JEE Main 2026 Physics Paper: 5 Apr, Shift 2

A series LCR circuit with $R = 20\ \Omega,\ L = 1.6\text{ H}$ and $C = 40\ \mu\text{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is $\underline{\hspace{3em}}\ \Omega$.

Under steady state condition the potential difference across the capacitor in the circuit is ______ V.

When an external resistance of $5\ \Omega$ is connected across terminals of a cell, a current of 0.25 A flows through it. When the $5\ \Omega$ resistor is replaced by a $2\ \Omega$ resistor, a current of 0.5 A flows through it. The internal resistance of the cell is $\underline{\hspace{3em}}\ \Omega$.

An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is reduced by $20\%$. The de Broglie wavelength of electron in the medium is $\alpha\lambda_0$, where $\lambda_0$ is its de Broglie wavelength in free space. The value of $\alpha$ is ______.

A circular loop of radius 20 cm and resistance $2\ \Omega$ is placed in a time varying magnetic field $\vec{B} = \left(2t^{2}+2t+3\right)T$. At $t = 0$, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at $t = 3\text{ s}$ is $\frac{\alpha}{50}\text{ A}$. The value of $\alpha$ is ______. (Take $\pi = 22/7$)

A metal rod of length $L$ rotates about one end at origin with a uniform angular velocity $\omega$. The magnetic field radially falls off as $B(r) = B_o e^{-\lambda r};\ \lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The electromagnetic wave exerts pressure on the surface on which they are allowed to fall.

Reason (R): There is no mass associated with the electromagnetic waves.

In the light of the above statements, choose the correct answer from the options given below:

A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth $(R_e)$. The increase in potential energy will be ______.

( $g$ is acceleration due to gravity at the surface of earth)

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is $600 \times 10^{-6}\text{ m}^3$. The elastic potential energy stored in the wire in stretched condition would be ______ J.

(Given Young modulus of copper $= 1.1 \times 10^{11}\text{ N/m}^2$)

The velocity $(v)$ versus time $(t)$ plot of a particle is shown in the figure, for a time interval of 40 s. The total distance travelled by the particle and the average velocity during this period are, respectively

______.

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v} = \left(\frac{v_0}{\sqrt{2}}\hat{x} + \frac{v_0}{\sqrt{2}}\hat{y}\right)$. There exists a uniform magnetic field $\vec{B} = B_0\hat{z}$ and a space varying electric field $\vec{E} = E_0 e^{-\lambda x}\hat{x}$ within the region $0 \leqslant x \leqslant L$. After travelling a distance such that $x$-coordinate has changed from $x = 0$ to $x = L$, the change in the kinetic energy is ______.

Assuming the experimental mass of ${}_{6}^{12}C$ as $12u$, the mass defect of ${}_{6}^{12}C$ atom is $\_\_\_\_\_\ \text{MeV/c}^{2}$. (Mass of proton $= 1.00727\text{u}$. mass of neutron $= 1.00866\text{u}, 1\text{u} = 931.5\text{MeV/c}^{2}$ and c is the speed of the light in vacuum).

Match List - I with List - II.

Choose the correct answer from the options given below:

A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses?

An object $AB$ is placed 15 cm on the left of a convex lens $P$ of focal length 10 cm. Another convex lens $Q$ is now placed 15 cm right of lens $P$. If the focal length of lens $Q$ is 15 cm, the final image is ______.

An object of uniform density rolls up the curved path with the initial velocity $v_0$ as shown in the figure. If the maximum height attained by an object is $\frac{7v_0^{2}}{10g}$ ( $g =$ acceleration due to gravity), the object is a ______.

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle $\theta_1$ and in the next 2 s it rotates through an angle $\theta_2$. The ratio $\frac{\theta_2}{\theta_1}$ is ______.

In a semiconductor $p$-n diode, the doping concentrations on $p$-side and $n$-side are $10^{15}$ atoms $/\text{cm}^{3}$ and $10^{18}$ atoms $/\text{cm}^{3}$, respectively. Which one of the following statements is true?

Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is ______ - ( $S$ is the surface tension of mercury).

The heat extracted out of $x$ gram of water initially at $50^{\circ}\text{C}$ to cool it down to $0^{\circ}\text{C}$ is sufficient to evaporate $(1000 - x)$ gram of water also initially at $50^{\circ}\text{C}$. The value of $x$ (closest integer) is ______. (Take latent heat of water $2256\text{ kJ/kg}$, specific heat capacity of water $4200\text{ J/kg.K}$)

An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3 =$ constant. The coefficient of volume expansion of the gas is ______.

Match List - I with List - II.

where h (Planck's constant), G (gravitational constant) and c (speed of light in vacuum) as

fundamental units.

Choose the correct answer from the options given below:

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A, respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA, respectively. The estimated error in the resistance measurement is $\underline{\qquad}\ \Omega$

The maximum intensity in a Young's double slit experiment is $I_0$. Distance between the slits $(d)$ is $5\lambda$, where $\lambda$ is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at $D = 10d$ is ______.

A mass of 1 kg is kept on an inclined plane with $30^\circ$ inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of $4\text{ m/s}$. The work done by the frictional force in time 2 s is ______ J. (Take $g = 10\text{ m/s}^2$)