MHT CET 2024 Physics Paper: 15 May, Shift 1

Alternating current of peak value $\left(\frac{2}{\pi}\right)$ A flows through the primary coil of a transformer. The coefficient of mutual inductance between primary and secondary coils is 1 H. The peak e.m.f. induced in secondary coil (Frequency of a.c. $= 50\text{ Hz}$)

A series $L - C - R$ circuit containing a resistance ' $R$ ' has angular frequency ' $\omega$ '. At resonance the voltage across resistance and inductor are ' $V_R$ ' and ' $V_L$ ' respectively, then value of capacitance will be

In an a.c. circuit, the reactance of a coil is $\sqrt{3}$ times its resistance. The phase difference between the voltage across the coil to the current through the coil will be

When a coil is connected to a d.c. source of e.m.f. 12 volt; then the current of 4 A flows in it. If the same coil is connected to a 12 volt, 50 Hz a.c. source, then the current flowing in it is 2.4 A. Then self-inductance of the coil will be

The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is

Three condensers of capacities ' $C_1$ ', ' $C_2$ ', ' $C_3$ ' are connected in series with a source of e.m.f. ' $V$ '. The potentials across the three condensers are in the ratio

A galvanometer has resistance $80\ \Omega$ and it is shunted with resistance $20\ \Omega$. If $20\%$ of the main current flows through galvanometer, then what is the value of main current?

A cell balances against a length of 150 cm on a potentiometer wire when it is shunted by a resistance of $5\ \Omega$. But when it is shunted by a resistance of $10\ \Omega$, then balancing length increases by 25 cm. The balancing length when the cell is in an open circuit is

Electrons are accelerated through a potential difference of 16 kV. If the potential difference is increased to 64 kV, then de-Broglie wavelength associated with electron will

Two photons having energies twice and thrice the work function of metal are incident one after another on the metal surface. Then the ratio of maximum velocities of the photoelectrons emitted in the two cases is respectively

When the number of turns in a coil are made 3 times without any change in the length of the coil, its self inductance becomes

Two solenoids of equal number of turns have their lengths as well as radii in the same ratio $1 : 3$. The ratio of their self inductance will be

Two point charges $+8q$ and $-2q$ are located at $X = 0$ (origin) and $X = L$ respectively. The net electric field due to these two charges is zero at point $P$ on $X$-axis. The location of point $P$ from the origin is

Consider a long uniformly charged cylinder having constant volume charge density ' $\lambda$ ' and radius ' $R$ '. A Gaussian surface is in the form of a cylinder of radius ' $r$ ' such that vertical axis of both the cylinders coincide. For a point inside the cylinder $(r < R)$, electric field is directly proportional to

If a unit positive charge is shifted from a region of low potential to a region of high potential, then the electric potential energy of the system

The weights of an object are measured in a coal mine of depth ' $h_1$ ', then at sea level of height ' $h_2$ ' and lastly at the top of a mountain of height ' $h_3$ ' as $W_1, W_2$ and $W_3$ respectively. Which one of the following relations is correct? [$h_1 \ll R, h_3 \gg h_2 = R, R =$ radius of the earth ]

A satellite of mass ' $m$ ' is revolving around the earth of mass ' $M$ ' in an orbit of radius ' $r$ ' with constant angular velocity ' $\omega$ '. The angular momentum of satellite is ( $G =$ Universal constant of gravitation)

The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, angle $\theta$ should be

Magnetic induction produced at the centre of a circular loop of radius ' $R$ ' carrying a current is ' B '. The magnetic moment of the loop is ( $\mu_0 =$ permeability of free space)

Two parallel wires separated by distance 'b' are carrying equal current ' $I$ ' in the same direction. The force per unit length of the wire is

The strength of magnetic field at a perpendicular distance ' $x$ ' near a long straight conductor carrying current ' I ' is ' B '. The magnetic field at a distance $\frac{x}{3}$ from straight conductor will be

A radioactive substance has half-life of 60 minutes. During 3 hours, the amount of substance decayed would be

Starting from mean position, a body oscillates simple harmonically with a period ' $T$ '. After what time will its kinetic energy be $75\%$ of the total energy? $(\sin 30^\circ = 0.5)$

The maximum velocity of a particle, executing S.H.M. with an amplitude 7 mm is $4.4\text{ m s}^{-1}$ The period of oscillation is $\left[\pi = \frac{22}{7}\right]$

A horizontal platform with a small object placed on it executes a linear S.H.M. in the vertical direction. The amplitude of oscillation is 40 cm. What should be the least period of these oscillations, so that the object is not detached from the platform? [Take $g = 10\text{ m/s}^2$]

For a symmetric (equilateral) prism, the prism formula can be written as

For a ray of light, the critical angle is minimum, when it travels from

Three thin rods, each of mass ' $M$ ' and length ' $L$ ' are placed along $X, Y$ and Z axes which are mutually perpendicular. One end of each rod is at origin. M. I. of the system about Z axis is

If the angular velocity of a body rotating about the given axis increases by $20\%$, then its kinetic energy of rotation will increase by

A thin uniform metal rod of mass ' $M$ ' and length ' $L$ ' is swinging about a horizontal axis passing through its end. Its maximum angular velocity is ' $\omega$ '. Its centre of mass rises to a maximum height of ( $g =$ Acceleration due to gravity)

In an extrinsic n-type semiconductor, the free electrons donated by the impurity atoms occupy energy levels in

For a transistor, current gain $(\beta) = 50$. To change the collector current by $350\,\mu\text{A}$, the base current should be changed by

Two different logic gates giving output ' 1 ' for the inputs $(1, 0)$ and then for $(0, 1)$ are

Two capillary tubes A and B of the same internal diameter are kept vertically in two different liquids whose densities are in the ratio $4 : 3$. If the surface tensions of these two liquids are in the ratio $6 : 5$, then the ratio of rise of liquid in capillary A to that in B is (assume their angles of contact are nearly equal)

The angle of contact between glass and water is $0^\circ$ and water rises in a glass capillary upto 6 cm (Surface tension of water is T). Another liquid of surface tension ' $2T$ ', angle of contact $60^\circ$ and relative density 2 will rise in the same capillary up to $(\cos 0^\circ = 1, \cos 60^\circ = 0.5)$

When a mercury drop of radius ' $R$ ' splits up into 1000 droplets of radius ' $r$ ', the change in surface energy is ( $T =$ surface tension of mercury)

When a system is taken from state ' $a$ ' to state ' $c$ ' along a path abc, it is found that $Q = 80\text{ cal}$ and $W = 35\text{ cal}$. Along path adc $Q = 65\text{ cal}$ the work done W along path adc is

Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. $[C_v$ for hydrogen $= \frac{5}{2}R, C_v$ for helium $= \frac{3}{2}R, C_v$ for water vapour $= 3R]$ What is the molar specific heat at constant pressure of the mixture?

The ratio of work done by an ideal rigid diatomic gas to the heat supplied by the gas in an isobaric process is

The internal energy of an ideal diatomic gas corresponding to volume ' $V$ ' and pressure ' P ' is 2.5 PV. The gas expands from 1 litre to 2 litre at a constant pressure of $10^{5}\text{ N/m}^2$. The heat supplied to a gas is

A quantity of heat ' $Q$ ' is supplied to monoatomic ideal gas which expands at constant pressure. The fraction of heat converted into work is $\left[\gamma = \frac{C_p}{C_v} = \frac{5}{3}\right]$

A sheet of steel is 40 cm long and 5 cm broad at $0^\circ\text{C}$. The surface area of the sheet increases by $1.4\text{ cm}^2$ at $100^\circ\text{C}$. Coefficient of linear expansion of steel is

An open organ pipe of length ' $l$ ' is sounded together with another open organ pipe of length $(l + l_1)$ in their fundamental modes. Speed of sound in air is ' $V$ '. The beat frequency heard will be ( $l_1 << l)$

The driver of a car travelling with a speed ' $V_1$ ' $\text{m/s}$ towards a wall sounds a siren of frequency ' $n$ ' Hz. If the velocity of sound in air is $V\text{ m/s}$, then the frequency of sound reflected from the wall and as heard by the driver, in Hz, is

When a sonometer wire vibrates in third overtone there are

Two progressive waves $Y_1 = \sin 2\pi\left(\frac{t}{0.4} - \frac{x}{4}\right)$ and $Y_2 = \sin 2\pi\left(\frac{t}{0.4} + \frac{x}{4}\right)$ superpose to form a standing wave. ' $x$ ' and ' $y$ ' are in SI system. Amplitude of the particle at $x = 0.5\text{ m}$ is $\left[\sin 45^\circ = \cos 45^\circ = \frac{1}{\sqrt{2}}\right]$

In biprism experiment, the fringe width is 0.6 mm. The distance between $6$th dark fringe and $8$th bright fringe on the same side of central bright fringe is

In double slit experiment, instead of taking slits of equal widths, one slit is made twice as wide as the other. Then in interference pattern

In Young's double slit experiment, 'I' is the minimum intensity and ' $I_1$ ' is the intensity at a point where the path difference is $\frac{\lambda}{4}$ where ' $\lambda$ ' is the wavelength of light used. The ratio $\frac{I}{I_1}$ is (Intensities of the two interfering waves are same) $(\cos 0^\circ = 1, \cos 90^\circ = 0)$

A body of mass 1 kg starts from rest and moves with uniform acceleration. In 2 seconds, its velocity is $10\text{ m/s}$. The power exerted on the body in one second is