JEE Main 2022 Physics Paper: 28 Jun, Shift 1

An AC source is connected to an inductance of 100 mH, a capacitance of 100 $\mu$F and a resistance of 120 $\Omega$ as shown in figure. The time in which the resistance having a thermal capacity 2 J/$^\circ$C will get heated by 16$^\circ$ C is _____________ s.

A telegraph line of length 100 km has a capacity of 0.01 $\mu$F/km and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is _____________ mH. (if $\pi = \sqrt{10}$)

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k2rt2, where k is a constant. The power delivered to the particle by the force acting on it is given as

Current measured by the ammeter (A) in the reported circuit when no current flows through 10 $\Omega$ resistance, will be ________________ A.

A meter bridge setup is shown in the figure. It is used to determine an unknown resistance R using a given resistor of 15 $\Omega$. The galvanometer (G) shows null deflection when tapping key is at 43 cm mark from end A. If the end correction for end A is 2 cm, then the determined value of R will be ____________ $\Omega$.

The de Broglie wavelengths for an electron and a photon are $\lambda$e and $\lambda$p respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?

A radar sends an electromagnetic signal of electric field (E0) = 2.25 V/m and magnetic field (B0) = 1.5 $\times$ 10 $-$8 T which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was transmitted at time t = 0 from radar, then after how much time echo will reach to the radar?

The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The magnitude of electric field (E) at the corner D of the square, is:

Given below are two statements:

Statement I: A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.

Statement II: An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero.

Choose the correct answer from the options given below:

Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is $\frac{x}{5}$ Mg for x = ______________. Neglect mass of the string and friction of the block (bigger mass) with ice slab.

(Given g = acceleration due to gravity)

An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface.

Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

A singly ionized magnesium atom (A = 24) ion is accelerated to kinetic energy 5 keV, and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be _____________ cm.

The Q-value of a nuclear reaction and kinetic energy of the projectile particle, Kp are related as:

Motion of a particle in x-y plane is described by a set of following equations $x = 4\sin\left(\frac{\pi}{2}-\omega t\right)\text{ m}$ and $y = 4\sin(\omega t)\text{ m}$. The path of the particle will be:

A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at 60$^\circ$ with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be ____________ ms${}^{-1}$. (if g = 10 m/s2)

The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of minimum deviation will be -

The position vector of 1 kg object is$\vec{r} = \left(3\hat{i} - \hat{j}\right)m$ and its velocity$\vec{v} = \left(3\hat{j} + \hat{k}\right)ms^{-1}$. The magnitude of its angular momentum is $\sqrt{x}$ Nm where x is ___________.

Match List-I with List-II

Choose the correct answer from the options given below:

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

Assertion A: n-p-n transistor permits more current than a p-n-p transistor.

Reason R: Electrons have greater mobility as a charge carrier.

Choose the correct answer from the options given below:

In the following circuit, the correct relation between output (Y) and inputs A and B will be:

For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode:

A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be:

The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be _____________ J. (Given R = 8.31 J/mol.K)

Given below are two statements:

Statement I: When $\mu$ amount of an ideal gas undergoes adiabatic change from state (P1, V1, T1) to state (P2, V2, T2), then work done is $W = \frac{\mu R(T_2 - T_1)}{1-\gamma}$, where $\gamma = \frac{C_p}{C_v}$ and R = universal gas constant. Statement II: In the above case, when work is done on the gas, the temperature of the gas would rise.

Choose the correct answer from the options given below:

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

Assertion A: Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.

Reason R: Coefficient of viscosity = $\frac{\text{Force}}{\text{Velocity gradient}}$

Choose the correct answer from the options given below:

The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be:

The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength 2440 $\text{Å}$ is used to see the object will be: