JEE Main 2026 (Online) 6th April Morning Shift

A LCR series circuit driven with $E_{r m s}=90 \mathrm{~V}$ at frequency $f_{\mathrm{d}}=30 \mathrm{~Hz}$ has resistance $R=80 \Omega$, an inductance with inductive reactance $X_L=20.0 \Omega$ and capacitance with capacitive reactance $X_C=...

The energy released when $\frac{7}{17.13} \mathrm{~kg}$ of ${ }_3^7 \mathrm{Li}$ is converted into ${ }_2^4 \mathrm{He}$ by proton bombardment is $\alpha \times 10^{32} \mathrm{eV}$. The value of $\alpha$ is $\_\_\_\_$ . (Nearest integer) (...

The ratio of momentum of the photons of the $1^{\text {st }}$ and $2^{\text {nd }}$ 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 $2 \mathrm{~kg}, 3 \mathrm{~kg}$ 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 h...

Refer to the circuit diagram given below. The heat generated across the $6 \Omega$ resistance in 100 second is $\frac{\alpha}{100} \mathrm{~J}$. 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 th...

A point light source emits E.M. waves in free space. A detector, placed at a distance of $L \mathrm{~m}$, measures the intensity as $I_{\mathrm{o}}$. The detector is now shifted to another location on the same spherical surface ensuring the...

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 t...

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

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 $100 \mathrm{~V} / \mathrm{m}$, then the value of $Q$ is $\_\_\_\_$ nC .
$$ \left...

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 $4 R$ in front of spherical interface. The magnitude of the ma...

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 rais...

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 pos...

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 $\alpha \times 10^{-14} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$ .
$$ \l...

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

A certain gas is isothermally compressed to $\left(\frac{1}{3}\right)^{\mathrm{rd}}$ of its initial volume $\left(V_{\mathrm{o}}=3\right.$ litre) by applying required pressure. If the bulk modulus of the gas is $3 \times 10^5 \mathrm{~N} / ...

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 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 t...

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.

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 constant with appropriate dimensions. The dimensions of $A B$ 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 $97.42 \pm 0.02 \mathrm{~g}$, $8.35 \pm 0.05 \mathrm{~mm}$ and $20.20 \pm 0.02 \mathrm{...

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...

An unpolarized light of intensity $I_0$ passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is $0^{\circ}$ and intensity of light emerged...

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 $5 \mathrm{~m} / \mathrm{s}$. The work done by the unknown resistive force is $\_\_\_\_$ J.
(take $\mathrm{g}=10 \mathrm{~m} / ...