MHT CET 2023 Physics Paper: 12 May, Shift 1

An inductor of $0.5\text{ mH}$, a capacitor of $20\ \mu\text{F}$ and a resistance of $20\ \Omega$ are connected in series with a $220\text{ V}$ a.c. source. If the current is in phase with the e.m.f. the maximum current in the circuit is $\sqrt{x}\text{ A}$. The value of '$x$' is

In the given circuit, if $\frac{dI}{dt} = -1\text{ A/s}$ then the value of $(V_A - V_B)$ at this instance will be

In the given circuit, r.m.s. value of current through the resistor $R$ is

In Lyman series, series limit of wavelength is $\lambda_1$. The wavelength of first line of Lyman series is $\lambda_2$ and in Balmer series, the series limit of wavelength is $\lambda_3$. Then the relation between $\lambda_1, \lambda_2$ and $\lambda_3$ is

The wavelength of 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 $\frac{20}{x}\lambda_{0}$. The value of $x$ is

The potential on the plates of capacitor are $+20\text{ V}$ and $-20\text{ V}$. The charge on the plate is $40\text{ C}$. The capacitance of the capacitor is

In the given capacitive network the resultant capacitance between point $A$ and $B$ is

The equivalent capacity between terminal $A$ and $B$ is

Two particles having mass '$M$' and '$m$' are moving in a circular path with radius '$R$' and '$r$' respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to the second particle will be

A railway track is banked for a speed ',$v$' by elevating outer rail by a height '$h$' above the inner rail. The distance between two rails is 'd' then the radius of curvature of track is ( $g =$ gravitational acceleration)

Resistance of a potentiometer wire is $2\ \Omega/\text{m}$. A cell of e.m.f. $1.5\text{ V}$ balances at $300\text{ cm}$. The current through the wire is

A potentiometer wire has length of $5\text{ m}$ and resistance of $16\ \Omega$. The driving cell has an e.m.f. of $5\text{ V}$ and an internal resistance of $4\ \Omega$. When the two cells of e.m.f.s $1.3\text{ V}$ and $1.1\text{ V}$ are connected so as to assist each other and then oppose each other, the balancing lengths are respectively

Radiations of two photons having energies twice and five times the work function of metal are incident successively on metal surface. The ratio of the maximum velocity of photo electrons emitted in the two cases will be

When light of wavelength $\lambda$ is incident on a photosensitive surface the stopping potential is '$V$'. When light of wavelength $3\lambda$ is incident on same surface the stopping potential is $\frac{V}{6}$. Then the threshold wavelength for the surface is

Two coils have a mutual inductance of $0.004\text{ H}$. The current changes in the first coil according to equation $I = I_0 \sin \omega t$, where $I_0 = 10\text{ A}$ and $\omega = 50\pi\text{ rad s}^{-1}$. The maximum value of e.m.f. in the second coil in volt is

Two inductors of $60\text{ mH}$ each are joined in parallel. The current passing through this combination is $2.2\text{ A}$. The energy stored in this combination of inductors in joule is

Two electric dipoles of moment $P$ and $27P$ are placed on a line with their centres $24\text{ cm}$ apart. Their dipole moments are in opposite direction. At which point the electric field will be zero between the dipoles from the centre of dipole of moment P?

Time period of simple pendulum on earth's surface is '$T$'. Its time period becomes '$xT$' when taken to a height $R$ (equal to earth's radius) above the earth's surface. Then the value of '$x$' will be

The height at which the weight of the body becomes $\left(\frac{1}{9}\right)$th its weight on the surface of earth is $(R =$ radius of earth)

Consider a light planet revolving around a massive star in a circular orbit of radius '$r$' with time period '$T$'. If the gravitational force of attraction between the planet and the star is proportional to $r^{-\frac{7}{2}}$, then $T^2$ is proportional to

A composite slab consists of two materials having coefficient of thermal conductivity $K$ and $2K$, thickness $x$ and $4x$ respectively. The temperature of the two outer surfaces of a composite slab are $T_2$ and $T_1\ (T_2 > T_1)$. 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

About black body radiation, which of the following is the wrong statement?

A black sphere has radius '$R$' whose rate of radiation is '$E$' at temperature '$T$'. If radius is made $R/3$ and temperature '$3T$', the rate of radiation will be

Two similar coils each of radius $R$ are lying concentrically with their planes at right angles to each other. The current flowing in them are I and 2I. The resultant magnetic field of induction at the centre will be $(\mu_0 =$ Permeability of vacuum)

The magnetic moment of a current (I) carrying circular coil of radius '$r$' and number of turns '$n$' depends on

A single turn current loop in the shape of a right angle triangle with side $5\text{ cm},\ 12\text{ cm},\ 13\text{ cm}$ is carrying a current of $2\text{ A}$. The loop is in a uniform magnetic field of magnitude $0.75\text{ T}$ whose direction is parallel to the current in the $13\text{ cm}$ side of the loop. The magnitude of the magnetic force on the $5\text{ cm}$ side will be $\frac{x}{130}\text{ N}$. The value of '$x$' is

$A, B$ and $C$ are three parallel conductors of equal lengths and carry currents I, I and 2I respectively as shown in figure. Distance $AB$ and $BC$ is same as '$d$'. If '$F_1$' is the force exerted by $B$ on $A$ and $F_2$ is the force exerted by $C$ on $A$, then

Four massless springs whose force constants are $2K,\ 2K,\ K$ and $2K$ respectively are attached to a mass $M$ kept on a frictionless plane as shown in figure. If mass $M$ is displaced in horizontal direction then frequency of oscillating system is

A simple pendulum performs simple harmonic motion about $x = 0$ with an amplitude '$a$' and time period '$T$'. The speed of the pendulum at $x = \frac{a}{2}$ is

Converging or diverging ability of a lens or mirror is called

One of the necessary condition for total internal reflection to take place is

( $i =$ angle of incidence, $i_c =$ critical angle)

A thin uniform circular disc of mass '$M$' and radius '$R$' is rotating with angular velocity '$\omega$', in a horizontal plane about an axis passing through its centre and perpendicular to its plane. Another disc of same radius but of mass $\left(\frac{M}{2}\right)$ is placed gently on the first disc co-axially. The new angular velocity will be

$I_1$ is the moment of inertia of a circular disc about an axis passing through its centre and perpendicular to the plane of disc. $I_2$ is its moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $\text{CM}$ at a distance $\frac{2R}{3}$ from centre. The ratio of $I_1$ and $I_2$ is $x : 17$. The value of '$x$' is (R = radius of the disc)

The following logic gate combination is equivalent to

The logic gate combination circuit shown in the figure performs the logic function of

When forward bias is applied to a p-n junction, then what happens to the potential barrier $(V_B)$ and the width $(X)$ of the depletion region?

The excess pressure inside a first spherical drop of water is three times that of second spherical drop of water. Then the ratio of mass of first spherical drop to that of second spherical drop is

A spherical drop of liquid splits into 1000 identical spherical drops. If '$E_1$' is the surface energy of the original drop and '$E_2$' is the total surface energy of the resulting drops, then $\frac{E_1}{E_2} = \frac{x}{10}$. Then value of '$x$' is

Consider a soap film on a rectangular frame of wire of area $3 \times 3\text{ cm}^{2}$. If the area of the soap film is increased to $5 \times 5\text{ cm}^{2}$, the work done in the process will be (surface tension of soap is $2.5 \times 10^{-2}\text{ N/m})$

The molar specific heat of an ideal gas at constant pressure and constant volume is $C_p$ and $C_v$ respectively. If $R$ is universal gas constant and $\gamma = \frac{C_p}{C_v}$ then $C_v =$

Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and $\gamma_2$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio $\frac{\gamma_2}{\gamma_1}$ is

A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If $\frac{C_p}{C_v} = \gamma = 1.5$, then the increase in its temperature is

41 tuning forks are arranged in increasing order of frequency such that each produces 5 beats/second with next tuning fork. If frequency of last tuning fork is double that of frequency of first fork. Then frequency of first and last fork is

Two sounding sources send waves at certain temperature in air of wavelength $50\text{ cm}$ and $50.5\text{ cm}$ respectively. The frequency of sources differ by $6\text{ Hz}$. The velocity of sound in air at same temperature is

The displacement of two sinusoidal waves is given by the equation

$\begin{matrix} y_1 = 8\sin(20x - 30t) \\ y_2 = 8\sin(25x - 40t) \end{matrix}$

then the phase difference between the waves after time $t = 2\text{ s}$ and distance $x = 5\text{ cm}$ will be

A uniform string is vibrating with a fundamental frequency '$n$'. If radius and length of string both are doubled keeping tension constant then the new frequency of vibration is

In two separate setups for Biprism experiment using same wavelength, fringes of equal width are obtained. If ratio of slit separation is $2 : 3$ then the ratio of the distance between the slit and screen in the two setups is

A beam of light is incident on a glass plate at an angle of $60^\circ$. The reflected ray is polarized. If angle of incidence is $45^\circ$ then angle of refraction is

In Young's double slit experiment the intensities at two points, for the path difference $\frac{\lambda}{4}$ and $\frac{\lambda}{3}$ ($\lambda =$ wavelength of light used) are $I_1$ and $I_2$ respectively. If $I_0$ denotes the intensity produced by each one of the individual slits then $\frac{I_1 + I_2}{I_0}$ is equal to $\left(\cos 60^\circ = 0.5, \cos 45^\circ = \frac{1}{\sqrt{2}}\right)$