JEE Main 2021 Physics Paper: 25 Jul, Shift 1

An inductor of 10 mH is connected to a 20V battery through a resistor of 10 k$\Omega$ and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after 1 $\mu$s is $\frac{x}{100}$ mA. Then x is equal to ___________. (Take e______1 = 0.37)

A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as: $\varepsilon(x) = \varepsilon_0 + kx$, for $\left(0 < x \le \frac{d}{2}\right)$

$\varepsilon(x) = \varepsilon_0 + k(d-x)$, for $\left(\frac{d}{2} \le x \le d\right)$

An electric bulb rated as 200 W at 100 V is used in a circuit having 200 V supply. The resistance 'R' that must be put in series with the bulb so that the bulb delivers the same power is _____________ $\Omega$.

In the given figure, there is a circuit of potentiometer of length AB = 10 m. The resistance per unit length is 0.1 $\Omega$ per cm. Across AB, a battery of emf E and internal resistance 'r' is connected. The maximum value of emf measured by this potentiometer is:

What should be the order of arrangement of de-Broglie wavelength of electron ($\lambda$e), an $\alpha$-particle ($\lambda$a) and proton ($\lambda$p) given that all have the same kinetic energy?

A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3M will be:

A circular conducting coil of radius 1 m is being heated by the change of magnetic field $\vec{B}$passing perpendicular to the plane in which the coil is laid. The resistance of the coil is 2 $\mu\Omega$. The magnetic field is slowly switched off such that its magnitude changes in time as

$B = \frac{4}{\pi} \times 10^{-3}\,T\left(1-\frac{t}{100}\right)$

The energy dissipated by the coil before the magnetic field is switched off completely is E = ___________ mJ.

A linearly polarized electromagnetic wave in vacuum

$E = 3.1 \cos\left[(1.8)z - (5.4 \times 10^{6})t\right] \hat{i}\text{ N/C}$

is incident normally on a perfectly reflecting wall at z = a. Choose the correct option

A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same charge 'q'. If the free charged particle is displaced from its equilibrium position through distance 'x' (x << 1 m), the particle executes SHM. Its angular frequency of oscillation will be ____________ $\times$ 105 rad/s if q2 = 10 C2.

The minimum and maximum distances of a planet revolving around the sun are x1 and x2. If the minimum speed of the planet on its trajectory is v0 then its maximum speed will be:

The value of aluminium susceptibility is 2.2 $\times$ 10$-$5. The percentage increase in the magnetic field if space within a current carrying toroid is filled with aluminium is $\frac{x}{10^4}$. Then the value of x is _________________.

Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are Y1 and Y2. The combination behaves as a single wire then its Young's modulus is:

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4th second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap? (Take g = 9.8 m/s2)

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as:

(where $\lambda$ is the decay constant)

The half-life of ${}^{198}Au$ is 3 days. If atomic weight of ${}^{198}Au$ is 198 g/mol then the activity of 2 mg of ${}^{198}Au$ is [in disintegration/second]:

In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be ____________ rad/s when k = 20 N/m.

A ray of laser of a wavelength 630 nm is incident at an angle of 30${}^\circ$ at the diamond-air interface. It is going from diamond to air. The refractive index of diamond is 2.42 and that of air is 1. Choose the correct option.

A particle of mass 'm' is moving in time 't' on a trajectory given by

$\vec{r} = 10\alpha t^{2}\hat{i} + 5\beta(t - 5)\hat{j}$

Where $\alpha$ and $\beta$ are dimensional constants.

The angular momentum of the particle becomes the same as it was for t = 0 at time t = ____________ seconds.

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

Assertion A: Moment of inertia of a circular disc of mass 'M' and radius 'R' about X, Y axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be Ix, Iy and Iz respectively. The respectively radii of gyration about all the three axes will be the same. Reason R: A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below:

Identify the logic operation carried out.

For a gas CP $-$ CV = R in a state P and CP $-$ CV = 1.10 R in a state Q, TP and TQ are the temperatures in two different states P and Q respectively. Then

A monoatomic ideal gas, initially at temperature T1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If l1 and l2 are the lengths of the gas column, before and after the expansion respectively, then the value of $\frac{T_1}{T_2}$ will be:

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is:

Student A and student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is 0.322 cm. The absolute value of the difference between the final circular scale readings observed by the students A and B is ______________.

[Figure shows position of reference 'O' when jaws of screw gauge are closed]

Given pitch = 0.1 cm.

Match List - I with List - II

Choose the correct answer from the options given below:

In the Young's double slit experiment, the distance between the slits varies in time as d(t) = d0 + a0 sin$\omega$t; where d0, $\omega$ and a0 are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as:

A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60 ${}^\circ$ to the vertical will be (g = 10 m/s2) ____________ m/s.