MHT CET 2024 Physics Paper: 4 May, Shift 1

An inductor of inductance $2\ \mu\text{H}$ is connected in series with a resistance, a variable capacitor and an a.c. source of frequency 5 kHz. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x}\text{ F}$, where the value of ' $x$ ' is (Take $\pi^2 = 10$)

In LCR series circuit if the frequency is increased, the impedance of the circuit

For the given figure, choose the correct option.

For hydrogen atom, ' $\lambda_{1}$ ' and ' $\lambda_{2}$ ' are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of ' $\lambda_{1}$ ' and ' $\lambda_{2}$ ' is $\frac{x}{32}$. The value of ' $x$ ' is

A parallel plate capacitor has plate area $40\text{ cm}^2$ and plate separation 2 mm. The space between the plates is filled with a dielectric medium of thickness 1 mm and dielectric constant 5. The capacitance of the system is ( $\varepsilon_0 =$ permittivity of vacuum)

A parallel plate air capacitor, with plate separation ' d ' has a capacitance of 9 pF. The space between the plates is now filled with two dielectrics, the first having $K_1 = 3$ and thickness $d_1 = d/3$, while the $2$nd has $K_2 = 6$ and thickness $d_2 = 2d/3$. The capacitance of the new capacitor is:

A potentiometer wire of length 1 m is connected in series with $495\ \Omega$ resistance and 2 V battery. If $0.2\text{ mV/cm}$ is the potential gradient, then the resistance of the potentiometer wire is

In a meter bridge experiment, the balance point is obtained if the gaps are closed by $2\ \Omega$ and $3\ \Omega$. A shunt of $X\ \Omega$ is added to $3\ \Omega$ resistor to shift the null point by 22.5 cm. The value of ' $x$ ' is

For a photosensitive material, work function is ' $W_0$ ' and stopping potential is ' V '. The wavelength of incident radiation is ( $h =$ Planck's constant, $c =$ velocity of light, $e =$ electronic charge)

The threshold frequency of a metal is ' $F_0$ '. When light of frequency $2F_0$ is incident on the metal plate, the maximum velocity of photoelectron is ' $V_1$ '. When the frequency of incident radiation is increased to ' $5F_0$ ', the maximum velocity of photoelectrons emitted is ' $V_2$ '. The ratio of $V_1$ to $V_2$ is

A square loop of area $25\text{ cm}^{2}$ has a resistance of $10\ \Omega$. The loop is placed in uniform magnetic field of magnitude 40 T. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in 1 second, will be

A circular coil of resistance $R$, area $A$, number of turns ' $N$ ' is rotated about its vertical diameter with angular speed ' $\omega$ ' in a uniform magnetic field of magnitude ' $B$ '. The average power dissipated in a complete cycle is

A graph of magnetic flux $(\phi)$ versus current ( 1) is shown for four inductors A, B, C, D. Smaller value of self inductance is for inductor

The electric potential at the centre of two concentric half rings of radii $R_1$ and $R_2$, having same linear charge density ' $\lambda$ ' is ($\varepsilon_0 =$ permittivity of free space)

A metallic sphere ' A ' isolated from ground is charged to $+50\,\mu\text{C}$. This sphere is brought in contact with other isolated metallic sphere ' $B$ ' of half the radius of sphere ' $A$ '. Then the charge on the two isolated spheres A \& B are in the ratio

The surface of water in a water tank of cross section area $750\text{ cm}^2$ on the top of a house is ' $h$ ' $\text{m}$ above the tap level. The speed of water coming out through the tap of cross section area $500\text{ mm}^2$ is $30\text{ cm/s}$. At that instant $\frac{dh}{dt}$ is $x \times 10^{-3}\text{ m/s}$. The value of ' $x$ ' will be

If ' $R$ ' is the radius of earth \& ' $g$ ' is acceleration due to gravity on earth's surface, then mean density of earth is

The height ' $h$ ' above the earth's surface at which the value of acceleration due to gravity $(g)$ becomes $\left(\frac{g}{3}\right)$ is ( $R =$ radius of the earth)

Two rods of same length \& material transfer a given amount of heat in 12 s when they are joined end to end. But when they are joined length wise parallel to each other they will transfer same amount of heat in same condition in time

A sphere is at temperature 600 K. In an external environment of 200 K, its cooling rate is ' $R$ ' When the temperature of the sphere falls to 400 K, then cooling rate ' $R'$ ' will become

The magnetic moments associated with two closely wound circular coils A and B of radius $r_A = 10\text{ cm}$ and $r_B = 20\text{ cm}$ respectively are equal if $(N_A, I_A$ and $N_B, I_B$ are number of turns and current of A and B respectively)

A massless square loop of wire of resistance ' $R$ ' supporting a mass ' M ' hangs vertically with one of its sides in a uniform magnetic field ' B ' directed outwards in the shaded region. A d.c. voltage ' V ' is applied to the loop. For what value of ' $V$ ' the magnetic force will exactly balance the weight of the supporting mass ' M '? (side of loop = L, $g =$ acceleration due to gravity)

A charged particle of charge ' $q$ ' is accelerated by a potential difference ' $V$ ' enters a region of uniform magnetic field ' $B$ ' at right angles to the direction of field. The charged particle completes semicircle of radius ' $r$ ' inside magnetic field. The mass of the charged particle is

A charged particle is moving in a uniform magnetic field in a circular path with radius ' $R$ '. When the energy of the particle is doubled, then the new radius will be

A simple pendulum of length $l_1$ has time period $T_1$. Another simple pendulum of length $l_2\ (l_1 > l_2)$ has time period $T_2$. Then the time period of the pendulum of length $(l_1 - l_2)$ will be

Two bodies A and B of equal mass are suspended from two separate massless springs of spring constants $K_1$ and $K_2$ respectively. The two bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitude of $B$ to that of $A$ is

The velocity of particle executing S.H.M. varies with displacement $(x)$ as $4V^2 = 50 - x^2$. The time period of oscillation is $\frac{x}{7}$ second. The value of ' $x$ ' is (Take $\pi = \frac{22}{7}$)

For a projectile, the maximum height and horizontal range are same. The angle of projection ' $\theta$ ' of the projectile is

Focal length of objective of an astronomical telescope is 1.5 m. Under normal adjustment, length of telescope is 1.56 m. Focal length of the eyepiece is

A person is observing a bacteria through a compound microscope. For better analysis and to improve the resolving power he should

In an equilateral prism the ray undergoes minimum deviation when it is incident at an angle of $50^\circ$. The angle of minimum deviation is

A ray of light is incident normally on a glass slab to thickness 5 cm and refractive index 1.6. The time taken to travel by a ray from source of light to surface of slab is same as to travel through glass slab. The distance of source from the surface is

A disc and a ring both have same mass and radius. The ratio of moment of inertia of the disc about its diameter to that of a ring about a tangent in its plane is

A rotating body has angular momentum ' $L$ '. If its frequency is doubled and kinetic energy is halved, its angular momentum will be

A solid cylinder of mass M and radius R is rotating about its geometrical axis. A solid sphere of the same mass and same radius is also rotating about its diameter with an angular speed half that of the cylinder. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder will be

The collector supply voltage is 6 V and a voltage drop across a resistor of $600\ \Omega$ in the collector circuit is 0.6 V, in a circuit of transistor connected in common emitter mode. If the current gain is 20 then the base current is

A semiconductor device X is connected in series with a battery and a resistor. The current of 10 mA is found to pass through the circuit. If the terminals of X are connected in reverse manner, the current drops to almost zero. X may be

A zener diode, having breakdown voltage 15 V is used in a voltage regulator circuit as shown. The current through the zener diode is

Water rises up to height ' $X$ ' in a capillary tube immersed vertically in water. When the whole arrangement is taken to a depth ' d ' in a mine, the water level rises up to height ' $Y$ '. If ' $R$ ' is the radius of earth then the ratio $\frac{Y}{X}$ is

The excess pressure inside a spherical drop of water A is four times that of another drop B. Then the ratio of mass of drop $A$ to that of drop $B$ is

An insulated container contains a monoatomic gas of molar mass ' $m$ '. The container is moving with velocity ' $V$ '. If it is stopped suddenly, the change in temperature is ( $R =$ gas constant)

A carnot engine, whose efficiency is $40\%$ takes heat from a source maintained at temperature 600 K. It is desired to have an efficiency $60\%$, then the intake temperature for the same exhaust (sink) temperature should be

According to the law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is

In an isobaric process of an ideal gas, the ratio of work done by the system to the heat supplied $\left(\frac{W}{Q}\right)$ is

Two waves $Y_1 = 0.25\sin 316t$ and $Y_2 = 0.25\sin 310t$ are propagating along the same direction. The number of beats produced per second are

The distance between two consecutive points with phase difference of $60^\circ$ in wave of frequency 500 Hz is 0.6 m. The velocity with which wave is travelling is

A progressive wave of frequency 400 Hz is travelling with a velocity $336\text{ m/s}$. How far apart are the two points which are $60^\circ$ out of phase?

A string A has twice the length, twice the diameter, twice the tension and twice the density of another string B. The overtone of A which will have the same fundamental frequency as that of $B$ is

Three identical polaroids $P_1, P_2$ and $P_3$ are placed one after another. The pass axis of $P_2$ and $P_3$ are inclined at an angle $60^\circ$ and $90^\circ$ with respect to axis of $P_1$. The source has an intensity $I_0$. The intensity of transmitted light through $P_3$ is $\left(\cos 60^\circ = 0.5, \cos 30^\circ = \frac{\sqrt{3}}{2}\right)$