MHT CET 2024 Physics Paper: 16 May, Shift 1

The alternating voltage is given by $v = v_0 \sin\left(\omega t + \frac{\pi}{3}\right)$ when will be the voltage maximum for first time?

In LCR series circuit, an alternating e.m.f. 'e' and current ' $i$ ' are given by equations $e = 160\sin(100t)$ Volt and $i = 250\sin\left(100t + \frac{\pi}{3}\right)\text{ mA}$. The average power dissipated in the circuit is

An electric lamp connected in series with a capacitor and an a.c. source is glowing with certain brightness. On increasing the value of capacitance the brightness of the lamp

When an electron orbiting in hydrogen atom in its ground state jumps to higher excited state, the de- Broglie wavelength associated with it

Frequency of the series limit of Balmer series of hydrogen atom of Rydberg's constant ' $R$ ' and velocity of light ' $C$ ' is

A series combination of $n_1$ capacitors, each of value $C_1$ is charged by a source of potential difference 6 V. Another parallel combination of $n_2$ capacitors, each of value $C_2$ is charged by a source of potential difference 2 V. Total energy of both the combinations is same. The value of $C_2$ in terms of $C_1$ is

Two identical capacitors A and B are connected in series to a battery of E.M.F., 'E'. Capacitor B contains a slab of dielectric constant $K,\ Q_{A}$ and $Q_{B}$ are the charges stored in A and B. When the dielectric slab is removed, the corresponding charges are $Q'_{A}$ and $Q'_{B}$. Then

In case of system of two-particles of different masses, the centre of mass lies

A particle starting from rest moves along the circumference of a circle of radius ' $r$ ' with angular acceleration ' $\alpha$ '. The magnitude of the average velocity in time it completes the small angular displacement ' $\theta$ ' is

The potential difference $(V_A - V_B)$ between the points A and B in the given part of the circuit

When a resistance of $100\ \Omega$ is connected in series with a galvanometer of resistance G, its range is V. To double its range a resistance of $1000\ \Omega$ is connected in series. The value of G is

The figure shows the variation of photocurrent with anode potential for four different radiations. Let $\mathrm{I_a}, \mathrm{I_b}, \mathrm{I_c}$ and $\mathrm{I_d}$ be the intensities for the curves $a, b, c$ and $d$ respectively $[f_a, f_b, f_c$ and $f_d$ are frequencies respectively]

A coil of resistance $250\,\Omega$ is placed in a magnetic field. If the magnetic flux $(\phi)$ linked with the coil varies with time $t(\text{s})$ as $\phi = 50t^{2} + 7$. The current in the coil at $t = 4\text{ s}$ is

The mutual inductance of two coils is 45 mH. The self-inductance of the coils are $L_1 = 75\text{ mH}$ and $L_2 = 48\text{ mH}$. The coefficient of coupling between the two coils is

A graph of magnetic flux $(\phi)$ versus current (I) is shown for 4 different inductors $P, Q, R, S$. Minimum value of inductance is for inductor

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

Two point charges $+8q$ and $-2q$ are located at $x = 0$ and $x = L$ respectively. The location of a point on the $x$-axis from the origin, at which the net electric field due to these two point charges is zero is

A cylinder contains water upto a height ' $H$ '. It has three orifices $O_1, O_2, O_3$ as shown in the figure. Let $V_1, V_2, V_3$ be the speed of efflux of water from the three orifices. Then

A simple pendulum has a periodic time ' $T_1$ ' when it is on the surface of earth of radius ' $R$ '. Its periodic time is ' $T_2$ ' when it is taken to a height ' $R$ ' above the earth's surface. The value of $\frac{T_2}{T_1}$ is

The speed with which the earth would have to rotate about its axis so that a person on the equator would weigh $\frac{3}{5}$ th as much as at present weight is ( $g =$ gravitational acceleration, $R =$ equatorial radius of the earth)

A satellite is orbiting just above the surface of the planet of density ' $\rho$ ' with periodic time ' $T$ '. The quantity $T^2\rho$ is equal to ( $G =$ universal gravitational constant)

A bucket full of hot water is kept in a room. If it cools from $75^\circ\text{C}$ to $70^\circ\text{C}$ in $t_1$ minutes, from $70^\circ\text{C}$ to $65^\circ\text{C}$ in $t_2$ minutes and $65^\circ\text{C}$ to $60^\circ\text{C}$ in $t_3$ minutes, then

The power radiated by a black body is P and it radiates maximum energy around the wavelength $\lambda_0$. Now the temperature of the black body is changed so that it radiates maximum energy around wavelength $\left(\frac{\lambda_0}{2}\right)$. The power radiated by it will now increase by a factor of

Assuming the expression for the pressure exerted by the gas, it can be shown that pressure is

The materials having negative magnetic susceptibility are

The co-ordinates of a moving particle at any time ' $t$ ' are given by $x = \alpha t^3$ and $y = \beta t^3$ where $\alpha$ and $\beta$ are constants. The speed of the particle at time ' $t$ ' is given by

The magnetic induction along the axis of a toroidal solenoid is independent of

Two coils P and Q each of radius R carry currents I and $\sqrt{8}\, I$ respectively in same direction. Those coils are lying in perpendicular planes such that they have a common centre. The magnitude of the magnetic field at the common centre of the two coils is ( $\mu_0 =$ permeability of free space)

If $\mathrm{M_O}$ is the mass of an oxygen isotope ${}_{8}\text{O}^{17}$ and $\mathrm{M_p}$ and $\mathrm{M_N}$ are the mass of proton and mass of neutron respectively, then the nucleus binding energy of the isotope is

A particle executing S.H.M. has velocities ' $V_1$ ' and ' $V_2$ ' at distances ' $x_1$ ' and ' $x_2$ ' respectively, from the mean position. Its frequency is

Optical path of a particular ray of light has travelled a distance of 3 cm in flint glass is same as that on travelling a distance ' $x$ ' cm through another medium. The value of ' $x$ ' is [refractive index of flint glass $= 1.6$, refractive index of another medium $= 1.25]$

A glass slab of thickness 4.8 cm is placed on the piece of paper on which an ink dot is marked. By how much distance would an ink dot appear to be raised? (The refractive index of glass $= 1.5$)

The angle of incidence is found to be twice the angle of refraction when ray of light passes from vacuum into a medium of refractive index ' $\mu$ '. The angle of incidence will be

Two spheres of equal masses, one of which is a thin spherical shell and the other solid sphere, have the same moment of inertia about their respective diameters. The ratio of their radii is

Two loops P and Q of radii $R_1$ and $R_2$ are made from uniform metal wire of same material. $I_p$ and $I_Q$ be the moment of inertia of loop P and Q respectively then ratio $R_1/R_2$ is $($ Given $I_P/I_Q = 27)$

The input signal given to C.E. amplifier having a voltage gain of 126 is $V_i = 2\cos\left(12t + \frac{\pi}{3}\right)$. The corresponding output signal will be

The truth table of the following circuit is

If the $p\text{-}n$ junction diode is unbiased,

When capillary is dipped vertically in water, rise of water in capillary is ' h '. The angle of contact is zero. Now the tube is depressed so that its length above the water surface is $\frac{h}{3}$. The new apparent angle of contact is $(\cos 0^\circ = 1)$

In most liquids, with rise in temperature, surface tension of a liquid

If heat energy $\Delta Q$ is supplied to an ideal diatomic gas, the increase in internal energy is $\Delta U$ and the amount of work done by the gas is $\Delta W$. The ratio $\Delta W : \Delta U : \Delta Q$ is

An ideal diatomic gas is heated at constant pressure. What is the fraction of total energy applied, which increases the internal energy for the gas?

In ideal gas of $27^\circ\text{C}$ is compressed adiabatically to $(8/27)$ of its original volume. If $\gamma = \frac{5}{3}$, the rise in temperature of a gas is

A string is under tension of 180 N and mass per unit length $2 \times 10^{-3}\text{ kg/m}$. It produces two consecutive resonant frequencies with a tuning fork, which are 375 Hz and 450 Hz. The mass of the string is

How many times more intense is a 60 dB sound than a 30 dB sound?

The angular separation of the central maximum in the Fraunhofer diffraction pattern is measured. The slit is illuminated by the light of wavelength $6000\text{ \AA}$. If the slit is illuminated by light of another wavelength, the angular separation decreases by $20\%$. The wavelength of light used is

Two sound waves each of wavelength ' $\lambda$ ' and having the same amplitude ' $A$ ' from two source ' $S_1$ ' and ' $S_2$ ' interfere at a point P. If the path difference, $S_2P - S_1P = \lambda/3$ then the amplitude of resultant wave at point ' P ' will be $[\cos(120^\circ) = -0.5]$

In Young's double slit experiment, intensity at a point is $\left(\frac{1}{4}\right)$ of the maximum intensity. The angular position of this point is

A simple pendulum of length L has mass m and it oscillates freely with amplitude A. At extreme position, its potential energy is ( $\text{g} =$ acceleration due to gravity)

The power $(P)$ is supplied to a rotating body having moment of inertia ' I ' and angular acceleration ' $\alpha$ '. Its instantaneous angular velocity ' $\omega$ ' is