JEE Main 2026 April 2 Shift 1 Physics Question Paper with Solutions PDF

Question 1:

The dimensional formula of \( \frac{1}{2}\varepsilon_0 E^2 \) (\(\varepsilon_0\) = permittivity of vacuum and \(E\) = electric field) is \(M^aL^bT^c\). The value of \(2a-b+c\) is:

• (A) \(0\)
• (B) \(1\)
• (C) \(-1\)
• (D) \(2\)

The diameter of a wire measured by a screw gauge of least count \(0.001\) cm is \(0.08\) cm. The length measured by a scale of least count \(0.1\) cm is \(150\) cm. When a weight of \(100\) N is applied to the wire, the extension in length is \(0.5\) cm measured by a micrometer of least count \(0.001\) cm. The error in the measured Young’s modulus is \(\alpha \times 10^9\) N/m\(^2\). The value of \(\alpha\) is:

• (A) \(1.3\)
• (B) \(1.65\)
• (C) \(0.13\)
• (D) \(0.25\)

The velocity of a particle is given as \[ \vec{v}=-x\hat{i}+2y\hat{j}-z\hat{k}\ m/s. \]
The magnitude of acceleration at the point \((1,2,4)\) is _____ m/s\(^2\).

• (A) \(\sqrt{6}\)
• (B) \(9\)
• (C) \(\sqrt{33}\)
• (D) \(0\)

The position of an object having mass \(0.1\) kg as a function of time \(t\) is given as
\[ \vec r = (10t^2\hat{i}+5t^3\hat{j})\ m. \]

At \(t=1\) s, which of the following statements are correct?

A. Linear momentum \( \vec p = (2\hat{i}+1.5\hat{j})\) kg m/s.

B. Force acting on the object \( \vec F = (2\hat{i}+3\hat{j})\) N.

C. Angular momentum about origin \( \vec L = 15\hat{k}\) J s.

D. Torque about origin \( \vec \tau = 20\hat{k}\) N m.

Choose the correct answer.

• (A) A, B and C only
• (B) B, C and D only
• (C) A, C and D only
• (D) A, B and D only

A planet \(P_1\) is moving around a star of mass \(2M\) in an orbit of radius \(R\). Another planet \(P_2\) is moving around another star of mass \(4M\) in an orbit of radius \(2R\). The ratio of time periods of revolution of \(P_2\) and \(P_1\) is:

• (A) \( \frac{1}{2} \)
• (B) \(2\)
• (C) \(4\)
• (D) \( \frac{1}{4} \)

A particle is rotating in a circular path and at any instant its motion can be described as
\[ \theta=\frac{5t^4}{40}-\frac{t^3}{3}. \]

The angular acceleration of the particle after \(10\) seconds is ____ rad/s\(^2\).

• (A) \(150\)
• (B) \(120\)
• (C) \(130\)
• (D) \(170\)

A parallel plate air capacitor has a capacitance \(C\). When it is half filled as shown in the figure with a dielectric constant \(K=5\), the percentage increase in the capacitance is:

• (A) \(33.34\)
• (B) \(66.67\)
• (C) \(200\)
• (D) \(400\)

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of \( \Delta Q : \Delta U : \Delta W \) is:

• (A) \(2:3:5\)
• (B) \(5:3:2\)
• (C) \(2:5:7\)
• (D) \(7:5:2\)

Two charged conducting spheres \(S_1\) and \(S_2\) of radii \(8\) cm and \(18\) cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on \(S_1\) and \(S_2\) spheres are \(E_{S_1}\) and \(E_{S_2}\) respectively. The value of \( \dfrac{E_{S_1}}{E_{S_2}} \) is:

• (A) \( \dfrac{3}{2} \)
• (B) \( \dfrac{2}{3} \)
• (C) \( \dfrac{4}{9} \)
• (D) \( \dfrac{9}{4} \)

The equation of a plane progressive wave is given by
\[ y = 5\cos\pi\left(200t - \frac{x}{150}\right) \]

where \(x\) and \(y\) are in cm and \(t\) is in seconds. The velocity of the wave is ____ m/s.

• (A) \(120\)
• (B) \(150\)
• (C) \(200\)
• (D) \(300\)

Two short electric dipoles \(A\) and \(B\) having dipole moments \(p_1\) and \(p_2\) respectively are placed with their axes mutually perpendicular as shown in the figure. The resultant electric field at a point \(x\) is making an angle of \(60^\circ\) with the line joining points \(O\) and \(x\). The ratio of dipole moments \( \dfrac{p_2}{p_1} \) is:

• (A) \( \dfrac{\sqrt3}{2} \)
• (B) \( 2\sqrt3 \)
• (C) \( \dfrac{1}{\sqrt3} \)
• (D) \( \sqrt3 \)

For the given circuit (shown in part A) the time dependent input voltage \(v_{in}(t)\) and corresponding output \(v_o(t)\) are shown in parts (B) and (C), respectively. Identify the components that are used in the circuit between \(X\) and \(Y\).

• (A) 
• (B) 
• (C) 
• (D) 

When a coil is placed in a time dependent magnetic field the power dissipated in it is \(P\). The number of turns, area of the coil and radius of the coil wire are \(N, A\) and \(r\) respectively. For a second coil the number of turns, area of the coil and radius of the coil wire are \(2N, 2A\) and \(3r\) respectively. If the first coil is replaced with second coil the power dissipated in it is \(\sqrt{2}\alpha P\). The value of \(\alpha\) is:

• (A) \(36\)
• (B) \(128\sqrt{2}\)
• (C) \(16\)
• (D) \(64\)

Two identical long current carrying wires are bent into the shapes shown. If the magnitude of magnetic fields at the centres \(P\) and \(Q\) of a semicircular arc are \(B_1\) and \(B_2\) respectively, then the ratio \( \dfrac{B_1}{B_2} \) is:

• (A) \( \dfrac{2+\pi}{1+\pi} \)
• (B) \( \dfrac{1+\pi}{1-\pi} \)
• (C) \( \dfrac{2+\pi}{1-\pi} \)
• (D) \( \dfrac{1+\pi}{2-\pi} \)

For a thin symmetric prism made of glass (refractive index \(1.5\)), the ratio of incident angle and minimum deviation will be _____.

• (A) \(3:4\)
• (B) \(3:2\)
• (C) \(2:1\)
• (D) \(1:2\)

Refer the figure below. \( \mu_1 \) and \( \mu_2 \) are refractive indices of air and lens material respectively. The height of image will be _____ cm.

• (A) \(1\)
• (B) \(0.5\)
• (C) \(1.2\)
• (D) \(0.25\)

For a certain metal, when monochromatic light of wavelength \(\lambda\) is incident, the stopping potential for photoelectrons is \(3V_0\). When the same metal is illuminated by light of wavelength \(2\lambda\), the stopping potential becomes \(V_0\). The threshold wavelength for photoelectric emission for the given metal is \(\alpha \lambda\). The value of \(\alpha\) is:

• (A) \(1\)
• (B) \(4\)
• (C) \(2\)
• (D) \(3\)

An electromagnetic wave travelling in \(x\)-direction is described by the field equation
\[ E_y = 300 \sin \omega\left(t - \frac{x}{c}\right). \]

If the electron is restricted to move in \(y\)-direction only with speed \(1.5 \times 10^6\) m/s, then the ratio of maximum electric and magnetic forces acting on the electron is:

• (A) \(200\)
• (B) \(150\)
• (C) \(400\)
• (D) \(300\)

Angular momentum of an electron in a hydrogen atom is \( \dfrac{3h}{\pi} \). Then the energy of the electron is ____ eV.

• (A) \(-1.51\)
• (B) \(-0.85\)
• (C) \(-0.38\)
• (D) \(-0.28\)

A liquid drop of diameter \(2\) mm breaks into \(512\) droplets. The change in surface energy is \( \alpha \times 10^{-6} \) J. (Take surface tension of liquid = \(0.08\) N/m). The value of \(\alpha\) is ____.

• (A) \(10\)
• (B) \(7\)
• (C) \(8\)
• (D) \(11\)

In single slit diffraction pattern, the wavelength of light used is \(628\) nm and slit width is \(0.2\) mm. The angular width of central maximum is \(\alpha \times 10^{-2}\) degrees. The value of \(\alpha\) is ____.

A vessel contains \(0.15\,m^3\) of a gas at pressure \(8\) bar and temperature \(140^\circC\) with \(c_p=3R\) and \(c_v=2R\). It expands adiabatically till pressure falls to \(1\) bar. The work done during this process is ____ kJ. (R is gas constant)

A \(1\,μC\) charge moving with velocity \[ \vec{v} = (\hat{i} - 2\hat{j} + 3\hat{k}) \, m/s \]
in the region of magnetic field \[ \vec{B} = (2\hat{i} + 3\hat{j} - 5\hat{k}) \, T \]
The magnitude of force acting on it is \( \sqrt{\alpha} \times 10^{-6} \) N. The value of \(\alpha\) is ____.

A uniform wire of length \(l\) of weight \(w\) is suspended from the roof with a weight \(W\) at the other end. The stress in the wire at \( \frac{l}{3} \) distance from the top is \[ \left(\frac{W}{A} + \frac{2}{\gamma}\frac{w}{A}\right) \]
where \(A\) is the cross sectional area of the wire. The value of \(\gamma\) is ____.

A tub is filled with water and a wooden cube \(10\,cm \times 10\,cm \times 10\,cm\) is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by \(3.87\) cm. The mass of the metal coin is ____ gram. (Take water density \(=1\,g/cm^3\) and density of wood as \(0.4\,g/cm^3\)).