MHT CET 2026 Physics Paper: 19 Apr, Shift 2

Two coils P and S have a mutual inductance of ($\pi$) mH. The secondary coil S has resistance $4\ \Omega$ and self inductance $(60/\pi)$ mH. If the current in the primary is $I_p = 12\sin(50\pi t)$, then the maximum value of the current induced in coil S is [Take $\pi^2 = 10$]

In an oscillating LC circuit the maximum charge on the capacitor is Q. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor (q) is

In series LCR circuit $R = 10\ \Omega$ and impedance is $30\ \Omega$. An r.m.s. voltage $210$ V, is applied across the circuit. The true power consumed in AC circuit is

When a.c. source is connected across a pure capacitor, the correct phase relation between current and emf is shown in figure.

The de-Broglie wavelength of an electron moving in the $n^{th}$ Bohr orbit of radius 'r' is

The magnetic moment of electron due to orbital motion is proportional to

($n$ = principal quantum number)

If the ionisation energy for the hydrogen atom is $13.6$ eV, then the energy required to excite it from the ground state to the next higher state is nearly

A parallel plate air capacitor has capacity 'C' farad, potential 'V' volt and energy 'E' joule. When the gap between the plates is completely filled with dielectric

Two particles of masses $2$ g and $4$ g are situated at the opposite ends, A and B of a wooden bar respectively. Let $l(AB) = 9$ cm. The center of mass of the system will be

A particle is performing U.C.M. along a circle of radius $R$. In half the period of revolution, its displacement and distance covered are respectively

A body of mass 'm' attached at the end of a string is just completing the loop in a vertical circle. The apparent weight of the body at the lowest point in its path is

($g$ = gravitational acceleration)

A stone of mass $40$ g is tied to a light inextensible string of length $50$ cm and whirled in a vertical circle at the rate of $30$ revolutions per minute. The tension in the string when it is at the lowest point of the circle is

(Take gravitational acceleration, $g = 10$ m/s$^{2}$ and $\pi^2 = 10$)

The resistances in the two gaps of a balanced meter bridge are 'X' $\Omega$ and '3X' $\Omega$ respectively. If the resistances are interchanged the balance point shifts by

When light of wavelength '$\lambda$' is incident on a photosensitive surface, the stopping potential is 'V'. When a light of wavelength $1.5\lambda$ is incident on the same surface, the stopping potential is ' $\frac{V}{4}$'. Threshold wavelength for the surface is

The magnetic energy stored in an inductor of inductance $4$ H carrying a current of $1.5$ A is

A solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, then the current in the coil

Two equal positive charges each of value 'q' are placed at points A and B, where $AB = 3x$. A third charge $-3q$ is placed at point C at a distance $x$ from A on AB. The potential energy of the system is nearly ($\epsilon_0$ = permittivity of free space)

A particle of mass 'm' and charge 'q', initially at rest, is accelerated by a uniform electric field 'E' through a distance 'D' and is then allowed to approach a fixed static charge 'Q' of the same sign. The distance of the closest approach of the charge q is

[ $\epsilon_0$ = permittivity of free space ]

An uniformly charged thin spherical shell of radius 'R' has uniform surface charge density '$\sigma$'. It is made of two hemispherical identical shells held together by pressing them with force 'F' as shown. F is proportional to

[$\epsilon_0$ = permittivity of free space]

A satellite is revolving around a planet in a circular orbit close to its surface. Let $\rho$ be mean density and $R$ be the radius of the planet; then the period of the satellite is

($G$ = Universal constant of gravitation).

Out of the following, which statement is NOT true about black body radiation?

Assuming the expression for the pressure exerted by the gas, it can be shown that pressure is

The magnetic induction produced inside an ideal solenoid, depends on which of the following quantities?

(a) number of turns per unit length.

(b) radius of the wire.

(c) current flowing throught it.

(d) permeability of the medium.

A current carrying circular coil of radius 'R' produces magnetic field $B_1$ at an axial point P at a distance 'x' from its centre and $B_2$ at point Q placed at its centre respectively. If $B_2 = 8B_1$, the value of x is

When a galvanometer is shunted by a resistance 'S', its current capacity increases 'n' times. If the same galvanometer is shunted by another resistance '$S'$', its current capacity will increase to '$n'$ '. The value of n in terms of $n'$, S and $S'$ is

A radioactive element has rate of disintegration $16{,}000$ disintegrations per minute at a particular instant. After four minutes, it becomes $2000$ disintegrations per minute. The decay constant per minute is

A spring force constant $180$ N/m is loaded with a mass $0.2$ kg. The amplitude of oscillations is $4$ cm. When mass comes to equilibrium position, its velocity is

A particle executing linear S.H.M. has velocities $V_1$ and $V_2$ at distance $x_1$ and $x_2$ respectively, from the mean position, its angular velocity is

The equation of the trajectory of a ball projected at an angle $\theta$ with the horizontal, is given as $y = x - \frac{gx^{2}}{2}$

The initial velocity of the ball is

[Given: $\tan 45^\circ = 1,\ \cos 45^\circ = \frac{1}{\sqrt{2}}$ ]

Light travels a distance 'x' in time '$t_0$' in air and '$4x$' in time '$t_1$' in another denser medium. The critical angle for this medium is

A force of $3\hat{i}+2\hat{j}-\hat{k}$ N acts on a particle with position vector $\hat{i}+\hat{j}-\hat{k}$ m. The magnitude of torque of given force is

In a transistor, comparing the doping of emitter, base and collector, the part which is heavily doped and that which is lightly doped are respectively

The Boolean expression for the given combination of logic gates is

In the following electrical circuit, the reading in the milliammeter is

(Take knee voltage of silicon diode $= 0.7$ V)

A metal wire of length 'L' and density 'd' floats horizontally on the free surface of water. The maximum radius of the wire does not sink in water is

[ $T$ = surface tension of water, $g$ = gravitational acceleration]

In most liquids, with rise in temperature surface tension of liquid

The energy needed for breaking a liquid drop of radius 'R' into 'n' droplets each of radius 'r' is [ $T$ = surface tension of the liquid]

An ideal gas at pressure 'P' and temperature 'T' is enclosed in a vessel of volume 'V'. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to $P'$. Assuming that the temperature of the gas remains constant during the leakage, the number of moles of the gas that have leaked is

An ideal gas having pressure P, volume V and temperature T undergoes a thermodynamic process in which $dW = 0$ and $dQ < 0$. Then, for the gas

An ideal gas ($\gamma = 1.5$) is expanded adiabatically. To reduce the root mean square velocity of molecules two times, the gas should be expanded

$15$ g of ice at $0^{\circ}$C is added to a vessel containing water at $40^{\circ}$C. The mass of water and water equivalent of the vessel is $60$ g. Assuming that negligible heat is taken from the surroundings, the final temperature of the mixture will be

[ $L$ice $= 80$ cal/g, $S$water $= 1$ cal/g ]

A cuboid has volume $V = l \times l \times \sqrt{l}$, where $l$ is the length of one side. When the length $l$ is measured by a meter scale of least count $1$ mm, the relative percentage error in the measurement of its volume is $6.25\%$. Then the relative percentage error in measurement of its length and the value of the length $l$ is

In a resonance tube open at one end, the end correction is $1.1$ cm. If the shortest length of resonating air column with a tuning fork is $18$ cm, the next resonating length will be

The equation of a progressive wave is given by $y = 6\cos(100t - 4x)$ where $y$ is in $\mu$m, $x$ in metre and $t$ in second. The ratio of the maximum particle velocity to the velocity of wave is

For stationary wave, $y = 12\cos\left(\frac{\pi x}{10}\right)\sin(36\pi t)$ cm, the distance between a node and the successive antinode is

Two waves of same frequency ($n$) approaching each other with same velocity of $18$ m/s interfere. The distance between two consecutive antinodes is

A body sends a wave $150$ mm long through medium P and $0.30$ m long in medium Q. If velocity of the wave in medium P is $80$ cm s$-1$, the velocity of wave in medium Q is

In a biprism experiment, a steady interference pattern is observed on the screen kept at a distance of 100 cm using a light of wavelength $5000$ Å. Without changing the distance between the virtual images of the slit, the source of light is replaced by a source of wavelength $6400$ Å. Now, to reduce the fringe width by $20\%$ of its initial value, the screen should be moved

In biprism experiment, the maximum intensity is $I_0$. If the path difference between the two interfering waves is $\frac{\lambda}{3}$, then intensity at the point on the screen is

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

A ray of light is incident at polarising angle $\theta$ on air-glass interface. If $\lambda_a$ and $\lambda_g$ are the wavelengths of light in air and glass respectively then