JEE Main 2026 April 8 Shift 2 Physics Question Paper with Solutions PDF

There are two projectiles thrown at angles \( \theta_1 \) \& \( \theta_2 \) such that their ranges are same. Their speeds of projection are also same and time periods are 10 sec and 5 sec respectively. Find the range.

• (1) \(250\ m\)
• (2) \(300\ m\)
• (3) \(650\ m\)
• (4) \(100\ m\)

For the logic gate shown in the diagram, find the output \(Y\) for the given inputs \(A\) and \(B\).

• (1) \(A\cdot \overline{B}\)
• (2) \(\overline{A} + \overline{B}\)
• (3) \(A + B\)
• (4) \(\overline{A\cdot B}\)

A block is attached to a spring and it oscillates with natural frequency \(f_1\). If the spring is cut into two half and only one of the half spring is connected to the block then the frequency becomes \(f_2\). Find \( \frac{f_2}{f_1} \).

• (1) \( \sqrt{2} \)
• (2) \( \frac{1}{\sqrt{2}} \)
• (3) \(2\)
• (4) \( \frac{1}{2} \)

A biconvex lens having radius of curvature \(20\,cm\) for both surfaces and one side of the lens is silvered as shown in the figure. Object is at distance \(x\) cm from the lens. Find \(x\) such that image is on the object itself. Given \( \mu = 1.5 \).

A solid cylinder of mass \(m\) and radius \(R\) is projected on a rough surface having kinetic friction coefficient \( \mu_k \) with velocity \(v_0\) and angular velocity \( \omega_0 \) as shown in the figure. Find out time after which rolling starts. \((\omega_0 = \frac{v_0}{4R})\)

• (1) \( \dfrac{3\omega_0 R}{\mu_k g} \)
• (2) \( \dfrac{2\omega_0 R}{\mu_k g} \)
• (3) \( \dfrac{\omega_0 R}{\mu_k g} \)
• (4) \( \dfrac{\omega_0 R}{3\mu_k g} \)

A new unit (\(\alpha\)) of length is chosen such that it is equal to the distance travelled by light in vacuum in 1 second. What is the distance between Venus and Earth in terms of this new unit. If light takes 6 min 40 sec to cover the distance.

Find dipole moment of a system consisting of charge \(q_1 = 3\,\mu C\) and \(q_2 = -9\,\mu C\) with position coordinates \(\vec r_1 = 2\hat i + 3\hat j + 3\hat k\) and \(\vec r_2 = \hat i + \hat j + \hat k\) respectively.

• (1) \(-3\hat i\ \mu C-m\)
• (2) \(-9\hat i\ \mu C-m\)
• (3) \(-6\hat i\ \mu C-m\)
• (4) \(-5\hat i\ \mu C-m\)

If \( H = \dfrac{\varepsilon^r E^p x^q}{t^s} \) find \(p, q, r\) and \(s\).
\[ H \rightarrow Magnetic field \]
\[ \varepsilon \rightarrow Permittivity of medium \]
\[ E \rightarrow Electric field \]
\[ x \rightarrow distance \]
\[ t \rightarrow time \]

• (1) \( r = 0,\ p = 1,\ q = -1,\ s = 1 \)
• (2) \( r = 1,\ p = -1,\ q = -1,\ s = 1 \)
• (3) \( r = 1,\ p = 1,\ q = +1,\ s = 1 \)
• (4) \( r = 0,\ p = -1,\ q = -1,\ s = 1 \)

Two photons of wavelength \( \lambda \) and \(2\lambda\) are incident on a metal surface and emit photoelectrons of maximum kinetic energies \(3k\) and \(k\). Find work function of the metal.

• (1) \( \dfrac{hc}{4\lambda} \)
• (2) \( \dfrac{hc}{2\lambda} \)
• (3) \( \dfrac{2hc}{3\lambda} \)
• (4) \( \dfrac{hc}{\lambda} \)

A solenoid having length 30 cm. If there are 10 turns/cm and current through solenoid changes from 2A to 4A in 3.14 sec. Find emf induced. (Area is A)

• (1) \(0.24\,A\ volt\)
• (2) \(0.40\,A\ volt\)
• (3) \(0.80\,A\ volt\)
• (4) \(0.20\,A\ volt\)

1 mole of ideal diatomic gas is enclosed in a cylinder piston arrangement having cross-sectional area of piston \(4\,cm^2\). If gas has only rotational modes and \(P_{atm}=100\ kPa\), some amount of heat is added to the system as a result piston moves up slowly by \(2.5\,cm\). If temperature change is \(1.2^\circ C\). Find heat given to gas.

• (1) \(19.9\,J\)
• (2) \(23.5\,J\)
• (3) \(14.6\,J\)
• (4) \(10\,J\)

Find charge on capacitor at steady state.

• (1) \(18\,\mu C\)
• (2) \(16\,\mu C\)
• (3) \(10\,\mu C\)
• (4) \(8\,\mu C\)

Find pressure difference between A and B.

• (1) \(75\,MPa\)
• (2) \(85\,MPa\)
• (3) \(95\,MPa\)
• (4) \(65\,MPa\)

A car is moving in a circular path of radius \(20\,m\) with speed \(54\,km/hr\). A pendulum is hanging from the roof of the car. Find the angle made by pendulum with vertical. (Take \(g=10\,m/s^2\)).

• (1) \( \tan^{-1}\left(\frac{9}{8}\right) \)
• (2) \( \tan^{-1}\left(\frac{8}{9}\right) \)
• (3) \( \tan^{-1}\left(\frac{4}{3}\right) \)
• (4) \( \tan^{-1}\left(\frac{3}{4}\right) \)

A balloon is moving with speed \(10\,m/s\) in upward direction. At height \(75\,m\) a stone is released then find distance travelled by stone in air.

• (1) \(70\,m\)
• (2) \(80\,m\)
• (3) \(90\,m\)
• (4) \(85\,m\)

Two nuclei \(A(200\,amu)\) and \(B(212\,amu)\) undergoes \(\alpha\)-decay and Q-value is same and equal to \(1\,MeV\). Find ratio of KE of \(\alpha\)-particle.

• (1) \( \dfrac{2597}{2600} \)
• (2) \( \dfrac{2600}{2597} \)
• (3) \( \dfrac{5200}{2597} \)
• (4) \( \dfrac{2597}{5200} \)

At \(t=0\) two particles \(A\) of mass \(3.4\,kg\) and \(B\) of mass \(2.5\,kg\) are moving along \(x\)-axis with initial velocities \(5\,m/s\) and \(10\,m/s\) respectively starting from \(x=0\). At \(t=5s\) position of \(A\) is \(x=104\,m\) and of \(B\) is \(x=137\,m\). Find ratio of momentum at \(t=10s\).

• (1) \(2.17\)
• (2) \(0.17\)
• (3) \(3.17\)
• (4) \(1.17\)

Incident ray is along \(3\hat i-2\hat j\) and refracted ray is along \(c\hat i-4\hat j\). Find \(c\).

• (1) \(1.6\)
• (2) \(0.6\)
• (3) \(2.6\)
• (4) \(4\)

A water droplet falls in air and attains terminal velocity \(v_1\). If it splits into \(64\) identical droplets each having terminal velocity \(v_2\). Find \( \dfrac{v_2}{v_1} \).

• (1) \( \frac{1}{2} \)
• (2) \( \frac{1}{4} \)
• (3) \( \frac{1}{16} \)
• (4) \( \frac{1}{32} \)

Initial pressure and volume of monoatomic gas is \(P\) and \(V\). It is expanded adiabatically to \(27\) times of initial volume. Find magnitude of change in internal energy.

• (1) \( \dfrac{3}{2}PV \)
• (2) \(PV\)
• (3) \( \dfrac{4}{3}PV \)
• (4) \( \dfrac{PV}{2} \)