MHT CET 2021 Physics Paper: 22 Sep, Shift 1

The frequency of the output signal of an LC oscillator circuit is '$F$' Hz with a capacitance of 0.1 $\mu\text{F}$. If the value of the capacitor is increased to $0.2\ \mu\text{F}$, then the frequency of the output signal will be

In an a.c. circuit, a resistance R = 40 $\Omega$ and an inductance 'L' are connected in series. If the phase angle between voltage and current is 45 ${}^\circ$, then the value of the inductive reactance is (tan 45${}^\circ$ = 1)

An a.c. source of angular frequency '$\omega$' is fed across a resistor '$R$' and a capacitor '$C$' in series. The current registered is I. If now the frequency of source is changed to $\frac{\omega}{3}$ (but maintaining the same voltage), the current in the circuit is found to be halved. The ratio of reactance to resistance at the original frequency '$\omega$' will be

In the given figure potential at point 'A' is 900 volt and point 'B' is earthed. What will be the potential at point 'P'?

When the battery across the plates of a charged condenser is disconnected and a dielectric slab is introduced between its plates then the energy stored

If the charge on the capacitor is increased by 2 C the energy stored in it increased by 21%. Total original charge on the capacitor is

The angular displacement of body performing circular motion is given by $\theta = 5\sin\frac{\pi t}{6}$. The angular velocity of the body at $t = 3$ second will be $\left[\sin\frac{\pi}{2} = 1, \cos\frac{\pi}{2} = 0\right]$

If $\omega_1$ is angular velocity of hour hand of clock and $\omega_2$ is angular velocity of the earth, then the ratio $\omega_1$: $\omega_2$ is

A body performing uniform circular motion of radius 'R' has frequency 'n'. It centripetal acceleration is

If a current flowing in a coil is reduced to half of its initial value, the relation between the new energy $(E_2)$ and the original energy $(E_1)$ stored in the coil will be

The Kirchhoff's current law and voltage law are respectively based upon the conservation of

In a wheatstone's bridge, three resistances $\mathrm{P, Q}$ and $\mathrm{R}$ are connected in the three arms and the fourth arm is formed by two resistances $S_1$ and $S_2$ connected in parallel. The condition for the bridge to be balanced is

Kinetic energy of a proton is equal to energy '$E$' of a photon. Let '$\lambda_1$' be the de-Broglie wavelength of proton and '$\lambda_2$' is the wavelength of photon. If $\frac{\lambda_1}{\lambda_2} \propto E^{n}$, then the value of '$n$' is

When a light of wavelength '$\lambda$' falls on the emitter of a photocell, maximum speed of emitted photoelectrons is '$V$'. If the incident wavelength is changed to $\frac{2\lambda}{3}$, maximum speed of emitted photoelectrons will be

A wire of length 1 m is moving at a speed of 2 m/s perpendicular homogenous magnetic field of 0.5 T. The ends of the wire are joined to resistance 6$\Omega$. The rate at which work is being done to keep the wire moving at that speed is

A circular coil of radius '$R$' has '$N$' turns of a wire. The coefficient of self induction of the coil will be ( $\mu_0 =$ permeability of free space)

A point charge $Q$ is placed at the centre of the line joining two equal point charges $+q$ and $+q$. The value of $Q$ if the system of the charges is in equilibrium, is

The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is '$V_e$', then the escape velocity from the planet is

A cylindrical rod is having temperatures $\theta_1$ and $\theta_2$ at its ends. The rate of heat flow is '$Q$' $\text{J s}^{-1}$. All the linear dimensions of the rod are doubled by keeping the temperatures constant. What is the new rate of flow of heat?

If the temperature of the sun is doubled, the rate of energy received by the earth will be increased by a factor

The translational kinetic energy of the molecules of a gas at absolute temperature (T) can be doubled

The permeability of a metal is $0.1256\text{ TmA}^{-1}$. Its relative permeability will be $\left(\frac{\mu_0}{4\pi} = 10^{-7}\text{ SI unit}\right)$ ($\pi = 3.14$)

When a battery is connected to the two ends of a diagonal of a square conductor frame of side '$a$', the magnitude of magnetic field at the centre will be ( $\mu_0 =$ permeability of free space)

Two concentric coplanar circular loops of radii '$r_1$' and '$r_2$ ' respectively carry currents '$i_1$ ' and '$i_2$' in opposite directions (one clockwise and other anticlockwise). The magnetic induction at the centre of the loops is half that due to '$i_1$' alone at the centre. If $r_2 = 2r_1$, the value of $\frac{i_2}{i_1}$

Assuming the atom is in the ground state, the expression for the magnetic field at a point nucleus in hydrogen atom due to circular motion of electron is [$\mu_0 =$ permeability of free space, $m =$ mass of electron, $\epsilon_0 =$ permittivity of free space, $h =$ Planck's constant ]

A nucleus breaks into two nuclear parts, which have their velocity ratio $2 : 1$. The ratio of their nuclear radii will be

If the amplitude of linear S.H.M. is decreased then

A mass $0.4\text{ kg}$ performs S.H.M. with a frequency $\frac{16}{\pi}\text{ Hz}$. At a certain displacement it has kinetic energy $2\text{ J}$ and potential energy $1.2\text{ J}$. The amplitude of oscillation is

A biconvex lens $(R_1 = R_2 = 30\text{ cm})$ has focal length equal to the focal length of concave mirror. The radius of curvature of concave mirror is [Refractive index of material of lens $= 1.6$ ]

The critical angle for light going from medium A into medium B is $\theta$. The speed of light in the medium A is $V_A$. What is the speed of light in the medium $B$?

Two rotating bodies $P$ and $Q$ of masses '$m$' and '$2m$' with moment of inertia $I_P$ and $I_Q \, (I_Q > I_P)$ have equal Kinetic energy of rotation. If $L_P$ and $L_Q$ be their angular momenta respectively then

A solid sphere of mass '$M$' and radius '$R$' is rotating about its diameter. A solid cylinder of same mass and same radius is also rotating about its geometrical axis with an angular speet twice that of the sphere. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder is

Choose the FALSE statement from the following.

In an n-p-n transistor 200 electrons enter the emitter in 10 $^{-8}$ second. If 1% electrons are lost in the base, then the current that enters the emitter and the current amplification factor are respectively [e = 1.6 $\times$ 10 $^{-19}$ C]

A logic gate which gives output 'HIGH' only when its two input terminals are at different logic levels with respect to each other is

Water rises in a capillary tube of radius '$r$' up to a height '$h$'. The mass of water in a capillary is '$m$'. The mass of water that will rise in a capillary tube of radius $\frac{r}{3}$ will be

A drop of liquid of density '$\rho$' is floating half immersed in a liquid of density '$d$'. If '$T$' is the surface tension, then the diameter of the drop of the liquid is

For a gas molecule with 6 degrees of freedom, which one of the following relation between gas constant '$R$' and molar specific heat '$C_v$' is correct?

Which of the following statements is true?

($\Delta U =$ increase in internal energy, $dW =$ work done by the system)

A polyatomic gas $(\gamma = 4/3)$ is compressed to $\left(\frac{1}{8}\right)$th of its volume adiabatically. If its initial pressure is $P_0$, its new pressure will be

Let '$\text{W}_1$' be the work done in blowing a soap bubble of radius '$r$' from soap at room temperature. The soap is now heated and second soap bubble of radius '$2r$' is blown from the heated soap solution. If '$W_2$' is the work done in forming this bubble then

A pipe open at both ends of length 1.5 m is dipped in water such that the second overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz. If speed of sound in air is 330 m/s then the length of the pipe immersed in water is (Neglect and correction)

A sound wave is travelling with a frequency of $50\text{ Hz}$. The phase difference between the two points in the path of a wave is $\frac{\pi}{3}$. The distance between those two points is (Velocity of sound in air $= 330\text{ m/s}$)

A transverse wave given by $y = 2\sin(0.01x + 30t)$ moves on a stretched string from one end to another end in 0.5 second. If '$x$' and '$y$' are in $\text{cm}$ and '$t$' is in second, then the length of the string is

A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9\text{ kg}$ is suspended from the wire. When this mass is replaced by a mass $M$, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of '$M$' is

The width of central maximum of a diffraction pattern on a single slit does not depend upon

A single slit diffraction pattern is formed with white light. For what wavelength of light the $3$rd secondary maximum in diffraction pattern coincides with the $2$nd secondary maximum in the pattern of red light of wavelength 6000 $\text{Å}$?

In Young's double slit experiment, the $10$th maximum of wavelength '$\lambda_1$' is at a distance of '$Y_1$ ' from the central maximum. When the wavelength of the source is changed to '$\lambda_2$ ', $5^{th}$ maximum is at a distance '$Y_2$ ' from the central maximum. The ratio $\frac{Y_1}{Y_2}$ is

A car of mass '$m$' moving with velocity '$u$' on a straight road in a straight line, doubles its velocity in time t. The power delivered by the engine of a car for doubling the velocity is