JEE Main 2024 Physics Paper: 9 Apr, Shift 2

A capacitor of reactance $4\sqrt{3}\ \Omega$ and a resistor of resistance $4\ \Omega$ are connected in series with an ac source of peak value $8\sqrt{2}\text{ V}$. The power dissipation in the circuit is __________ W.

A hydrogen atom in ground state is given an energy of $10.2\text{ eV}$. How many spectral lines will be emitted due to transition of electrons?

The effective resistance between $A$ and $B$, if resistance of each resistor is $R$, will be:

At room temperature $(27^\circ\text{C})$, the resistance of a heating element is $50\ \Omega$. The temperature coefficient of the material is $2.4 \times 10^{-4}\ {}^\circ\text{C}^{-1}$. The temperature of the element, when its resistance is $62\ \Omega$, is __________ ${}^\circ\text{C}$.

To determine the resistance (R) of a wire, a circuit is designed below. The $V\text{-}I$ characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of $R$ is _________ $\Omega$.

UV light of $4.13\text{ eV}$ is incident on a photosensitive metal surface having work function $3.13\text{ eV}$. The maximum kinetic energy of ejected photoelectrons will be:

A square loop of side $15\text{ cm}$ is being moved towards right at a constant speed of $2\text{ cm/s}$ as shown in figure. The front edge enters the $50\text{ cm}$ wide magnetic field at $t = 0$. The value of induced emf in the loop at $t = 10\text{ s}$ will be:

The magnetic field in a plane electromagnetic wave is

$B_y = \left(3.5\times 10^{-7}\right)\sin\left(1.5\times 10^{3}x + 0.5\times 10^{11}t\right)\text{ T}$. The corresponding electric field will be:

Five charges $+q, +5q, -2q, +3q$ and $-4q$ are situated as shown in the figure. The electric flux due to this configuration through the surface $S$ is:

An electric field $\vec{E} = (2x\hat{i})\text{ NC}^{-1}$ exists in space. A cube of side $2\text{ m}$ is placed in the space as per figure given below. The electric flux through the cube is ______ $\text{Nm}^{2}/\text{C}$.

A satellite of $10^{3}\text{ kg}$ mass is revolving in circular orbit of radius $2R$. If $\frac{10^{4}R}{6}\text{ J}$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius

(use $g = 10\text{ m/s}^{2}, R =$ radius of earth)

The temperature of a gas is $-78^\circ\text{C}$ and the average translational kinetic energy of its molecules is $K$. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes $2K$ is:

A $1\text{ kg}$ mass is suspended from the ceiling by a rope of length $4\text{ m}$. A horizontal force '$F$' is applied at the mid point of the rope so that the rope makes an angle of $45^\circ$ with respect to the vertical axis as shown in figure. The magnitude of $F$ is:

(Assume that the system is in equilibrium and $g = 10\text{ m/s}^2$)

Two cars are travelling towards each other at speed of $20\text{ m s}^{-1}$ each. When the cars are $300\text{ m}$ apart, both the drivers apply brakes and the cars retard at the rate of $2\text{ m s}^{-2}$. The distance between them when they come to rest is:

A straight magnetic strip has a magnetic moment of $44\text{ A m}^{2}$. If the strip is bent in a semicircular shape, its magnetic moment will be ________ $\text{A m}^{2}$.

(given $\pi = \frac{22}{7}$)

A proton and a deuteron $(q = +e, m = 2.0\text{u})$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deuteron path to the radius $r_p$ of the proton path is:

The energy released in the fusion of $2\text{ kg}$ of hydrogen deep in the sun is $E_{H}$ and the energy released in the fission of $2\text{ kg}$ of ${}^{235}\text{U}$ is $E_{U}$. The ratio $\frac{E_{H}}{E_{U}}$ is approximately: (Consider the fusion reaction as $4\,{}^{1}_{1}H + 2\text{e}^{-} \rightarrow {}^{4}_{2}\text{He} + 2v + 6\gamma + 26.7\text{ MeV}$, energy released in the fission reaction of ${}^{235}\text{U}$ is $200\text{ MeV}$ per fission nucleus and $\text{N}_{\text{A}} = 6.023 \times 10^{23})$

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $2 : 1$. After disintegration they will move:

A particle of mass $0.50\text{ kg}$ executes simple harmonic motion under force $F = -50(\text{N m}^{-1})x$. The time period of oscillation is $\frac{x}{35}\text{ s}$. The value of $x$ is _________.

(Given $\pi = \frac{22}{7}$)

The following figure represents two biconvex lenses $L_1$ and $L_2$ having focal length $10\text{ cm}$ and $15\text{ cm}$ respectively. The distance between $L_1$ & $L_2$ is:

A circular disc reaches from top to bottom of an inclined plane of length $l$. When it slips down the plane, it takes $t\text{ s}$. When it rolls down the plane then it takes $\left(\frac{\alpha}{2}\right)^{1/2} t\text{ s}$, where $\alpha$ is _________.

In the truth table of the above circuit the value of X and Y are:

The $I\text{-}V$ characteristics of an electronic device are shown in the figure. The device is:

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

A real gas within a closed chamber at $27^\circ\text{C}$ undergoes the cyclic process as shown in figure. The gas obeys $PV^3 = RT$ equation for the path $A$ to $B$. The net work done in the complete cycle is (assuming $R = 8\text{ J/mol K}$):

The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $h/\sqrt{2mE}$. The dimensional formula for Planck's constant is:

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is _________${}^\circ$.

A spherical ball of radius $1 \times 10^{-4}\text{ m}$ and density $10^{5}\text{ kg/m}^{3}$ falls freely under gravity through a distance $h$ before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of $h$ is approximately:

(The coefficient of viscosity of water is $9.8 \times 10^{-6}\text{ N s/m}^{2}$)

Monochromatic light of wavelength $500\text{ nm}$ is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index $= 1.5$), the central maximum is shifted to a position previously occupied by the $4$th bright fringe. The thickness of the glass-plate is __________ $\mu\text{m}$.

A force $(3x^2 + 2x - 5)\text{ N}$ displaces a body from $x = 2\text{ m}$ to $x = 4\text{ m}$. Work done by this force is ________ J.