral triangle PQR having three wires of $3\ \Omega$ each and leaves by point R. The currents $I_1$ and $I_2$ are respectively

The ratio of the accelerating potentials required to accelerate (i) an $\alpha$-particle and (ii) a proton to have the same de Broglie wavelength associated with them is

(mass of $\alpha$ - particle = $6.4 \times 10^{-27}$ kg, mass of proton = $1.6 \times 10^{-27}$ kg)

In photoelectric effect, keeping the frequency of incident radiation and accelerating potential fixed, if the intensity of incident light is increased,

A straight line conductor of length 0.4 m is moved with a speed of $7.0$ ms$^{-1}$ perpendicular to magnetic field of intensity $0.8$ Wb m$^{-2}$. The induced e.m.f. across the conductor is

Two coils having self-inductance $L_1 = 75$ mH and $L_2 = 48$ mH are coupled with each other. If the mutual inductance of the coils is 37.2 mH, then coefficient of coupling will be

Two planar concentric rings of metal wire having radii '$r_1$' and '$r_2$' (with $r_1 > r_2$) 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)

Two point charges +e and +4e are kept at a distance 'd' units apart. Third point charge +q is placed between the two charges at a distance 'x' units from charge +e so as to be in equilibrium. The value of 'x' is

Three point charges +q, +2q and +Q are placed at the vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of Q in terms of q is

Two planets A and B are orbiting around the sun. The distances of the two planets A and B from the sun are $r_A$ and $r_B$ respectively. Also $r_B = 225\,r_A$. If the orbital speed of the planet A is 'V' then the orbital speed of planet B will be

In a composite slab there are two materials having coefficients of thermal conductivity K and 2K, thickness x and 4x repectively. The temperature of the two outer surfaces of a composite slab are $T_2$ and $T_1\ (T_2 > T_1).\ T_2$ is on side K and $T_1$ is on side 2K. The rate of heat transfer through the slab in a steady state is $\left[\frac{A(T_2-T_1)K}{x}\right] \cdot f$, where f is equal to

A black body emits radiation of maximum intensity of wavelength '$\lambda$' at temperature 'T' K. Its corresponding wavelength at temperature $(2.5T)$ K will be

The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at $47^\circ$ C is (molecular weight of hydrogen and oxygen are 2 and 32 respectively)

A machine gun fires a bullet of mass 40g with a speed of $600$ ms$^{-1}$. The person holding the gun can bare maximum force of 168N on it. The number of bullets that can be fired from the gun per second is

Two wires of same length are bent to form the circular loop with two turns and a square loop of one turn. Both of them carry same current. The ratio of magnetic moment of circular loop of two turns to that of square loop is

The magnetic field at a distance 'r' from a long straight wire carrying current I is 0.4 tesla. The magnetic field at a distance 2r will be

In the cyclotron, as radius of the circular path of the charged particle increases, ($\omega$ = angular velocity, V = linear velocity)

The current passing through the galvanometer is 4 % of the total current in the curcuit. If the resistance of the galvanometer is 'G', the shunt resistance 'S' connected across the galvanometer is

The activity of a radioactive sample is measured as $N_0$ counts per minute at time $t = 0$ and $\frac{N_0}{e}$ counts per minute at time $t = 3$ minute. The time (in minute) in which the activity reduces to half the value, is

For a particle performing linear S.H.M. of amplitude 'r', the potential energy is '$\lambda$' times its total energy. The displacement of particle is

The displacement of a particle performing linear S.H.M. is given by $y = A\cos[\pi(t + \phi)]$. If at $t = 0$, the displacement is $y = 2$ cm and velocity is $2\pi$ cm/s, the value of amplitude A in cm is

A light spring is suspended with mass '$m_1$' at its lower end and its upper end is fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is T second. When a mass ' ' is added to '$m_1$' and the system is made to oscillate the period is found to be $\frac{3}{2}$ T. The ratio $m_2\ \left(\frac{m_1}{m_2}\right)$ is

A ball P is projected at an angle of $60^\circ$ with the vertical with certain initial speed. Another ball Q of the same mass as that of ball P is projected vertically upwards with the same initial speed as that of P. At the highest point, the ratio of potential energy of ball P to that of ball Q is

$(\sin 30^\circ = 0.5)$

A ray of light incident on one face of an equilateral glass prism having refractive index $\sqrt{2}$, produces the emergent ray which just grazes along the adjacent face. The value of angle of incidence is $(\sin 90^\circ = 1)\ \left(\sin 30^\circ = \frac{1}{2}\right)\ \left(\sin 45^\circ = \frac{1}{\sqrt{2}}\right)$

A mass tied to a string is whirled in a horizontal circular path with a constant angular velocity and its angular momentum is 'L'. If the length of the string is now halved, keeping angular velocity same then the angular momentum will be

A solid sphere of radius R and mass M is rotating about its diameter. The moment of intertia of the solid sphere rotating about an axis at a distance $\frac{R}{3}$ from the centre and parallel to that diameter is

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $K_c$. Radius of gyration of the same disc about a diamter of the disc is $K_d$. the ratio $K_d : K_c$ is

In common emitter configuration of transistor amplifier, $r_i, R_L$ and $\beta$ represent the input resistance, load resistance and the a.c. current gain respectively. The voltage gain $A_V$ and power gain $A_P$ are represented in magnitude respectively by

In the following digital circuit, the output 'Y' will be '1' (one) for inputs 'A' and 'B' having values

A semiconductor X is made by doping a germanium crystal with indium $(Z = 49)$. A second semiconductor Y is made by doping germanium crystal with arsenic $(Z = 33)$. Both are joined end to end and connected to a battery as shown. Which of the following statements is correct?

When a capillary tube of radius 'r' is immersed in water, rise of water is upto height 'h'. The mass of water in capillary tube is 'm'. When another capillary tube of radius 'xr' is immersed in water, the mass of water that will rise in this tube is

Two soap bubbles, A and B, have radii in the ratio $3 : 2$. The excess pressure inside the bubble A to that of B is in the ratio

The excess pressure inside the first soap bubble is three times that inside the second soap bubble. The ratio of the volume of the first soap bubble to the volume of the second soap bubble is

A carnot engine having efficiency $\frac{1}{6}$, operates between the source temperature $T_H$ and the sink temperature $T_C$. Its efficiency increases to $\frac{1}{3}$, when $T_C$ is decreased by 64 K. The temperatures $T_H$ and $T_C$ are repectively

A thermodynamic system is compressed adiabatically, then its temperature

Two cylinders A and B fitted with pistons contain equal amount of an ideal diatomic gas at 303 K. The piston of cylinder A is free to move and that of cylinder B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder B is 63 K then the rise in temperature of the gas in A is

A force 'F' is applied on a square plate of side 'L'. If the percentage error in determining 'L' is 3% and that in 'F' is 2% then the percentage error in determining the pressure is

There are two vectors $\vec{A} = 6\hat{i} + 9\hat{j} - \hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} - p\hat{k}$ which have the same direction. The value of 'p' is

The beats are produced when there is a superposition of two sound waves which will have

Two sounding waves send waves at certain temperature in air of wavelength 50 cm and 50.5 cm repectively. The frequency of sources differ by 6 Hz. The velocity of sound in air at same temperature is

In a pipe closed at one end, air column is vibrating in the fourth overtone so the vibrating air column has '$x$' nodes and '$y$' antinodes. The values of $x$ and $y$ are respectively

In a sonometer experiment, the fundamental frequency of vibration of wire is '$n_1$' when wire is stretched by hanging a metal bob. If the bob is completely immersed in water, the frequency of vibration of wire becomes '$n_2$'. The relative density of the metal of the bob is

An unpolarised light of intensity $64$ Wm${}^{-2}$ passes through three polarizers successively such that the transmission axis of last polarizer is crossed with the first. The intensity of the emerging light is $6$ Wm${}^{-2}$. The angle between the transmission axis of the first two polarizers is

For obtaining maximum contrast between the bright and dark fringes in an interference pattern, the intensities of the two light coherent sources should be

In Young's experiment, the intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources is $36 : 1$. The ratio of the amplitudes of the two individual sources will be