MHT CET 2024 Physics Paper: 3 May, Shift 1

A transformer having efficiency $90\%$ is working on 200 V and 3 kw power supply. If the current in the secondary coil is 6 A, the voltage across the secondary coil and the current in the primary coil are respectively

Three inductances are connected as shown in figure. The equivalent inductance is

In an $AC$ circuit $E = 200\sin(50t)$ volt and $I = 100\sin\left(50t + \frac{\pi}{3}\right)\text{ mA}$. The power dissipated in the circuit is

$\left(\begin{matrix}\sin 30^\circ = \cos 60^\circ = 0.5 \\ \sin 60^\circ = \cos 30^\circ = \sqrt{3}/2\end{matrix}\right)$

An alternating voltage $v = 200\sqrt{2} \sin(100t)$ is connected to a $1\ \mu F$ capacitor through an a. c. ammeter. The reading of the ammeter shall be

An inductance coil has a resistance of $80\ \Omega$. When on AC signal of frequency 480 Hz is applied to the coil, the voltage leads the current by $45^\circ$. The inductance of the coil in henry is

$\left[\sin 45^\circ = \cos 45^\circ = 1/\sqrt{2}\right]$

If ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths of the first line of the Lyman and Paschen series respectively, then $\lambda_2 : \lambda_1$ is

Two circular metal plates each of radius ' $r$ ' are kept parallel to each other distance ' $d$ ' apart. The capacitance of the capacitor formed is ' $C_1$ '. If the radius of each of the plates is increased to $\sqrt{2}$ times the earlier radius and their distance of separation decreased to half the initial value, the capacitance now becomes ' $C_2$ '. The ratio of the capacitances $C_1 : C_2$ is

In the following circuit, a power of 50 watt is absorbed in the section AB of the circuit. The value of resistance ' $x$ ' is

The range of voltmeter of resistance ' $G$ ' $\Omega$ is ' $V$ ' volt. The resistance required to be connected in series with it in order to convert it into a voltmeter of range ' $nV$ ' volt, will be

The ratio of the wavelength of a photon of energy ' $E$ ' to that of the electron of same energy is ( $m =$ mass of an electron, $c =$ speed of light, $h =$ Planck's constant)

When photons of energy hv fall on a photosensitive surface of work function $E_0$, photoelectrons of maximum energy $k$ are emitted. If the frequency of radiation is doubled the maximum kinetic energy will be equal to ( $h =$ Planck's constant)

In an a. c. generator, when the plane of the coil is perpendicular to the magnetic field

Two equal point charges ' $q$ ' each exert a force ' $F$ ' on each other, when they are placed distance ' $x$ ' apart in air. When the same charges are placed distance ' $y$ ' apart in a medium of dielectric constant ' $k$ ', they exert the same force. The ratio of distance ' $y$ ' to ' $x$ ' is equal to

An electric dipole of moment$\vec{p}$is lying along a uniform electric field $\vec{E}$. The work done in rotating the dipole through $\frac{\pi^c}{3}$ is $\left[\sin 30^\circ = \cos 60^\circ = 0.5,\ \cos 30^\circ = \sin 60^\circ = \sqrt{3}/2\right]$

Three charges $2q, -q$ and $-q$ are located at the vertices of an equilateral triangle. At the centre of the triangle

A gardening pipe having an internal radius ' $R$ ' is connected to a water sprinkler having ' $n$ ' holes each of radius ' $r$ '. The water in the pipe has a speed ' $v$ '. The speed of water leaving the sprinkler is

Earth has mass ' $M_1$ ' radius ' $R_1$ ' and for moon mass ' $M_2$ ' and radius ' $R_2$ '. Distance between their centres is ' $r$ '. A body of mass ' $M$ ' is placed on the line joining them at a distance $\frac{r}{3}$ from the centre of the earth. To project a mass ' $M$ ' to escape to infinity, the minimum speed required is

The distance of the two planets A and B from the sun are $r_A$ and $r_B$ respectively. Also $r_B$ is equal to $100r_A$. If the orbital speed of the planet $A$ is ' $v$ ' then the orbital speed of the planet B is

Given that ' $x$ ' joule of heat is incident on a body. Out of that, total heat reflected and transmitted is ' $y$ ' joule. The absorption coefficient of body is

Two spherical black bodies of radii ' $R_1$ ' and ' $R_2$ ' and with surface temperature ' $T_1$ ' and ' $T_2$ ' respectively radiate the same power. The ratio of ' $R_1$ ' to ' $R_2$ ' will be

Two blocks of masses 6 kg and 4 kg are placed in contact with each other on a smooth surface as shown. If a force of 5 N is applied on a heavier block, the force on the lighter block is

The relation between total magnetic field (B), magnetic intensity $(H)$, permeability of free space $(\mu_0)$ and susceptibility $(\chi)$ is

A magnetic needle of magnetic moment $6 \times 10^{-2}\text{ Am}^{2}$ and moment of inertia $9.6 \times 10^{-5}\text{ kg m}^{2}$ performs simple harmonic motion in a magnetic field of 0.01 T. Time taken to complete 10 oscillations is [Take $\pi = 3.14$]

A current of 5 A flows through a toroid having a core of mean radius 20 cm. If 4000 turns of the conducting wire are wound on the core, then the magnetic field inside the core of the toroid is [permeability of free space $= 4\pi \times 10^{-7}$ SI units]

A particle having a charge 50 e is revolving in a circular path of radius 0.4 m with $1\text{ r.p.s}$. The magnetic field produced at the centre of the circle is $(\mu_0 = 4\pi \times 10^{-7}$ SI units and $e = 1.6 \times 10^{-19}\text{ C}$)

In the uranium radioactive series, the initial nucleus is ${}^{238}_{92}\text{U}$ and that the final nucleus is ${}^{206}_{82}\text{Pb}$. When uranium nucleus decays into lead, the number of $\alpha$-particles and $\beta$-particles emitted are

A small sphere oscillates simple harmonically in a watch glass whose radius of curvature is 1.6 m. The period of oscillation of the sphere in second is (acceleration due to gravity, $g = 10\text{ m/s}^2$)

A tube of uniform bore of cross-sectional area ' $A$ ' has been set up vertically with open end facing up. Now ' $M$ ' gram of a liquid of density ' $d$ ' is poured into it. The column of liquid in this tube will oscillate with a period ' T ', which is equal to [ $g =$ acceleration due to gravity]

A ray of light is incident at $60^\circ$ on one face of a prism of angle $30^\circ$ and the emergent ray makes $30^\circ$ with the incident ray. The refractive index of the prism is $\left(\sin 30^\circ = 0.5, \sin 60^\circ = \sqrt{3}/2\right)$

A convex lens of focal length ' $f$ ' $m$ forms a real, inverted image twice in size of the object. The object distance from the lens in metre is

Ratio of radius of gyration of a circular disc to that of circular ring each of same mass and radius around their respective axes is

Two circular loops P and Q of radii ' r ' and ' nr ' are made respectively from a uniform wire. Moment of inertia of loop Q about its axis is four times that of loop P about its axis. The value of ' $n$ ' is

In case of rotational dynamics, which one of the following statements is correct? [$\vec{\omega} =$ angular velocity,$\vec{v} =$ linear velocity

$\vec{r} =$ radius vector, $\vec{\alpha} =$ angular acceleration

$\vec{a} =$ linear acceleration,$\vec{L} =$ angular momentum

$\vec{p} =$ linear momentum, $\vec{\tau} =$ torque,

$\vec{f} =$ centripetal force]

An n-p-n transistor can be considered to be equivalent to two diodes connected. The correct figure out of the following is

In common emitter transistor amplifier, load resistance is $6.5\text{ k}\Omega$ and an input resistance is $1.3\text{ k}\Omega$. If the current gain is 78, the voltage gain is

Find the magnitude of current in the given circuit.

The pressure inside two soap bubbles, (A) is 1.01 and that of (B) is 1.02 atmosphere respectively. The ratio of their respective radii (A to B) is (outside pressure $= 1\text{ atm}$.)

A diatomic ideal gas is used in Carnot engine as a working substance. If during the adiabatic expansion part of the cycle, the volume of the gas increases from V to 32 V, the efficiency of the engine is

The r.m.s. velocity of hydrogen at S.T.P. is ' $u$ ' $\text{m/s}$. If the gas is heated at constant pressure till its volume becomes three times, then the final temperature of the gas and the r.m.s. speed are respectively

There are two samples A and B of a certain gas, which are initially at the same temperature and pressure. Both are compressed from volume v to $\frac{v}{2}$. Sample A is compressed isothermally while sample B is compressed adiabatically. The final pressure of $A$ is

Two rods, one of aluminium and the other of steel, having initial lengths ' $L_1$ ' and ' $L_2$ ' are connected together to form a single rod of length $(L_1 + L_2)$. The coefficients of linear expansion of aluminium and steel are ' $\alpha_1$ ' and ' $\alpha_2$ ' respectively. If the length of each rod increases by the same amount, when their temperatures are raised by $t^{\circ}\text{C}$, then the ratio $\frac{L_1}{L_1 + L_2}$ will be

A metal ball of radius $9 \times 10^{-4}\text{ m}$ and density $10^{4}\text{ kg/m}^{3}$ falls freely under gravity through a distance ' h ' and enters a tank of water. Considering that the metal ball has constant velocity, the value of $h$ is [coefficient of viscosity of water $= 8.1 \times 10^{-4}\text{ Pa-s},\ \mathrm{g} = 10\text{ m/s}^{2}$ density of water $= 10^{3}\text{ kg/m}^{3}]$

The pitch of a whistle of an engine appears to drop by $30\%$ of original value when it passes a stationary observer. If the speed of sound in air is $350\text{ ms}^{-1}$, then the speed of engine in $\text{ms}^{-1}$ is

The fundamental frequency of an air column in a pipe open at both ends is ' $f_1$ '. Now $80\%$ of its length is immersed in water, the fundamental frequency of the air column becomes $f_2$. The ratio of $f_1 : f_2$ is

The displacement of a wave is given by $y = 0.002\sin(100t + x)$ where ' $x$ 'and ' $y$ ' are in metre and ' $t$ ' is in second. This represents a wave

The path difference between two waves $Y_1 = a_1\sin\left(\omega t - \frac{2\pi x}{\lambda}\right)$ and $Y_2 = a_2\cos\left(\omega t - \frac{2\pi x}{\lambda} + \phi\right)$ is

A single slit diffraction pattern is formed with light of wavelength $6195\text{ Å}$. The second secondary maximum for this wavelength coincides with the third secondary maximum in the pattern for light of wavelength ' $\lambda_0$ '. The value of ' $\lambda_0$ ' is

When wavefronts pass from denser medium to rarer medium, the width of the wavefront

In an interference experiment, the $n$th bright fringe for light of wavelength $\lambda_1 (n = 0, 1, 2, 3 \ldots)$ coincides with the $m$th dark fringe for light of wavelength $\lambda_2 (m = 1, 2, 3 \ldots)$. The ratio $\frac{\lambda_1}{\lambda_2}$ is

A ball ' $A$ ' is projected vertically upwards with certain initial speed. Another ball 'B' of same mass is projected at an angle of $30^\circ$ with vertical with the same initial speed. At the highest point, the ratio of potential energy of ball A to that of ball B will be

$\left(\sin 90^\circ = 1, \sin 60^\circ = \cos 30^\circ = \frac{\sqrt{3}}{2}, \sin 30^\circ = \cos 60^\circ = \frac{1}{2}\right)$