JEE Main 2026 Apr 5 Shift 1 — Physics

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and $7^{\text{th}}$ Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has

$L$, $C$ and $R$ represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $\mathrm{M\,L^2\,T^{-4}\,A^{-2}}$ corresponds to __________.

When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in $g$ is approximately $\alpha$ %. The value of $\alpha$ is ______.

(Take radius of the earth = 6400 km.)

Three masses $m_1 = 4$ kg, $m_2 = 4$ kg and $m_3 = 6$ kg are suspended from a fixed smooth frictionless pully as shown in the figure below. The value of $T_1/T_2$ is ______

(take $g = 10 \text{ m/s}^2$)

A pulley fixed to the ceiling. Over the pulley, tension $T_1$ on both sides; mass $m_1$ hangs on the left side, mass $m_2$ hangs on the right side, and mass $m_3$ hangs below $m_2$ connected by a string with tension $T_2$.

A wedge $Y$ with mass of 10 kg and all frictionless surfaces and the inclined surface making $37°$ with horizontal. A block $X$ with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At $t = 0$ wedge ($Y$) is pulled toward right with constant force ($f$) of 24 N. Taking the block $X$ at rest at $t = 0$, the time taken by it to slide down 8.8 m on the slope, while $Y$ is on the move, is ______ s.

(take $\tan(37°) = 3/4$ and $g = 10 \text{ m/s}^2$)

A wedge $Y$ with incline angle $37°$; block $X$ at the top of the incline; a horizontal force $f = 24$ N applied to the wedge toward the right.

The Young's modulus of steel wire of radius $r$ and length $L$ is $Y$.

If the radius $r$ and length $L$ of the wire are doubled then the value of $Y$

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

Statement I: Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U = n\,C_V\left(T_{\text{f}} - T_i\right) = \dfrac{nR}{\gamma - 1}\left(T_{\text{f}} - T_i\right)$, where $\gamma = \dfrac{C_p}{C_v}$, $T_i$ = initial temperature, $T_{\text{f}}$ = final temperature.

Statement II: Relation between degree of freedom $f$ and $\gamma$ ($= C_p/C_v$) is $\left(\gamma = 1 + \dfrac{2}{f}\right)$

Choose the correct answer from the options given below

Consider the following statements:

A. Zeroth law of thermodynamics gives concept of temperature B. First law of thermodynamics gives concept of internal energy C. In isothermal expansion of ideal gas, $\Delta Q \neq \Delta W$ D. Product of intensive and extensive variables is extensive E. The ratio of any extensive variable to mass will be an extensive variable

Choose the correct combination of statements from the options given below:

Refer to the figure given below. The values of $I_1$, $I_2$ and $I_3$ are ________.

A diamond-shaped circuit. Left branch: a 10 V battery in series with a 1 Ω resistor carrying current $I_1$ (horizontal middle branch). Upper-left arm has a 4 Ω resistor, upper-middle a 2 Ω resistor with current $I_2$ leaving the top node toward a 5 V battery on the right vertex. Lower-left arm has a 4 Ω resistor carrying current $I_3$, and a 2 Ω resistor in the lower-middle branch.

An electron of mass $m$ is moving in an electric field $\vec{E} = -2E_0\hat{i}$ ($E_0$ = constant $> 0$), with an initial velocity $\vec{V} = v_0\hat{i}$ ($v_0$ = constant $> 0$). If $\lambda_0 = \dfrac{h}{4mv_0}$, its de Broglie wavelength at time $t$ is ______.

($e$ = charge of electron)

In the hydrogen atom, the electron makes a transition from the higher orbit ($i$) to a lower orbit ($f$). The ratio of the radius of the orbits in given by $r_i : r_f = 16 : 4$. The wavelength of photon emitted due to this transition is ______ nm.

(Given Rydberg constant $= 1.0973 \times 10^7 \text{ /m}$)

A displacement current of 4.0 A can be set up in the space between two parallel plates of $6 \text{ } \mu\text{F}$ capacitor. The rate of change of potential difference across the plates of the capacitor is nearly $\alpha \times 10^6$ V/s. The value of $\alpha$ is ________.

Refer to the figure given below, current between terminals $A$ and $B$ is __________ A.

A ladder network between terminals $A$ (bottom left) and $B$ (bottom right) with four parallel horizontal rows. Each of the top three rows contains three series cells of 5 V each, each cell in series with a 3 Ω resistor (three cells and three 3 Ω resistors per row). The bottom row contains three 3 Ω resistors in series with no cells.

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is $2.4 \text{ } \mu\text{m}$. If the experiment is carried out in another medium having refractive index 1.2, the fringe width will be ____ $\mu$m.

A ray of light passing through an equilateral prism is having velocity $2.12 \times 10^8$ m/s in the prism material, then the minimum angle of deviation is ________ degrees.

Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V. The work function of the used metal in the experiment is $\alpha \times 10^{-19}$ J. The value of $\alpha$ is _____.

($h = 6.62 \times 10^{-34}$ J s, $e = 1.6 \times 10^{-19}$ C and $c = 3 \times 10^8$ m/s)

A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be

Two wires as shown in the figure below, made of steel and have breaking stress of $12 \times 10^8 \text{ N/m}^2$. Area of cross-section of upper wire is $0.008 \text{ cm}^2$ and of lower wire is $0.004 \text{ cm}^2$. The maximum mass that can be added to pan without breaking any wire is ______ kg.

(take $g = 10 \text{ m/s}^2$)

An upper wire hangs from the ceiling supporting a 30 kg block; a lower wire hangs from the 30 kg block supporting a 10 kg block; a pan hangs below the 10 kg block.

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$, (keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is

For the given logic circuit, which of the following inputs combination will make both LED$-$1 and LED$-$2 to glow?

Logic circuit with inputs A, B, C. Inputs A and B feed an OR gate whose output drives LED-1 (through a resistor to ground) and also feeds one input of an AND gate; input C feeds the other input of the AND gate. The AND gate output and a line from A feed a final gate whose output drives LED-2 through a resistor.

A cube has side length 5 cm and modulus of rigidity $10^5 \text{ N/m}^2$. The displacement produced by a force of 10 N in the upper face of cube is _____ mm.

From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is ____ m.

(Take $g = 10 \text{ m/s}^2$ and neglect the air resistance)

A transverse wave on a string is described by $y = 3\sin(36t + 0.018x + \pi/4)$, where $x$, $y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is ____ cm. (Nearest integer)

($\pi = 3.14$)

The charged particle moving in a uniform magnetic field of $\left(3\hat{i} + 2\hat{j}\right) \text{T}$ has an acceleration $\left(4\hat{i} - \dfrac{x}{2}\hat{j}\right) \text{m/s}^2$. The value of $x$ is

In the given circuit below inductance values of $L_1$, $L_2$ and $L_3$ are same. The magnetic energy stored in the entire circuit is ($U_t$) and that stored in the $L_2$ inductor is ($U_l$). $U_t / U_l$ is ________.

(Ignore the mutual inductance if any)

Inductor $L_1$ in series with a parallel combination of inductors $L_2$ (upper branch) and $L_3$ (lower branch).