JEE Main 2025 Apr 7 Shift 1 — Physics

If $\epsilon_0$ denotes the permittivity of free space and $\Phi_E$ is the flux of the electric field through the area bounded by the closed surface, then dimensions of $\left(\epsilon_0 \frac{d\phi_E}{dt}\right)$ are that of :

Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is:

An object of mass 1000 g experiences a time dependent force $\vec{F} = \left(2t\,\hat{i} + 3t^2\,\hat{j}\right)N$. The power generated by the force at time t is:

A rod of length 5 L is bent right angle keeping one side length as 2 L.

an L-shaped bent rod on x–y axes; vertical arm of length 3L along the y-axis, horizontal arm of length 2L along the x-axis

The position of the centre of mass of the system:

(Consider L = 10 cm)

A cubic block of mass m is sliding down on an inclined plane at $60°$ with an acceleration of $\frac{g}{2}$, the value of coefficient of kinetic friction is

Two projectiles are fired from ground with same initial speeds from same point at angles $(45° + \alpha)$ and $(45° - \alpha)$ with horizontal direction. The ratio of their times of flights is

Two wires A and B are made of same material having ratio of lengths $\frac{L_A}{L_B} = \frac{1}{3}$ and their diameters ratio $\frac{d_A}{d_B} = 2$. If both the wires are stretched using same force, what would be the ratio of their respective elongations ?

Match the LIST-I with LIST-I

LIST-I	LIST-II
A. Triatomic rigid gas	I. $\frac{C_p}{C_v} = \frac{5}{3}$
B. Diatomic non-rigid gas	II. $\frac{C_p}{C_v} = \frac{7}{5}$
C. Monoatomic gas	III. $\frac{C_p}{C_v} = \frac{4}{3}$
D. Diatomic rigid gas	IV. $\frac{C_p}{C_v} = \frac{9}{7}$

Choose the correct answer from the options given below:

Two harmonic waves moving in the same direction superimpose to form a wave $x = a\ \cos(1.5t)\ \cos(50.5t)$ where t is in seconds. Find the period with which they beat. (close to nearest integer)

An ac current is represented as

$$i = 5\sqrt{2} + 10\cos\left(650\pi t + \frac{\pi}{6}\right)\ \mathrm{Amp}$$

The r.m.s value of the current is

A wire of resistance R is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points A and B is R/n. The value of n is :

a triangular pyramid (tetrahedron) network of six equal resistive wire segments, with vertices A and B at the two ends of the base edge

A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E?

Two charges $q_1$ and $q_2$ are separated by a distance of 30 cm. A third charge $q_3$ initially at 'C' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of $q_3$ from C to D is given by $\frac{q_3 \mathrm{K}}{4\pi \epsilon_0}$, the value of K is:

charge $q_1$ at point A, charge $q_2$ at point B 30 cm to its right; charge $q_3$ at point C, 40 cm vertically above A; a quarter-circle arc of radius 40 cm centred at A from C down to point D on the line AB beyond B

The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility $\chi_{\mathrm{Mg}} = 1.2 \times 10^{-5}$) is :

Uniform magnetic fields of different strengths ($\mathrm{B_1}$ and $\mathrm{B_2}$), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q, at the interface at an instant, moves into the region 2 with velocity $v$ and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface ?

a horizontal interface separating Region 1 (above, field $B_1$ into the page shown by crosses) and Region 2 (below, field $B_2$ into the page shown by crosses)

(Consider the velocity of the particle to be normal to the magnetic field and $\mathrm{B_2} > \mathrm{B_1}$)

Two plane polarized light waves combine at a certain point whose electric field components are

$$E_1 = E_0\ \mathrm{Sin}\ \omega t$$

$$E_2 = E_0\ \mathrm{Sin}\left(\omega t + \frac{\pi}{3}\right)$$

Find the amplitude of the resultant wave.

A lens having refractive index 1.6 has focal length of 12 cm, when it is in air. Find the focal length of the lens when it is placed in water. (Take refractive index of water as 1.28)

For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is

In a hydrogen like ion, the energy difference between the 2$^{\text{nd}}$ excitation energy state and ground is 108.8 eV. The atomic number of the ion is:

In the following circuit, the reading of the ammeter will be

(Take Zener breakdown voltage = 4 V)

a 12 V battery in series with a 100 Ω resistor; across the output, a Zener diode, a voltmeter (V) and a 400 Ω resistor in parallel, with an ammeter (A) in the 400 Ω branch

A, B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure.

three circles of equal radius touching each other — A (disc) on top, B (solid sphere) at bottom left and C (spherical shell) at bottom right; a vertical axis PQ passes through the centre of A and between B and C

The moment of inertia of the given system about PQ axis is $\frac{x}{15}\mathrm{I}$, where I is the moment of inertia of the disc about its diameter. The value of $x$ is __________.

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is $1727°\mathrm{C}$ and power radiated by the wire is 94.2 W. Its emissivity is $\frac{x}{8}$ where $x =$ ____________.

(Given $\sigma = 6.0 \times 10^{-8}\ \mathrm{W\ m^{-2}\ K^{-4}}$, $\pi = 3.14$ and assume that the emissivity of wire material is same at all wavelength.)

An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is _______ $\times\ 10^{-1}$ J.

(Take $\pi = 3.14$)

P–V diagram with V (cm³) on the vertical axis marked 150, 250, 350 and P (kPa) on the horizontal axis marked 300, 400, 500; the cyclic process is a circle centred near (400 kPa, 250 cm³) spanning these ranges

For ac circuit shown in figure, $\mathrm{R} = 100\ \mathrm{k\Omega}$ and $\mathrm{C} = 100\ \mathrm{pF}$ and the phase difference between $\mathrm{V_{in}}$ and $(\mathrm{V_B} - \mathrm{V_A})$ is $90°$. The input signal frequency is $10^x$ rad/sec, where '$x$' is ______.

an ac source $V_{in}$ driving two parallel branches — one branch has R in series with C to ground with node $V_A$ between them, the other has C in series with R to ground with node $V_B$ between them

A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height H above first liquid. If viewed from above, the apparent shift in the position of bottom of container is 40 cm. The value of H is _________ cm. (Consider liquids are immissible)