JEE Main 2026 April 6 Shift 1 Physics Question Paper with Solutions PDF

Potential energy of a particle is given as \( u = \dfrac{A\sqrt{x}}{B+x} \). Find the dimensions of \(A\) and \(B\).

• (1) \( M^{3}L^{3/2}T^{-2},\, L \)
• (2) \( ML^{5/2}T^{-1},\, L^{2} \)
• (3) \( ML^{5/2}T^{-2},\, L \)
• (4) \( M^{7/2}T^{-3},\, L \)

In an AC circuit supply voltage \( (V_{rms}) = 1000\,V \), \( R = 80\,\Omega \), \( X_L = 80\,\Omega \) and source frequency \( f = 50\,Hz \). Find the power factor.

• (1) \( \dfrac{1}{\sqrt{2}} \)
• (2) \( \dfrac{1}{\sqrt{3}} \)
• (3) \( \dfrac{1}{\sqrt{5}} \)
• (4) \( \dfrac{1}{\sqrt{6}} \)

Electric field due to a half ring at the center is \(100\,N/C\). Find the charge on the ring. Radius of the ring is \(10\,cm\).

• (1) \( \dfrac{\pi}{9} \times 10^{-9}\,C \)
• (2) \( \dfrac{\pi}{27} \times 10^{-9}\,C \)
• (3) \( \dfrac{\pi}{18} \times 10^{-9}\,C \)
• (4) \( \dfrac{\pi}{36} \times 10^{-9}\,C \)

A particle is released from point \(A\) of the track as shown in the figure. Find \(h\) so that the normal reaction at the highest point is 3 times the weight of the block. The surface is smooth.

• (1) \(h = 4R\)
• (2) \(h = 3R\)
• (3) \(h = 2.5R\)
• (4) \(h = 6R\)

Find transverse magnification due to curved boundary between two mediums as shown in the figure. Refractive index of second medium \(n_2 = 1.4\).

• (1) \(-1.5\)
• (2) \(-1.67\)
• (3) \(+1.2\)
• (4) \(-0.8\)

Find heat dissipated in \(6\Omega\) resistance in \(100\) seconds in the given circuit.

• (1) \(31\,J\)
• (2) \(35\,J\)
• (3) \(40\,J\)
• (4) \(28\,J\)

In YDSE a glass slab of thickness \(8\,\mu m\) is introduced in front of a slit. If central maxima shifts to the position of 4^th minima, then find refractive index of glass slab \((\lambda = 500\,nm)\):

• (1) \( \mu = 1.11 \)
• (2) \( \mu = 1.22 \)
• (3) \( \mu = 1.32 \)
• (4) \( \mu = 2.2 \)

A particle is performing SHM of amplitude \(A\). Find the time required for particle to go from mean position to \( \dfrac{A}{\sqrt{2}} \). Time period of SHM is \(5\) sec :-

• (1) \( \dfrac{5}{4} \) sec.
• (2) \( \dfrac{5}{12} \) sec.
• (3) \( \dfrac{5}{8} \) sec.
• (4) \( \dfrac{5}{6} \) sec.

Find coefficient of friction \( \mu \) so that the blocks are at rest.

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

For the given circuit, find the ratio of instantaneous voltage across the inductor when current is \(2\,mA\) and when current is \(4\,mA\).

• (1) \(1.5\)
• (2) \(1\)
• (3) \(2\)
• (4) \(1.25\)

A sphere of mass \(5\,kg\) and radius \(4\,cm\) is rotating about a fixed axis along its diameter with \(1200\,rpm\). To stop it in \(10\,s\), a torque is applied. Find magnitude of torque required and number of revolutions made before it stops respectively :-

• (1) \(0.08\,N-m\) and \(50\) rev.
• (2) \(0.04\,N-m\) and \(100\) rev.
• (3) \(0.016\,N-m\) and \(200\) rev.
• (4) \(0.2\,N-m\) and \(100\) rev.

Intensity of two sources is same and path difference at point \(A\) and \(B\) are \( \frac{\lambda}{6} \) and \( \frac{\lambda}{3} \) respectively. Ratio of intensity at \(A\) and \(B\) will be.

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

Find minimum \(R_s\) so that LED light does not get damaged (power rating of LED is \(2\,mW\)).

• (1) \(1\Omega\)
• (2) \(2\Omega\)
• (3) \(3\Omega\)
• (4) \(4\Omega\)

The dimensions of a solid cylinder is measured as given

Mass \(= 19.42 \pm 0.02 \,kg\)

Diameter \(= 20.20 \pm 0.02 \,cm\)

Length \(= 10.10 \pm 0.02 \,cm\)

Find out % error in density.

• (1) \(0.5%\)
• (2) \(0.3%\)
• (3) \(0.4%\)
• (4) \(0.7%\)

Electric field in space is given by
\[ \vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k} \]

A charge \(q = 3\,C\) is taken from \(r_1(0,-1,-3)\) to \(r_2(5,1,2)\). Find magnitude of \( \Delta U \).

Bulk modulus of an ideal gas for isothermal process initially is \(B\). Gas is compressed from volume \(V_0\) to \( \frac{V_0}{3} \) isothermally. Find the work done by gas.

• (1) \(BV_0\ln3\)
• (2) \(\frac{BV_0}{3}\ln3\)
• (3) \(BV_0\ln\left(\frac{1}{3}\right)\)
• (4) \(3BV_0\ln\left(\frac{1}{2}\right)\)

A cube of side \(1\,mm\) is placed at centre of circular coil of radius \(10\,cm\). Current flowing in coil is \(2\,A\). Find magnetic field energy stored in cube. (\(\pi = 3.14\))

• (1) \(3.17 \times 10^{-14}\,J\)
• (2) \(6.28 \times 10^{-14}\,J\)
• (3) \(12.56 \times 10^{-14}\,J\)
• (4) \(9.42 \times 10^{-14}\,J\)

Unpolarised light with intensity \(I_0\) is incident on a polariser. Find angle between axis of polariser and analyser such that intensity of emergent light becomes \( \frac{3I_0}{8} \).

• (1) \(60^\circ\)
• (2) \(30^\circ\)
• (3) \(90^\circ\)
• (4) \(0^\circ\)

Shortest wavelength of Lyman series is \(x\). Find the difference of wavelengths of first Balmer and second Balmer line in terms of \(x\).

• (1) \( \left(\frac{28}{15}\right)x \)
• (2) \( \left(\frac{26}{15}\right)x \)
• (3) \( \left(\frac{13}{15}\right)x \)
• (4) \( \left(\frac{11}{15}\right)x \)

A small drop of mass \(1\,g\) starts falling from rest from a height of \(1\,km\). When it reaches the ground with speed \(5\,m/s\), magnitude of work done by resistance force is \(x\times10^{-3}\,J\). Find \(x\).

• (1) \(845\)
• (2) \(247.5\)
• (3) \(987.5\)
• (4) None

If \(P\) is the midpoint of median, find distance of COM from \(P\).

Two wires are joined together and elongated with force as shown in the figure. If \( \dfrac{Y_1}{Y_2} = \dfrac{20}{11} \), find \( \dfrac{\ell_1}{\ell_2} \) so that they have same elongation.

• (1) \( \frac{11}{20} \)
• (2) \( \frac{20}{11} \)
• (3) \( \frac{11}{10} \)
• (4) \( \frac{10}{11} \)

Find the ratio of momentum of photons of 1^st and 2^nd line of Balmer series of hydrogen atom.

• (1) \( \frac{10}{20} \)
• (2) \( \frac{11}{27} \)
• (3) \( \frac{15}{20} \)
• (4) \( \frac{20}{27} \)

A point source is kept at centre of a sphere. The intensity of light at point \(A\) is \(I\). Find intensity at point \(B\).

• (1) \(I/2\)
• (2) \(2I\)
• (3) \(I\)
• (4) \(I/3\)