JEE Main 2026 Apr 5 Shift 2 — Physics

Match List - I with List - II.

List - I | List - II

A. Meter (L) — I. $\sqrt{\dfrac{hc}{G}}$

B. Second (S) — II. $\sqrt{\dfrac{Gh}{c^5}}$

C. Kilogram (M) — III. $\sqrt{\dfrac{K^2 L^2 c^3}{Gh}}$

D. Kelvin (K) — IV. $\sqrt{\dfrac{Gh}{c^3}}$

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 $10 \text{ V}$ and $5 \text{ A}$, respectively. The least counts of voltmeter and ammeter are $500 \text{ mV}$ and $200 \text{ mA}$, respectively. The estimated error in the resistance measurement is __________ $\Omega$

A mass of $1 \text{ kg}$ is kept on a inclined plane with $30°$ 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 $2 \text{ s}$ is __________ J. (Take $g = 10 \text{ m/s}^2$)

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

velocity-time graph — $v(t)$ in m/s rises linearly from 0 to +5, returns to 0 at $t = 20$ s, dips linearly to −5 and returns to 0 at $t = 40$ s (triangular waveform between +5 and −5 m/s)

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first $2 \text{ s}$ it rotates through an angle $\theta_1$ and in the next $2 \text{ s}$ it rotates through an angle $\theta_2$. The ratio $\dfrac{\theta_2}{\theta_1}$ 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 $\dfrac{7 v_0^2}{10\, g}$ ($g$ = acceleration due to gravity), the object is a __________.

an object at the bottom of a concave curved ramp moving with initial velocity $v_0$ toward the ramp, which curves upward to a vertical rise

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)

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).

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.

List - I | List - II

A. $\sin^2 \omega t$ — I. Periodic with time period $T = \dfrac{\pi}{\omega}$ but not simple harmonic motion (SHM)

B. $\sin^3 (2\omega t)$ — II. Periodic with time period $T = \dfrac{2\pi}{\omega}$ but Not SHM

C. $\sin(\omega t) + \cos(\pi \omega t)$ — III. Periodic with time period $T = \dfrac{\pi}{\omega}$ and SHM

D. $\cos \omega t + \cos 2\omega t$ — IV. Non-periodic

Choose the correct answer from the options given below :

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 $B(r) = B_0\, e^{-\lambda r}$; $\lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

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

circuit with three parallel branches — top branch: $2\ \Omega$ resistor; middle branch: $2\ \mu\text{F}$ capacitor in series with $4\ \Omega$ resistor; bottom branch: $2 \text{ V}$ battery in series with $6\ \Omega$ resistor

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v} = \left( \dfrac{v_0}{\sqrt{2}}\, \hat{x} + \dfrac{v_0}{\sqrt{2}}\, \hat{y} \right)$. 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 $0 \leq x \leq L$. After travelling a distance such that $x$-coordinate has changed from $x = 0$ to $x = L$, the change in the kinetic energy 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 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 $15 \text{ cm}$ on the left of a convex lens $P$ of focal length $10 \text{ cm}$. Another convex lens $Q$ is now placed $15 \text{ cm}$ right of lens $P$. If the focal length of lens $Q$ is $15 \text{ cm}$, the final image is __________.

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 __________.

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 __________.

Assuming the experimental mass of $^{12}_{6}\text{C}$ as $12 \text{ u}$, the mass defect of $^{12}_{6}\text{C}$ 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).

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

A copper wire of length $3 \text{ m}$ is stretched by $3 \text{ mm}$ 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 heat extracted out of $x$ gram of water initially at $50\ °\text{C}$ to cool it down to $0\ °\text{C}$ is sufficient to evaporate $(1000 - x)$ gram of water also initially at $50\ °\text{C}$. The value of $x$ (closest integer) is ________.

(Take latent heat of water $2256 \text{ kJ/kg}$, specific heat capacity of water $4200 \text{ J/kg.K}$)

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 _________ $\Omega$.

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

A circular loop of radius $20 \text{ cm}$ and resistance $2\ \Omega$ is placed in a time varying magnetic field $\vec{B} = \left( 2t^2 + 2t + 3 \right) \text{ T}$. 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 $\dfrac{\alpha}{50} \text{ A}$. The value of $\alpha$ is __________.

(Take $\pi = 22/7$)