JEE Main 2022 Physics Paper: 25 Jun, Shift 2

In a series LCR circuit, the inductance, capacitance and resistance are L = 100 mH, C = 100 $\mu$F and R = 10 $\Omega$ respectively. They are connected to an AC source of voltage 220 V and frequency of 50 Hz. The approximate value of current in the circuit will be ___________ A.

A sinusoidal voltage V(t) = 210 sin 3000 t volt is applied to a series LCR circuit in which L = 10 mH, C = 25 $\mu$F and R = 100 $\Omega$. The phase difference ($\Phi$) between the applied voltage and resultant current will be:

Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness $\frac{d}{2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?

For a particle in uniform circular motion, the acceleration$\vec{a}$at any point P(R, $\theta$) on the circular path of radius R is (when $\theta$ is measured from the positive x-axis and v is uniform speed):

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if:

A curve in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ___________ m/s.

Two cells of same emf but different internal resistances r1 and r2 are connected in series with a resistance R. The value of resistance R, for which the potential difference across second cell is zero, is:

If n represents the actual number of deflections in a converted galvanometer of resistance G and shunt resistance S. Then the total current I when its figure of merit is K will be:

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ____________ %.

A proton, a neutron, an electron and an $\alpha$ particle have same energy. If $\lambda$p, $\lambda$n, $\lambda$e and $\lambda_\alpha$ are the de Broglie's wavelengths of proton, neutron, electron and $\alpha$ particle respectively, then choose the correct relation from the following:

The electromagnetic waves travel in a medium at a speed of 2.0 $\times$ 108 m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be:

27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger drop will be _____________ V.

Two satellites S1 and S2 are revolving in circular orbits around a planet with radius R1 = 3200 km and R2 = 800 km respectively. The ratio of speed of satellite S1 to be speed of satellite S2 in their respective orbits would be $\frac{1}{x}$ where x = ___________.

A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force F = $\sqrt{x}$N as shown in figure.

The value of x = _____________.

Given below are two statements:

Statement I: Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature.

Statement II: Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field.

Choose the correct answer from the options given below:

Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by $X_P(t) = \alpha t + \beta t^2$ and $X_Q(t) = ft - t^2$. At what time, both the buses have same velocity?

A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to

Which of the following figure represents the variation of $\ln\left(\frac{R}{R_0}\right)$ with $\ln A$ (if R = radius of a nucleus and A = its mass number)

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R. If A and B reached the maximum height h1 and h2 respectively, then $R = 4\sqrt{h_1 h_2}$

Reason R: Product of said heights.

$h_1 h_2 = \left(\frac{u^2 \sin^2\theta}{2g}\right) \cdot \left(\frac{u^2 \cos^2\theta}{2g}\right)$

Choose the correct answer:

Moment of Inertia (M.I.) of four bodies having same mass 'M' and radius '2R' are as follows: I1 = M.I. of solid sphere about its diameter

I2 = M.I. of solid cylinder about its axis

I3 = M.I. of solid circular disc about its diameter

I4 = M.I. of thin circular ring about its diameter

If 2(I2 + I3) + I4 = x. I1, then the value of x will be __________.

In an experiment of CE configuration of n-p-n transistor, the transfer characteristics are observed as given in figure.

If the input resistance is 200 $\Omega$ and output resistance is 60 $\Omega$, the voltage gain in this experiment will be ____________.

Identify the logic operation performed by the given circuit:

When a gas filled in a closed vessel is heated by raising the temperature by 1$^\circ$C, its pressure increases by 0.4%. The initial temperature of the gas is ___________ K.

The ratio of specific heats $\left(\frac{C_P}{C_V}\right)$ in terms of degree of freedom (f) is given by:

A copper block of mass 5.0 kg is heated to a temperature of 500$^{\circ}$C and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper: 0.39 J g$^{-}$1 $^{\circ}\text{C}^{-}$1 and latent heat of fusion of water: 335 J g$^{-}$1]

A solid metallic cube having total surface area 24 m2 is uniformly heated. If its temperature is increased by 10$^\circ$C, calculate the increase in volume of the cube. (Given $\alpha$ = 5.0 $\times$ 10 $-$4 $^\circ\text{C}^{-}$1).

For $z = a^{2} x^{3} y^{\frac{1}{2}}$, where 'a' is a constant. If percentage error in measurement of 'x' and 'y' are 4% and 12% respectively, then the percentage error for 'z' will be _______________%.

A light whose electric field vectors are completely removed by using a good polaroid, allowed to incident on the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

The interference pattern is obtained with two coherent light sources of intensity ratio 4: 1. And the ratio $\frac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}}$ is $\frac{5}{x}$. Then, the value of x will be equal to: