MHT CET 2021 Physics Paper: 24 Sep, Shift 1

The peak value of an alternating emf '$e$' given by $e = e_0 \cos \omega t$ is 10 volt and its frequency is $50\text{ Hz}$. At time $t = \frac{1}{600}\text{ s}$, the instantaneous e.m.f is $\left(\cos \frac{\pi}{6} = \sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}\right)$

A step up transformer operates on $220\text{ V}$ and supplies current of $2\text{ A}$. The ratio of primary and secondary windings is $1 : 20$. The current in the primary is

In the part of an a.c. circuit as shown, the resistance $R = 0.2\,\Omega$. At a certain instant $(V_A - V_B) = 0.5\text{ V},\ I = 0.5\text{ A}$ and $\frac{\Delta I}{\Delta t} = 8\text{ A/s}$. The inductance of the coil is

Which graph shows the correct variation of r.m.s. current 'I' with frequency 'f' of a.c. in case of (LCR) parallel resonance circuit?

In the circuit shown in the figure, a.c. source gives voltage $V = 20\cos(2000t)$. Impedance and r.m.s. current respectively will be

An electron makes a transition from an excited state to the ground state of a hydrogen like atom. Out of the following statements which one is correct?

The ratio of maximum to minimum wavelength in Balmer series of hydrogen atom is

Two identical capacitors have the same capacitance '$C$'. One of them is charged to potential '$V_1$' and the other to $V_2$. The negative ends of the capacitors are connected together. When positive ends are also connected, the decrease in energy of the combined system is

The plates of a parallel plate capacitor of capacity '$C_1$' are moved closer together until they ant half their original separation. The new capacitance '$C_2$' is

A body attached to one end of a string performs motion along a vertical circle. Its centripetal acceleration, when the string is horizontal, will be [$g =$ acceleration due to gravity]

In a potentiometer experiment, when three cells $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are connected in series, the balancing length is found to be $420\text{ cm}$. If cells $\mathrm{A}$ and $\mathrm{B}$ are connected in series the balancing length is $220\text{ cm}$ and for cells $\mathrm{B}$ and $\mathrm{C}$ connected in series the balancing length is $320\text{ cm}$. The emf of cells $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are respectively in the ratio of

In photoelectric experiment keeping the frequency of incident radiation and accelerating potential fixed, if the intensity of incident light is increased,

A photon has wavelength $3\text{ nm}$, then its momentum and energy respectively will be $[h = 6.63 \times 10^{-34}\text{ Js}, c =$ velocity of light $= 3 \times 10^{8}\text{ m/s}]$

A coil has an area $0.06\text{ m}^{2}$ and it has 600 turns. After placing the coil in a magnetic field of strength $5 \times 10^{-5}\text{ Wb m}^{-2}$, it is rotated through $90^\circ$ in 0.2 second. The magnitude of average e.m.f induced in the coil is

$[\cos 0^\circ = \sin 90^\circ = 1$ and $\sin 0^\circ = \cos 90^\circ = 0]$

. If the current of '$I$' A gives rise to a magnetic flux '$\phi$' through a coil having '$N$' turns then mangetic energy stored in the medium surrounding the coil is

The electric field intensity on the surface of a charged solid sphere of radius '$r$' and volume charge density '$\rho$' is given by ($\epsilon_0 =$ permittivity of free space)

Let A, B and C be the three points in a uniform electric field ( $\vec{E})$ as shown. The electric potential is

A glass tube of uniform cross-section is connected to a tap with a rubber tube. The tap is opened slowly. Initially the flow of water in the tube is streamline. The speed of flow of water to convert it into a turbulent flow is [radius of tube $= 1\text{ cm}, \eta = 1 \times 10^{-3}\,\frac{\text{Ns}}{\text{m}^2}, R_n = 2500$ and density of water $= 10^{3}\text{ kg/m}^3$ ]

The period of revolution of planet $\text{A}$ around the sun is 8 times that of planet $\text{B}$. How many times the distance of A from the sun is greater than that of B from the sun?

If the horizontal velocity given to a satellite is greater than critical velocity but less than the escape velocity at the height, then the satellite will

The temperature difference between two sides of an iron plate, $1.8\text{ cm}$ thick is $9^\circ\text{C}$. Heat is transmitted through the plate $10\text{ kcal/s m}^2$ at steady state. The thermal conductivity of iron is

At what temperature does the average translational kinetic energy of a molecule in a gas becomes equal to kinetic energy of an electron accelerated from rest through potential difference of 'V' volt? ($N =$ number of molecules, $R =$ gas constant, $c =$ electronic charge)

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring balance reads $49\text{ N}$, when the lift is stationary. If the lift moves downward with an acceleration of $5\text{ m/s}^{2}$, the reading of the spring balance will be $(g = 9.8\text{ m/s}^{2})$

A current '$I$' is flowing in a conductor of length '$L$' when it is bent in the form of a circular loop, its magnetic moment will be

A current carrying loop is placed in a uniform magnetic field. The torque acting on the loop does not depend upon

Two long conductors, separated by a distance '$d$' carry currents '$I_1$' and '$I_2$ ' in the same directions. They exert a force '$F$' on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to '$3d$'. The new value of the force between them is

A body is executing S.H.M. under the action of force having maximum magntude $50\text{ N}$. When its energy is half kinetic and half potential; the magnitude of the force acting on the particle is

Two identical springs of constant '$K$' are connected in series and parallel in shown in figure. A mass '$M$' is suspended from them. The ratio of their frequencies is series to parallel combination will be

A particle performing linear S.H.M. of amplitude $0.1\text{ m}$ has displacement $0.02\text{ m}$ and acceleration $0.5\text{ m/s}^2$. The maximum velocity of the particle in $\text{m/s}$ is

The radii of curvature of both the surfaces of a convex lens of focal length '$f$' and focal power '$P$' are equal. One of the surfaces is made plane by grinding. The new focal length and focal power of the lens is respectively

A glass slab has refractive index '$\mu$' with respect to air and the critical angle for a ray of light in going from glass to glass to air is '$\theta$' If a ray of light is incident from air on the glass with angle of incidence '$\theta$', then the corresponding angle of refraction is

A body of mass '$\mathrm{m}$' and radius of gyration '$\mathrm{K}$' has an angular momentum $\mathrm{L}$. Its angular velocity is

Two identical particles each of mass '$m$' are separated by a distance '$d$'. The axis of rotation passes through the midpoint of '$d$' and is perpendicular to the length $d$. If '$K$' is the average rotational kinetic energy of the system, then the angular frequency is

For the output of the following logic circuit to be '1', the values of inputs A and B should be respectively

Two identical ideal diodes are connected to an ammeter and a d.c source (1 volt) as shown. In which one of the following circuits, ammeter will not show any deflection?

A p-n junction photodiode is fabricated from a semiconductor with a band gap of $2.5\text{ eV}$. It can detect a signal of wavelength [Planck's constant $= 6.6 \times 10^{-34}\text{ Js}, \text{c} = 3 \times 10^{8}\text{ m/s}, \text{e} = 1.6 \times 10^{-19}\text{ C}$]

A thin metal disc of radius 'r' floats on water surface and bends the surface downwards along the perimeter making an angle '$\theta$' with the vertical edge of the disc. If the weight of water displaced by the disc is '$W$', the weight of the metal disc is [T = surface tension of water]

The work done in blowing a soap bubble of volume '$V$' is '$W$'. The work required to blow a soap bubble of volume '$2V$' is [$T =$ surface tension of soap solution]

Internal energy of $n_1$ moles of hydrogen at temperature '$T$' is equal to internal energy of '$n_2$' moles of helium at temperature $2T$, then the ratio $n_1 : n_2$ is

[Degree of freedom of $\text{He} = 3$, Degree of freedom of $\text{H}_2 = 5$]

For a monoatomic gas, the work done at constant pressure is '$W$'. The heat supplied at constant volume for the same rise in temperature of the gas is

$[\gamma = \frac{C_p}{C_v} = \frac{5}{3}$ for monoatomic gas]

An ideal gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2\,V$ and a final pressure $P_i$. The same gas is expanded adiabatically to a volume $2\,V$, the final pressure is $P_a$. In terms of the ratio of the two specific heats for the gas '$\gamma$', the ratio $\frac{P_i}{P_a}$ is

A monoatomic ideal gas initially at temperature $T_1$ is enclosed in a cylinder fitted with 8 frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion respectively. Then $\frac{T_2}{T_1}$ is

A sonometer wire of length 25 cm vibrates in unison with a tuning fork. When its length is decreased by 1 cm, 6 beats are heard per second. What is the frequency of the tuning fork?

When an air column in a pipe open at both ends vibrates such that four antinodes and three nodes are formed, then the corresponding mode of vibration is

The wavelength of sound in any gas depends upon

Two tuning forks of frequencies $320\text{ Hz}$ and $480\text{ Hz}$ are sounded together to produce sound waves. The velocity of sound in air is $320\text{ ms}^{-1}$. The difference between wavelengths of these waves is nearly

A beam of light having wavelength $5400\text{ \AA}$ from a distant source falls on a single slit $0.96\text{ mm}$ wide and the resultant diffraction pattern is observed on a screen $2\text{ m}$ away. What is the distance between the first dark fringe on either side of central bright fringe?

Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\pi/2$ at point $A$ and $\pi$ at point $B$. Then the difference between the resultant intensities at $A$ and $B$ is

In Young's double slit experiment, in an interference pattern, a minimum is observed exactly in front of one slit. The distance between the two coherent sources is '$d$' and '$D$' is the distance between the source and screen. The possible wavelengths used are inversely proportional to

A stone is projected vertically upwards with velocity 'V'. Another stone of same mass is projected at an angle of $60^\circ$ with the vertical with the same speed $(\text{V})$. The ratio of their potential energies at the highest points of their journey, is

$\left[\sin 30^\circ = \cos 60^\circ = 0.5, \cos 30^\circ = \sin 60^\circ = \frac{\sqrt{3}}{2}\right]$