JEE Main 2023 Physics Paper: 13 Apr, Shift 1

In the given figure, an inductor and a resistor are connected in series with a battery of emf E volt. $\frac{E^a}{2b}\text{ J/s}$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $\frac{b}{a}$ will be __________.

The radius of $2$nd orbit of $\text{He}^{+}$ of Bohr's model is $r_1$ and that of fourth orbit of $\text{Be}^{3+}$ is represented as $r_2$. Now the ratio $\frac{r_2}{r_1}$ is $x : 1$. The value of $x$ is ___________.

Different combination of 3 resistors of equal resistance $R$ are shown in the figures. The increasing order for power dissipation is:

A potential $V_0$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_1$. The wire is then cut into two equal halves and a potential of $V_0$ is applied across the length of each half. The total power dissipation across two wires is $P_2$. The ratio $P_2 : P_1$ is $\sqrt{x} : 1$. The value of $x$ is ___________.

When a resistance of $5\ \Omega$ is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of $250\text{ mA}$, however when $1050\ \Omega$ resistance is connected with it in series, it gives full scale deflection for 25 volt. The resistance of galvanometer is ____________ $\Omega$.

The difference between threshold wavelengths for two metal surfaces $\text{A}$ and $\text{B}$ having work function $\phi_A = 9\text{ eV}$ and $\phi_B = 4.5\text{ eV}$ in $\text{nm}$ is:

$\{$ Given, hc $= 1242\text{ eVnm}\}$

Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions:

Two charges each of magnitude $0.01\text{ C}$ and separated by a distance of $0.4\text{ mm}$ constitute an electric dipole. If the dipole is placed in an uniform electric field '$\vec{E}$' of 10 dyne/C making $30^\circ$ angle with $\vec{E}$, the magnitude of torque acting on dipole is:

A thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel at $5\text{ m}$ distance from each other. Points 'P' and 'Q' are at $\frac{3}{\pi}$ m and $\frac{4}{\pi}$ m perpendicular distances from line charge towards sheet charge, respectively. '$E_P$ ' and '$E_Q$' are the magnitudes of resultant electric field intensities at point 'P' and 'Q', respectively. If $\frac{E_P}{E_Q} = \frac{4}{a}$ for $2|\sigma| = |\lambda|$, then the value of $a$ is ___________.

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at $A$ is $1.5\text{ cm}^2$, and $B$ is $25\text{ mm}^2$, if the speed of liquid at $B$ is $60\text{ cm/s}$ then $(P_A - P_B)$ is:

(Given $P_A$ and $P_B$ are liquid pressures at $A$ and $B$ points.

density $\rho = 1000\text{ kg m}^{-3}$

$A$ and $B$ are on the axis of tube

A planet having mass $9M_e$ and radius $4R_e$, where $M_e$ and $R_e$ are mass and radius of earth respectively, has escape velocity in $\text{km/s}$ given by:

(Given escape velocity on earth $V_e = 11.2 \times 10^{3}\text{ m/s}$)

The rms speed of oxygen molecule in a vessel at particular temperature is $\left(1 + \frac{5}{x}\right)^{\frac{1}{2}} v$, where $v$ is the average speed of the molecule. The value of $x$ will be:

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

Under isothermal condition, the pressure of a gas is given by $\text{P} = a\,\text{V}^{-3}$, where $a$ is a constant and $\text{V}$ is the volume of the gas. The bulk modulus at constant temperature is equal to

The elastic potential energy stored in a steel wire of length $20\text{ m}$ stretched through $2\text{ cm}$ is $80\text{ J}$. The cross sectional area of the wire is __________ $\text{mm}^2$.

$($ Given, $Y = 2.0 \times 10^{11}\text{ Nm}^{-2})$

Two trains 'A' and 'B' of length '$l$' and '$4l$' are travelling into a tunnel of length '$L$' in parallel tracks from opposite directions with velocities $108\text{ km/h}$ and $72\text{ km/h}$, respectively. If train 'A' takes $35\text{ s}$ less time than train 'B' to cross the tunnel, then length '$L$' of tunnel is:

(Given $L = 60l$)

The source of time varying magnetic field may be

(A) a permanent magnet

(B) an electric field changing linearly with time

(C) direct current

(D) a decelerating charge particle

(E) an antenna fed with a digital signal

Choose the correct answer from the options given below:

${}^{238}_{92}A \rightarrow {}^{234}_{90}B + {}^{4}_{2}D + Q$

In the given nuclear reaction, the approximate amount of energy released will be: [Given, mass of ${}^{238}_{92}\text{A} = 238.05079 \times 931.5\text{ MeV/c}^{2},$

mass of ${}^{234}_{90}B = 234.04363 \times 931.5\text{ MeV/c}^{2},$

mass of ${}^{4}_{2}D = 4.00260 \times 931.5\text{ MeV/c}^{2}]$

Which graph represents the difference between total energy and potential energy of a particle executing SHM vs its distance from mean position?

At a given point of time the value of displacement of a simple harmonic oscillator is given as $y = A\cos(30^\circ)$. If amplitude is $40\text{ cm}$ and kinetic energy at that time is $200\text{ J}$, the value of force constant is $1.0 \times 10^{x}\text{ N m}^{-1}$. The value of $x$ is ____________.

A vessel of depth '$d$' is half filled with oil of refractive index $n_1$ and the other half is filled with water of refractive index $n_2$. The apparent depth of this vessel when viewed from above will be-

A fish rising vertically upward with a uniform velocity of $8\text{ ms}^{-1}$, observes that a bird is diving vertically downward towards the fish with the velocity of $12\text{ ms}^{-1}$. If the refractive index of water is $\frac{4}{3}$, then the actual velocity of the diving bird to pick the fish, will be __________ $\text{ms}^{-1}$.

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $\pi : 22$ then, the value of its angular speed will be ____________ $\text{rad/s}$.

A disc is rolling without slipping on a surface. The radius of the disc is $R$. At $t = 0$, the top most point on the disc is $A$ as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is

From the given transfer characteristic of a transistor in $\text{CE}$ configuration, the value of power gain of this configuration is $10^{x}$, for $\mathrm{R}_{\mathrm{B}} = 10\text{ k}\Omega$, and $\mathrm{R}_{\mathrm{C}} = 1\text{ k}\Omega$. The value of $x$ is __________.

For the following circuit and given inputs A and B, choose the correct option for output '$Y$'

A body of mass $(5 \pm 0.5)\text{ kg}$ is moving with a velocity of $(20 \pm 0.4)\text{ m/s}$. Its kinetic energy will be

Two bodies are having kinetic energies in the ratio 16: 9. If they have same linear momentum, the ratio of their masses respectively is:

The ratio of powers of two motors is $\frac{3\sqrt{x}}{\sqrt{x} + 1}$, that are capable of raising $300\text{ kg}$ water in 5 minutes and $50\text{ kg}$ water in 2 minutes respectively from a well of $100\text{ m}$ deep. The value of $x$ will be