JEE Main 2024 Physics Paper: 31 Jan, Shift 1

If the wavelength of the first member of Lyman series of hydrogen is $\lambda$. The wavelength of the second member will be

A parallel plate capacitor with plate separation $5\text{ mm}$ is charged up by a battery. It is found that on introducing a dielectric sheet of thickness $2\text{ mm}$, while keeping the battery connections intact, the capacitor draws $25\%$ more charge from the battery than before. The dielectric constant of the sheet is _________.

A coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$. If the distance of the coin from the center of the disc is $r$, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is:

Equivalent resistance of the following network is __________ $\Omega$.

Two conductors have the same resistances at $0^\circ\text{C}$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients for their series and parallel combinations are:

When a metal surface is illuminated by light of wavelength $\lambda$, the stopping potential is $8\text{ V}$. When the same surface is illuminated by light of wavelength $3\lambda$, stopping potential is $2\text{ V}$. The threshold wavelength for this surface is:

A coil is placed perpendicular to a magnetic field of $5000\text{ T}$. When the field is changed to $3000\text{ T}$ in $2\text{ s}$, an induced emf of $22\text{ V}$ is produced in the coil. If the diameter of the coil is $0.02\text{ m}$, then the number of turns in the coil is:

A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L \left(L = l^2\right)$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x} \times 10^{-7}\text{ H}$, where $x =$ _________.

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5 \times 10^{10}\text{ Hz}$ and an amplitude of $50\text{ V m}^{-1}$. The total average energy density of the electromagnetic field of the wave is: [Use $\varepsilon_0 = 8.85 \times 10^{-12}\text{ C}^2/\text{N m}^2$ ]

Two charges $q$ and $3q$ are separated by a distance '$r$' in air. At a distance $x$ from charge $q$, the resultant electric field is zero. The value of $x$ is:

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $0.02\%$ is _______ $m$.

(Take density of sea water $= 10^{3}\text{ kg m}^{-3}$, Bulk modulus of rubber $= 9 \times 10^{8}\text{ N m}^{-2}$, and $g = 10\text{ m s}^{-2}$)

Four identical particles of mass $m$ are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is $\left(\frac{2\sqrt{2}+1}{32}\right)\frac{Gm^{2}}{L^{2}}$, the length of the sides of the square is

The parameter that remains the same for molecules of all gases at a given temperature is:

In the given arrangement of a doubly inclined plane two blocks of masses $M$ and $m$ are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of $m$, for which $M = 10\text{ kg}$ will move down with an acceleration of $2\text{ m/s}^{2}$, is: (take $g = 10\text{ m/s}^{2}$ and $\tan 37^\circ = 3/4)$

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $0.02\%$ is _______ $m$.

(Take density of sea water $= 10^{3}\text{ kgm}^{-3}$, Bulk modulus of rubber $= 9 \times 10^{8}\text{ Nm}^{-2}$, and $g = 10\text{ ms}^{-2}$)

The relation between time '$t$' and distance '$x$' is $t = \alpha x^2 + \beta x$, where $\alpha$ and $\beta$ are constants. The relation between acceleration $(a)$ and velocity $(v)$ is:

A rigid wire consists of a semicircular portion of radius $R$ and two straight sections. The wire is partially immersed in a perpendicular magnetic field $B = B_0\hat{k}$ as shown in figure. The magnetic force on the wire if it has a current $i$ is:

An electron moves through a uniform magnetic field $\vec{B} = B_0\hat{i} + 2B_0\hat{j}\text{ T}$. At a particular instant of time, the velocity of electron is $\vec{u} = 3\hat{i} + 5\hat{j}\text{ m/s}$. If the magnetic force acting on electron is $\vec{F} = 5e\hat{k}\text{ N}$, where $e$ is the charge of electron, then the value of $B_0$ is _________ $T$.

The mass defect in a particular reaction is $0.4\text{ g}$. The amount of energy liberated is $n \times 10^{7}\text{ kWh}$, where $n =$ __________. (speed of light $= 3 \times 10^{8}\text{ m/s})$

A particle performs simple harmonic motion with amplitude $A$. Its speed is increased to three times at an instant when its displacement is $\frac{2A}{3}$. The new amplitude of motion is $\frac{nA}{3}$. The value of $n$ is ___________.

The refractive index of a prism with apex angle $A$ is $\cot A/2$. The angle of minimum deviation is:

A solid circular disc of mass $50\text{ kg}$ rolls along a horizontal floor so that its center of mass has a speed of $0.4\text{ m/s}$. The absolute value of work done on the disc to stop it is ________ J.

Identify the logic operation performed by the given circuit.

The given figure represents two isobaric processes for the same mass of an ideal gas, then

A force is represented by $F = ax^2 + bt^{\frac{1}{2}}$

where $x =$ distance and $t =$ time. The dimensions of $b^2/a$ are:

If the percentage errors in measuring the length and the diameter of a wire are $0.1\%$ each. The percentage error in measuring its resistance will be:

A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is $60\text{ cm}$, the length of the closed pipe will be:

Two waves of intensity ratio $1 : 9$ cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is $I_1$ (b) Waves are coherent is $I_2$ and differ in phase by $60^\circ$. If $\frac{I_1}{I_2} = \frac{10}{x}$ then $x =$ _________.