MHT CET 2024 Physics Paper: 9 May, Shift 1

Average power associated with an ideal inductor and ideal capacitor over a complete cycle of a.c. is respectively

LC series resonant circuit produces resonant frequency ' $f$ '. If ' $L$ ' is tripled and ' $C$ ' is increased by $3C$, the resonant frequency will be

When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit

When a hydrogen atom is raised from the ground state to the excited state

In hydrogen atom, ratio of the shortest wavelength in the Balmer series to that in the Paschen series is

According to Bohr's theory of hydrogen atom, the ratio of the maximum and minimum wavelength of Lyman series will be

In the given circuit diagram, in the steady state the current through the battery and the charge on the capacitor respectively are

A parallel plate capacitor of capacitance ' $C$ ' is connected to a battery and charged to a potential difference ' $V$ '. Another capacitor of capacitance 3 C is similarly charged to a potential difference 3 V. The charging battery is then disconnected and capacitors are connected in parallel to each other in such a way that positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

The function of dielectric in a capacitor is

In the system of two particles of masses ' $m_1$ ' and ' $m_2$ ', the first particle is moved by a distance 'd' towards the centre of mass. To keep the centre of mass unchanged, the second particle will have to be moved by a distance

In an ammeter, $4\%$ of the main current is passing through the galvanometer, If shunt resistance is $5\ \Omega$, then resistance of galvanometer will be

When the two known resistances ' $R$ ' and ' $S$ ' are connected in the left and right gaps of a meter bridge respectively, the null point is found at a distance ' $l_1$ ' from the zero end of a meter bridge wire. An unknown resistance ' X ' is now connected in parallel with ' S ' and null point is found at a distance ' $l_2$ ' from zero end of meter bridge wire. The unknown resistance ' X ' is

The gyromagnetic ratio and Bohr magneton are given respectively by [Given $e =$ charge on electron, $m =$ mass of electron, $h =$ Planck's constant]

Two identical photocathodes receive light of frequencies ' $n_1$ ' and ' $n_2$ '. If the velocities of the emitted photoelectrons of mass ' $m$ ' are ' $V_1$ ' and ' $V_2$ ' respectively, then ( $h =$ Planck's constant)

The magnetic flux through a coil of resistance ' $R$ ' changes by an amount ' $\Delta\phi$ ' in time ' $\Delta t$ '. The amount of induced current and induced charge in the coil are respectively

Two coils have a mutual inductance $5 \times 10^{-3}\text{ H}$. The current changes in the first coil according to the equation $I_1 = I_0 \sin \omega t$ where $I_0 = 10\text{ A}$ and $\omega = 100\pi\text{ rad/s}$. What is the value of the maximum e.m.f. in the coil?

A metal rod of length ' $l$ ' rotates about one of its ends in a plane perpendicular to a magnetic field of induction ' $B$ '. If the e.m.f. induced between the ends of the rod is ' $e$ ', then the number of revolutions made by the rod per second is

If the electric flux entering and leaving an enclosed surface is $\phi_1$ and $\phi_2$ then charge enclosed in the surface is ($\varepsilon_0 =$ permittivity of free space)

Water is flowing in a conical tube as shown in figure. Velocity of water at area ' $A_2$ ' is $60\text{ cm/s}$. The value of ' $A_1$ ' and ' $A_2$ ' is $10\text{ cm}^2$ and $5\text{ cm}^2$ respectively. The pressure difference at both the cross- section is

When an air bubble rises from the bottom of lake to the surface, its radius is doubled. The atmospheric pressure is equal to that of a column of water of height ' $H$ '. The depth of the lake is

The period of a planet around the sun is 8 times that of earth. The ratio of radius of planet's orbit to the radius of the earth's orbit is

Two satellites A and B having ratio of masses $3 : 1$ are revolving in circular orbits of radii ' $r$ ' and ' 4 r '. The ratio of total energy of satellites A to that of B is

Three identical metal spheres (of same surface area) have red, black and white colors and they are heated up to same temperature. They are allowed to cool. Arrange them from maximum rate of cooling to minimum rate of cooling

The temperature of a gas is $-80^\circ\text{C}$. To what temperature the gas should be heated so that the r.m.s. speed is increased by 2 times?

A velocity - time graph of a body is shown below. The distance covered by the body from 6 second to 9 second is

The magnetic induction due to an ideal solenoid is independent of

The magnetic field intensity inside current carrying solenoid is $\mathrm{H} = 2.4 \times 10^{3}\text{ A/m}$. If length and number of turns of a solenoid is 15 cm and 60 turns respectively. The current flowing in the solenoid is

In S.H.M. the displacement of a particle at an instant is $Y = A\cos 30^\circ$, where $A = 40\text{ cm}$ and kinetic energy is 200 J. If force constant is $1 \times 10^{x}\text{ N/m}$, then x will be $\left(\cos 30^\circ = \sqrt{3}/2\right)$

A particle is performing S.H.M. with an amplitude 4 cm. At the mean position the velocity of the particle is $12\text{ cm/s}$. When the speed of the particle becomes $6\text{ cm/s}$, the distance of the particle from mean position is

Three immiscible transparent liquids with uniform refractive indices $\frac{3}{2}, \frac{4}{3}$ and $\frac{6}{5}$ are arranged one on top of another. The depths of the liquids are 3 cm 4 cm and 6 cm respectively. The apparent depth of the vessel is

A point object kept at P in front of a glass sphere of radius ' $R$ ' has its image formed at $Q$ such that $\text{PO} = \text{QO}$. The refractive index of material of glass sphere is 1.4. The distance PO is equal to

Velocity of light in diamond is $\left(\frac{5}{12}\right)$th times that in air. Velocity of light in water is $\left(\frac{3}{4}\right)$th times that in air. The angle of incidence of ray of light travelling from water to diamond is (angle of refraction $(r) = 30^\circ) [$ Given $\rightarrow \sin 30^\circ = \frac{1}{2}]$

The moment of inertia of thin square plate PQRS of uniform thickness, about an axis passing through centre ' O ' and perpendicular to the plane of the plate is $(I_1, I_2, I_3, I_4$ are respectively the moments of inertia about axis $1, 2, 3, 4$ which are in the plane of the plate as shown in figure)

A circular disc of radius ' $R$ ' and thickness $\frac{R}{6}$ has moment of inertia 'I' about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere then moment of inertia of sphere about an axis passing through diameter is

A thin uniform rod of length ' $L$ ' and mass ' $M$ ' is swinging freely along a horizontal axis passing through its centre. Its maximum angular speed is ' $\omega$ '. Its centre of mass rises to a maximum height of [ $g =$ gravitational acceleration]

The current amplification factor of a transistor is 50. The input resistance when used in common emitter mode is $1\text{ k}\Omega$. The peak value for an a.c. input voltage of 0.01 V peak is

In the logic circuit diagram, when all the four inputs $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ are one, the outputs $\mathrm{Y}_1, \mathrm{Y}_2, \mathrm{Y}_3$ are respectively $(1, 1, 0)$. When all the inputs $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ are changed to 'zero', the outputs $\mathrm{Y}_1, \mathrm{Y}_2, \mathrm{Y}_3$ respectively change to

For the diagram shown, the resistance between points A and B when the ideal diode ' $D$ ' is forward biased is ' $R_1$ ' and that when reverse biased is ' $R_2$ '. The ratio $\frac{R_1}{R_2}$ is

A gas is contained in closed vessel. The initial temperature of the gas is $100^\circ\text{C}$. If the pressure of the gas is increased by $4\%$, the increase in the temperature of the gas is

The internal energy of a gas will increase when it

For an ideal gas, in an isobaric process, the ratio of heat supplied ' $Q$ ' to the work done ' $w$ ' by the system is ( $\gamma =$ ratio of specific heat at constant pressure to that at constant volume)

At certain temperature, $\text{rod A}$ and $\text{rod B}$ of different materials have lengths $\text{L}_{\text{A}}$ and $\text{L}_{\text{B}}$ respectively. Their coefficients of linear expansion are $\alpha_A$ and $\alpha_B$ respectively. It is observed that the difference between their lengths remains constant at all temperatures. The ratio $\text{L}_{\text{A}} : \text{L}_{\text{B}}$ is given by

A tuning fork of frequency 340 Hz is vibrated just above a tube of 120 cm height. Water is slowly poured in the tube. What is the minimum height of water necessary for resonance?

Two sound waves having same amplitude ' $A$ ' and angular frequency ' $\omega$ ' but having a phase difference of $\left(\frac{\pi}{2}\right)^{c}$ are superimposed then the maximum amplitude of the resultant wave is

When the tension in string is increased by $3\text{ kg wt}$, the frequency of the fundamental mode increases in the ratio $2:3$. The initial tension in the string is

A sonometer wire is stretched by hanging a metal bob, the fundamental frequency of the wire is ' $n_1$ '. When 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

Out of the following musical instruments, which is 'NOT' a percussion instrument?

Two wavelength 590 nm and 596 nm of sodium light are used one after other, to study the diffraction taking place at a single slit of aperture 2.4 mm. The distance between the slit and screen is 2 m. The separation between the positions of first secondary maximum of the diffraction pattern obtained in the two cases is

A wavefront is a surface

The potential energy of a long spring when it is stretched by 3 cm is ' $U$ '. If the spring is stretched by 9 cm, potential energy stored in it will be