JEE Main 2022 Physics Paper: 30 Jun, Shift 1

A series LCR circuit with $R = \frac{250}{11}\ \Omega$ and $X_L = \frac{70}{11}\ \Omega$ is connected across a 220 V, 50 Hz supply. The value of capacitance needed to maximize the average power of the circuit will be _________ $\mu$F. (Take: $\pi = \frac{22}{7}$)

In series RLC resonator, if the self inductance and capacitance become double, the new resonant frequency (f2) and new quality factor (Q2) will be:

(f1 = original resonant frequency, Q1 = original quality factor)

A hydrogen atom in ground state absorbs 12.09 eV of energy. The orbital angular momentum of the electron is increased by:

A hydrogen atom in its first excited state absorbs a photon of energy x $\times$ 10$-$2 eV and excited to a higher energy state where the potential energy of electron is${}^{-1}$.08 eV. The value of x is ______________.

Co is the capacitance of a parallel plate capacitor with air as a medium between the plates (as shown in Fig. 1). If half space between the plates is filled with a dielectric of relative permittivity $\varepsilon$r (as shown in Fig. 2), the new capacitance of the capacitor will be:

A person starts his journey from centre 'O' of the park and comes back to the same position following path OPQO as shown in the figure. The radius of path taken by the person is 200 m and he takes 3 min 58 sec to complete his journey. The average speed of the person is _____________ ms${}^{-1}$. (take $\pi$ = 3.14)

An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14 $\Omega$. If this single copper wire of the cable is replaced by seven identical well insulated copper wires each of radius 3 mm connected in parallel, then the new resistance of the combination will be:

The circuit diagram of potentiometer used to measure the internal resistance of a cell (E) is shown in figure. The key 'K' is kept closed so as to send constant current through potentiometer wire. When key 'K1' is kept open the null point is found to be at 120 cm on the potentiometer wire. When the key 'K1' is closed the null point is shifted at 80 cm at the potentiometer wire. The internal resistance of the given cell is _____________ $\Omega$.

A source of monochromatic light liberates 9 $\times$ 1020 photon per second with wavelength 600 nm when operated at 400 W. The number of photons emitted per second with wavelength of 800 nm by the source of monochromatic light operating at same power will be:

An expression for oscillating electric field in a plane electromagnetic wave is given as Ez = 300 sin(5$\pi\times$ 103x $-$ 3$\pi\times$ 1011t) Vm${}^{-1}$

Then, the value of magnetic field amplitude will be:

(Given: speed of light in Vacuum c = 3 $\times$ 108 ms${}^{-1}$)

Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. The potential energy of bigger drop will be ____________ E. Where E is the potential energy of a single smaller drop.

The radii of two planets A and B are in the ratio 2: 3. Their densities are 3$\rho$ and 5$\rho$ respectively. The ratio of their acceleration due to gravity is:

A 2 kg block is pushed against a vertical wall by applying a horizontal force of 50 N. The coefficient of static friction between the block and the wall is 0.5. A force F is also applied on the block vertically upward (as shown in figure). The maximum value of F applied, so that the block does not move upward, will be:

(Given: g = 10 ms${}^{-}$2)

A coil of n number of turns wound tightly in the form of a spiral with inner and outer radii r1 and r2 respectively. When a current of strength I is passed through the coil, the magnetic field at its centre will be:

A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accelerated proton will be:

(Take: e = 1.6 $\times$ 10$-$19 C, mp = 1.67 $\times$ 10$-$27 kg)

Two projectiles P1 and P2 thrown with speed in the ratio $\sqrt{3}$: $\sqrt{2}$, attain the same height during their motion. If P2 is thrown at an angle of 60$^\circ$ with the horizontal, the angle of projection of P1 with horizontal will be:

At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms${}^{-2}$. At t = 20 s, a ball is released from the top of the truck. The ball strikes the ground in 1 s after the release. The velocity of the ball, when it strikes the ground, will be:

(Given g = 10 ms${}^{-2}$)

The refractive index of an equilateral prism is $\sqrt{2}$. The angle of emergence under minimum deviation position of prism, in degree, is ___________.

Four particles with a mass of 1 kg, 2 kg, 3 kg and 4 kg are situated at the corners of a square with side 1 m (as shown in the figure). The moment of inertia of the system, about an axis passing through the point O and perpendicular to the plane of the square, is ______________ kg m2.

The circuit diagram used to study the characteristic curve of a zener diode is connected to variable power supply (0 $-$ 15 V) as shown in figure. A zener diode with maximum potential Vz = 10 V and maximum power dissipation of 0.4 W is connected across a potential divider arrangement. The value of resistance RP connected in series with the zener diode to protect it from the damage is ________________ $\Omega$.

The excess pressure inside a liquid drop is 500 Nm${}^{-2}$. If the radius of the drop is 2 mm, the surface tension of liquid is x $\times$ 10$-$3 Nm${}^{-1}$. The value of x is _____________.

A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm3 to 150 cm3 adiabatically. In this process, the value of workdone on the gas will be:

The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. When the bulb is placed in a liquid, the pressure becomes 180 cm of mercury. Temperature of the liquid is:

(Given 0$^\circ$ C = 273 K)

If n main scale divisions coincide with (n + 1) vernier scale divisions. The least count of vernier callipers, when each centimetre on the main scale is divided into five equal parts, will be:

An air bubble of negligible weight having radius r rises steadily through a of density $\sigma$ at speed v. The coefficient of viscosity of the is given by:

An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car at the speed of 72 kmh${}^{-1}$ in the direction of wind which is blowing at 72 kmh${}^{-1}$ speed. Frequency of siren is 720 Hz. The employee hears an apparent frequency of ____________ Hz.

(Assume speed of sound to be 340 ms${}^{-1}$)

Which of the following equations correctly represents a travelling wave having wavelength $\lambda$ = 4.0 cm, frequency $\nu$ = 100 Hz and travelling in positive x-axis direction?

Find the ratio of maximum intensity to the minimum intensity in the interference pattern if the widths of the two slits in Young's experiment are in the ratio of 9: 16. (Assuming intensity of light is directly proportional to the width of slits)