JEE Main 2024 Physics Paper: 27 Jan, Shift 1

The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

The charge accumulated on the capacitor connected in the following circuit is _______ $\mu\text{C}$ (Given $C=150\ \mu\text{F})$

A train is moving with a speed of $12\text{ m/s}$ on rails which are $1.5\text{ m}$ apart. To negotiate a curve of radius $400\text{ m}$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g = 10\text{ m/s}^2)$:

A wire of resistance $\text{R}$ and length $\text{L}$ is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be:

A wire of length $10\text{ cm}$ and radius $\sqrt{7} \times 10^{-4}\text{ m}$ is connected across the right gap of a meter bridge. When a resistance of $4.5\ \Omega$ is connected on the left gap by using a resistance box, the balance length is found to be at $60\text{ cm}$ from the left end. If the resistivity of the wire is $\text{R} \times 10^{-7}\ \Omega\text{ m}$, then value of $\text{R}$ is:

A rectangular loop of length $2.5\text{ m}$ and width $2\text{ m}$ is placed at $60^\circ$ to a magnetic field of $4\text{ T}$. The loop is removed from the field in $10\text{ sec}$. The average emf induced in the loop during this time is

Two coils have mutual inductance $0.002\text{ H}$. The current changes in the first coil according to the relation $i = i_0 \sin \omega t$, where $i_0 = 5\text{ A}$ and $\omega = 50\pi$ rad/s. The maximum value of emf in the second coil is $\frac{\pi}{\alpha}\text{ V}$. The value of $\alpha$ is _______.

A plane electromagnetic wave propagating in $x$-direction is described by

$E_y = \left(200\text{ V m}^{-1}\right) \sin\left[1.5 \times 10^{7} t - 0.05 x\right]$;

The intensity of the wave is:

(Use $\epsilon_0 = 8.85 \times 10^{-12}\text{ C}^2\text{ N}^{-1}\text{ m}^{-2}$)

A thin metallic wire having cross sectional area of $10^{-4}\text{ m}^{2}$ is used to make a ring of radius $30\text{ cm}$. A positive charge of $2\pi\text{ C}$ is uniformly distributed over the ring, while another positive charge of 30 $\text{pC}$ is kept at the centre of the ring. The tension in the ring is ______ $\text{N}$; provided that the ring does not get deformed (neglect the influence of gravity). (given, $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ SI units)

An electric charge $10^{-6}\,\mu\text{C}$ is placed at origin $(0, 0)\text{ m}$ of $X - Y$ co-ordinate system. Two points $P$ and $Q$ are situated at $(\sqrt{3}, \sqrt{3})\text{ m}$ and $(\sqrt{6}, 0)\text{ m}$ respectively. The potential difference between the points $P$ and $Q$ will be:

If average depth of an ocean is $4000\text{ m}$ and the bulk modulus of water is $2 \times 10^{9}\text{ N m}^{-2}$, then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$. The value of $\alpha$ is _______ (Given, $g = 10\text{ m s}^{-2},\ \rho = 1000\text{ kg m}^{-3}$)

The acceleration due to gravity on the surface of earth is $g$. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be:

The average kinetic energy of a monatomic molecule is $0.414\text{ eV}$ at temperature: (Use $K_B = 1.38 \times 10^{-23}\text{ J/mol-K}$)

If average depth of an ocean is $4000\text{ m}$ and the bulk modulus of water is $2 \times 10^{9}\text{ Nm}^{-2}$, then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$. The value of $\alpha$ is _______ (Given, $\text{g} = 10\text{ ms}^{-2},\ \rho = 1000\text{ kg m}^{-3}$)

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is $5.0\text{ cm}$. The magnitude of the magnetic field at a point $\text{P}$ midway between the wires is _______ $\mu\text{T}$

(Given: $\mu_0 = 4\pi \times 10^{-7}\text{ TmA}^{-1}$)

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\vec{E}$ and $\vec{B}$ represent the electric and magnetic fields respectively, then the region of space may have:

(A) $E = 0,\ B = 0$

(B) $E = 0,\ B \neq 0$

(C) $E \neq 0,\ B = 0$

(D) $E \neq 0,\ B \neq 0$

Choose the most appropriate answer from the options given below:

In a nuclear fission process, a high mass nuclide $(A \approx 236)$ with binding energy $7.6\text{ MeV/}$ Nucleon dissociated into middle mass nuclides $(\text{A} \approx 118)$, having binding energy of $8.6\text{ MeV/Nucleon}$. The energy released in the process would be ______ $\text{MeV}$.

A particle executes simple harmonic motion with an amplitude of $4\text{ cm}$. At the mean position, velocity of the particle is $10\text{ cm/s}$. The distance of the particle from the mean position when its speed becomes $5\text{ cm/s}$ is $\sqrt{\alpha}\text{ cm}$, where $\alpha =$ ________.

Position of an ant ($\text{S}$ in metres) moving in $\text{Y-Z}$ plane is given by $S = 2t^{2}\hat{j} + 5\hat{k}$ (where $t$ is in second). The magnitude and direction of velocity of the ant at $t = 1\text{ s}$ will be:

A particle starts from origin at $t = 0$ with a velocity $5\hat{i}\text{ m/s}$ and moves in $x - y$ plane under action of a force which produces a constant acceleration of $(3\hat{i} + 2\hat{j})\text{ m/s}^{2}$. If the $x$-coordinate of the particle at that instant is $84\text{ m}$, then the speed of the particle at this time is $\sqrt{\alpha}\text{ m/s}$. The value of $\alpha$ is _________.

If the refractive index of the material of a prism is $\cot\left(\frac{A}{2}\right)$, where $A$ is the angle of prism then the angle of minimum deviation will be

Two immiscible liquids of refractive indices $\frac{8}{5}$ and $\frac{3}{2}$ respectively are put in a beaker as shown in the figure. The height of each column is $6\text{ cm}$. A coin is placed at the bottom of the beaker. For near normal vision, the apparent depth of the coin is $\frac{\alpha}{4}\text{ cm}$. The value of $\alpha$ is _________.

A convex lens of focal length $40\text{ cm}$ forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length $20\text{ cm}$. The photoelectric current now is:

Four particles each of mass $1\text{ kg}$ are placed at four corners of a square of side $2\text{ m}$. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is _____ $\text{kg m}^{2}$.

Which of the following circuits is reverse - biased?

$0.08\text{ kg}$ air is heated at constant volume through $5^\circ\text{C}$. The specific heat of air at constant volume is $0.17\text{ kcal/kg}\,{}^\circ\text{C}$ and $J = 4.18$ joule/ $\text{cal}$. The change in its internal energy is approximately.

Identify the physical quantity that cannot be measured using spherometer:

Given below are two statements:

Statement (I): Planck's constant and angular momentum have same dimensions. Statement (II): Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements:

Statement (I) :Viscosity of gases is greater than that of liquids.

Statement (II): Surface tension of a liquid decreases due to the presence of insoluble impurities. In the light of the above statements, choose the most appropriate answer from the options given below: