JEE Main 2026 Physics Paper: 6 Apr, Shift 1

A LCR series circuit driven with $E_{rms} = 90\text{ V}$ at frequency $f_{\text{d}} = 30\text{ Hz}$ has resistance $R = 80\ \Omega$, an inductance with inductive reactance $X_L = 20.0\ \Omega$ and capacitance with capacitive reactance $X_C = 80.0\ \Omega$. The power factor of the circuit is ______.

The ratio of momentum of the photons of the $1$st and $2$nd line of Balmer series of Hydrogen atoms is $\alpha/\beta$. The possible values of $\alpha$ and $\beta$ are:-

The position of center of mass of three masses $2\text{ kg}, 3\text{ kg}$ and 15 kg placed with respect to mid point $(p)$ of normal bisector, as shown in the figure is ______.

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height $h$ as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height $h = \alpha R$. The value of $\alpha$ is ______

Refer to the circuit diagram given below. The heat generated across the $6\ \Omega$ resistance in 100 second is $\frac{\alpha}{100}\text{ J}$. The value of $\alpha$ is ______. (Nearest integer)

An inductor of inductance 10 mH having resistance of $100\,\Omega$ is connected to battery of E.M.F. 1.0 V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is 2 mA and 4 mA is ______.

A point light source emits E.M. waves in free space. A detector, placed at a distance of $L\text{ m}$, measures the intensity as $I_o$. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as $45^\circ$. The measured intensity at new location will be ______.

A thin half ring of radius 35 cm is uniformly charged with a total charge of $Q$ coulomb. If the magnitude of the electric field at centre of the half ring is $100\text{ V/m}$, then the value of $Q$ is ______ nC. $(\epsilon_0 = 8.85 \times 10^{-12}\text{ C}^{2}/\text{N m}^{2}$ and $\pi = 3.14)$

A three coulomb charge moves from the point $(0, -2, -5)$ to the point $(5, 1, 2)$ in an electric field expressed as $\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}\text{ N/C}$. The work done in moving the charge is ______ J.

Two blocks ( $P$ and $Q$) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pully which is fixed on the edge of a cube $(S)$, as shown in the figure below. Block $P$ is positioned on the top surface which has no friction and block $Q$ is in contact with side-surface, having coefficient friction $\mu$. The cube ( $S$) moves towards the right with acceleration of $\frac{g}{2}$, where $g$ is gravitational acceleration. During this movement the block $P$ and $Q$ remain stationary. The value of $\mu$ is ______ (take $g = 10\text{ m/s}^{2}$)

A certain gas is isothermally compressed to $\left(\frac{1}{3}\right)^{\text{rd}}$ of its initial volume $(V_{\text{o}} = 3$ litre) by applying required pressure. If the bulk modulus of the gas is $3 \times 10^{5}\text{ N/m}^2$, the magnitude of work done on the gas is ______ J.

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $4 \times 10^{8}\text{ N/m}^2$ and its radius is 4 mm, then maximum acceleration the lift can take is $\underline{\qquad}\ \text{m/s}^2$.

(take $\text{g} = 10\text{ m/s}^2$ and $\pi = 3.14$)

The two wires $A$ and $B$ of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire $A$ and wire $B$ is 20/11. When the joined wire is kept under certain tension the elongations in the wires $A$ and $B$ are equal. If the length of wire $A$ is 2.2 m, then the length of wire $B$ is

______ m.

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $\alpha \times 10^{-14}\text{ J}$. The value of $\alpha$ is $\underline{\qquad}\ .\ \left(\mu_0 = 4\pi \times 10^{-7}\text{ Tm/A}, \pi = 3.14\right)$

The energy released when $\frac{7}{17.13}\text{ kg}$ of ${}^{7}_{3}\text{Li}$ is converted into ${}^{4}_{2}\text{He}$ by proton bombardment is $\alpha \times 10^{32}\text{ eV}$. The value of $\alpha$ is ______. (Nearest integer) (Mass of ${}^{7}_{3}\text{Li} = 7.0183\text{u}$, mass of ${}^{4}_{2}\text{He} = 4.004\text{u}$, mass of proton $= 1.008\text{u}$ and $1\text{u} = 931\text{ MeV/c}^{2}$ and Avogadro number $= 6.0 \times 10^{23}$)

A particle is executing simple harmonic motion. Its amplitude is $A$ and time period is 5 sec. The time required by it to move from $x = A$ to $x = \frac{A}{\sqrt{2}}$ is ______ sec.

A spherical interface lens of radius $R$ separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of $4R$ in front of spherical interface. The magnitude of the magnification of point source image is ______.

A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are ______ and ______ respectively.

The maximum rated power of the LED is 2 mW and it is used in the circuit with input voltage of 5 V as shown in the figure below. The current through resistance $R_S$ is 0.5 mA.

The minimum value of the resistance of $R_S$, to ensure that the LED is not damaged is $\underline{\qquad\quad}\ \text{k}\Omega$.

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K the second vessel temperature is raised to 500 K. The final pressure in the vessels is ______ kPa.

The potential energy of a particle changes with distance $x$ from a fixed origin as $V = \frac{A\sqrt{x}}{x+B}$, where $A$ and $B$ are constants with appropriate dimensions. The dimensions of $AB$ are ______

The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m, l$ and $d$ are $97.42 \pm 0.02\text{ g},\ 8.35 \pm 0.05\text{ mm}$ and $20.20 \pm 0.02\text{ mm}$, respectively. Calculated percentage fractional error in $\rho$ is ______.

An unpolarized light of intensity $I_0$ passes through polarizer and then through a certain optically active and finally it goes to analyser. If the angle between analyser and polariser is $0^\circ$ and intensity of light emerged from analyser is $\frac{3}{8}I_0$, the angle of rotation of the light by the with respect to analyser is ______ degrees.

In interference experiment the path difference between two interfering waves at a point $A$ on the screen is $\lambda/3$, where $\lambda$ is the wavelength of these waves, and at another point $B$ the path difference is $\lambda/6$. The ratio of intensities at points $A$ and $B$ is ______.

The rain drop of mass 1 g, starts with zero velocity from a height of 1 km. It hits the ground with a speed of $5\text{ m/s}$. The work done by the unknown resistive force is ______ J.

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