MHT CET 2023 Physics Paper: 14 May, Shift 2

What will be the phase difference between virtual voltage and virtual current when current in the circuit is wattless?

The power factor of an R-L circuit is $\frac{1}{\sqrt{2}}$. If the frequency of $AC$ is doubled the power factor will now be

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

A coil having an inductance of $\frac{1}{\pi}\text{ H}$ is connected in series with a resistance of $300\ \Omega$. If $20\text{ V}$ from a $200\text{ Hz}$ source are impressed across the combination, the value of the phase angle between the voltage and the current is

Ratio of longest wavelength corresponding to Lyman and Balmer series in hydrogen spectrum is

Two condensers one of capacity $\frac{C}{2}$ and other capacity $C$ are connected to a battery of voltage $V$ as shown. The work done in charging fully both the condensers is

A parallel plate capacitor with air medium between the plates has a capacitance of $10\mu\text{F}$. The area of capacitor is divided into two equal halves and filled with two media (as shown in figure) having dielectric constant $K_1 = 2$ and $K_2 = 4$. The capacitance of the system will be

When moving coil galvanometer (MCG) is converted into a voltmeter, the series resistance is '$n$' times the resistance of galvanometer. How many times that of MCG the voltmeter is now capable of measuring voltage?

In potentiometer experiment, the balancing length is $8\text{ m}$ when two cells $E_1$ and $E_2$ are joined in series. When two cells are connected in opposition the balancing length is $4\text{ m}$. The ratio of the e.m.f. of the two cells $\left(\frac{E_1}{E_2}\right)$ is

When radiation of wavelength '$\lambda$' is incident on a metallic surface, the stopping potential is 4.8 V. If the surface is illuminated with radiation of double the wavelength then the stopping potential becomes $1.6\text{ V}$. The threshold wavelength for the surface is

A coil having effective area A, is held with its plane normal to magnetic field of induction B. The magnetic induction is quickly reduced by $25\%$ of its initial value in 2 second. Then the e.m.f. induced across the coil will be

A long solenoid has 1500 turns. When a current of $3.5\text{ A}$ flows through it, the magnetic flux linked with each turn of solenoid is $2.8 \times 10^{-3}$ weber. The self-inductance of solenoid is

The self induction (L) produced by solenoid of length '$l$' having '$N$' number of turns and cross sectional area '$A$' is given by the formula ($\phi =$ magnetic flux, $\mu_0 =$ permeability of vacuum)

If $E_a$ and $E_q$ represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance '$r$' from the centre of the dipole, then

A charge $17.7 \times 10^{-4}\text{ C}$ is distributed uniformly over a large sheet of area $200\text{ m}^2$. The electric field intensity at a distance $20\text{ cm}$ from it in air will be $\left[\varepsilon_0 = 8.85 \times 10^{-12}\text{ C}^2/\text{N m}^2\right]$

Earth is assumed to be a sphere of radius R. If '$g_\phi$' is value of effective acceleration due to gravity at latitude $30^\circ$ and '$g$' is the value at equator, then the value of $|g - g_\phi|$ is ($\omega$ is angular velocity of rotation of earth, $\cos 30^\circ$ $= \frac{\sqrt{3}}{2}$)

A body (mass $m$) starts its motion from rest from a point distant $R_0\ (R_0 > R)$ from the centre of the earth. The velocity acquired by the body when it reaches the surface of earth will be ( $G =$ universal constant of gravitation, $M =$ mass of earth, $R$ = radius of earth)

A metal rod cools at the rate of $4^\circ\text{C/min}$ when its temperature is $90^\circ\text{C}$ and the rate of $1^\circ\text{C/m}$in when its temperature is $30^\circ\text{C}$. The temperature of the surrounding is

The molecular mass of a gas having r.m.s. speed four times as that of another gas having molecular mass 32 is

The temperature of a gas is measure of

A machine gun fires bullets of mass $30\text{ g}$ with velocity of $1000\text{ m/s}$. The man holding the gun can exert a maximum force of $300\text{ N}$ on it. How many bullets can he fire per second at most?

In the hysteresis curve the value of magnetization (B) which will be present in a substance when value of magnetizing force $(\mathrm{H})$ is made zero $(\mathrm{H} = 0)$ is called as

The position '$x$' of a particle varies with a time as $x = at^2 - bt^3$ where '$a$' and '$b$' are constants. The acceleration of the particle will be zero at

A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having $n$ turns. If the same current passes in both the cases, the ratio of magnetic fields produced at the centre for one turn to that of $n$ turns is

Figure shows two semicircular loops of radii $R_1$ and $R_2$ carrying current $I$. The magnetic field at the common centre '$O$' is

Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be

A light spring is suspended with mass $m_1$ at its lower end and its upper end fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is $T$ second. When a mass $m_2$ is added to $m_1$ and the system is made to oscillate, the period is found to be $\frac{3}{2}T$. The ratio $m_1 : m_2$ is

A uniform circular disc of mass $12\text{ kg}$ is held by two identical springs. When the disc is slightly pressed down and released, it executes S.H.M. of period 2 second. The force constant of each spring is (nearly) (Take $\pi^2 = 10$)

A block of mass '$M$' rests on a piston executing S.H.M. of period one second. The amplitude of oscillations, so that the mass is separated from the piston, is (acceleration due to gravity, $g = 10\text{ m s}^{-2},\ \pi^2 = 10$)

When a monochromatic ray of light is passed through an equilateral glass prism, it is found that the refracted ray in glass is parallel to the base of the prism. If '$i$' and '$e$' denote the angles of incidence and emergence respectively, then

Refractive index of a glass convex lens is 1.5. The radius of curvature of each of the two surfaces of the lens is $20\text{ cm}$. The ratio of the power of the lens when immersed in a liquid of refractive index 1.25 to that when placed in air is

A mass '$M$' is moving with constant velocity parallel to $\mathrm{X}$-axis. Its angular momentum with respect to the origin is

Four identical uniform solid spheres each of same mass '$M$' and radius '$R$' are placed touching each other as shown in figure, with centres A, B, C, D. $I_A, I_B, I_C$ and $I_D$ are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane. The difference in $I_A$, and $I_B$ is

A solid cylinder and a solid sphere having same mass and same radius roll down on the same inclined plane. The ratio of the acceleration of the cylinder '$a_c$' to that of sphere '$a_s$' is

When the conductivity of a semiconductor is only due to the breaking of the covalent bonds, the semiconductor is called

In an n-p-n transistor, the collector current is $28\text{ mA}$. If $80\%$ of electrons reach the collector, its base current in $\text{mA}$ is

The output of following combination is same as that of

Two spherical soap bubbles of radii '$a$' and '$b$' in vacuum coalesce under isothermal conditions. The resulting bubble has a radius equal to

It is easier to spray water to which soap is added because addition of soap to water

1000 small water drops of equal size combine to form a big drop. The ratio of final surface energy to the total initial surface energy is

At constant temperature, increasing the pressure of a gas by $5\%$ its volume will decrease by

An ideal refrigerator has freezer at a temperature of $-13^\circ\text{C}$. The coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) is

The pressure and density of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ changes adiabatically from $(P, \rho)$ to $(P', \rho')$. If $\frac{\rho'}{\rho} = 32$ then $\frac{P'}{P}$ should be

A sonometer wire $49\text{ cm}$ long is in unison with a tuning fork of frequency '$n$'. If the length of the wire is decreased by $1\text{ cm}$ and it is vibrated with the same tuning fork, 6 beats are heard per second. The value of '$n$' is

A source of sound is moving towards a stationary observer with $\left(\frac{1}{10}\right)$th the of the speed of sound. The ratio of apparent to real frequency is

A wire $PQ$ has length $4.8\text{ m}$ and mass $0.06\text{ kg}$. Another wire QR has length $2.56\text{ m}$ and mass $0.2\text{ kg}$. Both wires have same radii and are joined as a single wire. This wire is under tension of $80\text{ N}$. A wave pulse of amplitude $3.5\text{ cm}$ is sent along the wire $PQ$ from end $P$. the time taken by the wave pulse to travel along the wire from point P to R is?

Sound waves of frequency $600\text{ Hz}$ fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration is (speed of sound $= 300\text{ m s}^{-1}$)

Two wavelengths of sodium light $590\text{ nm}$ and $596\text{ nm}$ are used one after another to study diffraction due to single slit of aperture $2 \times 10^{-6}\text{ m}$. The distance between the slit and the screen is $1.5\text{ m}$. The separation between the positions of first maximum of the diffraction pattern obtained in the two cases is

When two light waves each of amplitude '$A$' and having a phase difference of $\frac{\pi}{2}$ superimposed then the amplitude of resultant wave is

On placing a thin film of mica of thickness $12 \times 10^{-5}\text{ cm}$ in the path of one of the interfering beams in Young's double slit experiment using monochromatic light, the fringe pattern shifts through a distance equal to the width of bright fringe. If $\lambda = 6 \times 10^{-5}\text{ cm}$, the refractive index of mica is