JEE Main 2026 April 5 Shift 2 Physics Question Paper with Solutions PDF

Question 1:

Match List - I with List - II (where h is Planck's constant, G is gravitational constant and c is speed of light):

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A, respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA, respectively. The estimated error in the resistance measurement is :

• (A) 0.25 \(\Omega\)
• (B) 2 \(\Omega\)
• (C) 2.5 \(\Omega\)
• (D) 0.18 \(\Omega\)

A mass of 1 kg is kept on a inclined plane with \(30^\circ\) inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of 4 m/s. The work done by the frictional force in time 2 s is \dots J. (Take \(g = 10 m/s^2\))

• (A) 20
• (B) 25
• (C) 30
• (D) 10

The velocity (\(v\)) versus time (\(t\)) plot of a particle is shown in the figure,for a time interval of 40 s. The total distance travelled by the particle and the average velocity during this period are, respectively :

• (A) 25 m and zero
• (B) 50 m and zero
• (C) 100 m and zero
• (D) 100 m and 2.5 m/s

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle \(\theta_1\) and in the next 2 s it rotates through an angle \(\theta_2\). The ratio \(\frac{\theta_2}{\theta_1}\) is :

• (A) 6
• (B) 3
• (C) 4
• (D) \(1/3\)

An object of uniform density rolls up the curved path with the initial velocity \(v_o\) as shown in the figure. If the maximum height attained by an object is \(\frac{7v_o^2}{10 g}\) (\(g=\) acceleration due to gravity), the object is a \dots

• (A) solid cylinder
• (B) ring
• (C) disc
• (D) solid sphere

A body of mass \(m\) is taken from the surface of earth to a height equal to twice the radius of earth (\(R_e\)). The increase in potential energy will be \dots (\(g\) is acceleration due to gravity at the surface of earth)

• (A) \(\frac{1}{2} mgR_e\)
• (B) \(\frac{3}{4} mgR_e\)
• (C) \(\frac{1}{4} mgR_e\)
• (D) \(\frac{2}{3} mgR_e\)

Eight mercury drops, each of radius \(r\), coalesce to form a bigger drop. The surface energy released in this process is \dots (\(S\) is the surface tension of mercury).

• (A) \(8\pi r^2 S\)
• (B) \(16\pi r^2 S\)
• (C) \(64\pi r^2 S\)
• (D) \(4\pi r^2 S\)

An ideal gas at pressure \(P\) and temperature \(T\) is expanding such that \(PT^3 =\) constant. The coefficient of volume expansion of the gas is \dots

• (A) \(\frac{2}{T}\)
• (B) \(\frac{1}{T}\)
• (C) \(\frac{4}{T}\)
• (D) \(\frac{3}{T}\)

Match List - I with List - II.

A metal rod of length \(L\) rotates about one end at origin with a uniform angular velocity \(\omega\). The magnetic field radially falls off as \(B(r) = B_o e^{-\lambda r}\); \(\lambda\) being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

• (A) \(B_o \omega \left[ \frac{1}{\lambda^2} - e^{-\lambda L} \left( \frac{1}{\lambda^2} + \frac{L}{\lambda} \right) \right]\)
• (B) \(B_o \omega \left[ \frac{1}{\lambda^2} + e^{-\lambda L} \left( \frac{1}{\lambda^2} + \frac{L}{\lambda} \right) \right]\)
• (C) \(B_o \omega \left[ \frac{4}{\lambda^2} - e^{-2\lambda L} \left( \frac{1}{\lambda^2} + \frac{2L}{\lambda} \right) \right]\)
• (D) \(B_o \omega \left[ \frac{3}{\lambda^2} - e^{-3\lambda L} \left( \frac{3}{\lambda^2} + \frac{L}{\lambda} \right) \right]\)

Under steady state condition the potential difference across the capacitor in the circuit is \dots V.

• (A) 0.5
• (B) 1.5
• (C) 0
• (D) 2

A particle of charge \(q\) and mass \(m\) is projected from origin with an initial velocity \(\vec{v} = \left( \frac{v_o}{\sqrt{2}} \hat{x} + \frac{v_o}{\sqrt{2}} \hat{y} \right)\). There exists a uniform magnetic field \(\vec{B} = B_o \hat{z}\) and a space varying electric field \(\vec{E} = E_o e^{-\lambda x} \hat{x}\) within the region \(0 \le x \le L\). After travelling a distance such that \(x\)-coordinate has changed from \(x=0\) to \(x=L\), the change in the kinetic energy is \dots

• (A) \(\frac{q E_o}{\lambda} [ 1 - e^{-\lambda L} ]\)
• (B) \(\left( \frac{v_o q B_o}{2 \lambda} \right) [ 2 - e^{-2\lambda L} ]\)
• (C) \(\frac{q E_o}{\lambda} [ 1 + e^{-\lambda L} ]\)
• (D) \(q \left( \frac{E_o + v_o B_o}{\lambda} \right) [ 1 - e^{-\lambda L/2} ]\)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The electromagnetic wave exerts pressure on the surface on which they are allowed to fall.

Reason (R) : There is no mass associated with the electromagnetic waves.

In the light of the above statements, choose the correct answer from the options given below :

• (A) Both (A) and (R) are true and (R) is the correct explanation of (A)
• (B) Both (A) and (R) are true but (R) is not the correct explanation of (A)
• (C) (A) is true but (R) is false
• (D) (A) is false but (R) is true

A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses ?

• (A) behaves as concave lens if \(|f_{convex}| > |f_{concave}|\)
• (B) behaves as concave lens if \(|f_{convex}| < |f_{concave}|\)
• (C) behaves as convex lens if \(|f_{convex}| > |f_{concave}|\)
• (D) Focal length of the lens system will change if the positions of two lenses are interchanged

An object AB is placed 15 cm on the left of a convex lens P of focal length 10 cm. Another convex lens Q is now placed 15 cm right of lens P. If the focal length of lens Q is 15 cm, the final image is \dots

• (A) virtual, formed at 7.5 cm right of lens Q, with a size bigger than that of AB
• (B) real, formed at 7.5 cm right of lens Q, with a size same as that of AB
• (C) formed at infinity
• (D) real, formed at 7 cm right of lens Q, with a size smaller than that of AB

The maximum intensity in a Young's double slit experiment is \( I_o \). Distance between the slits (\( d \)) is \( 5\lambda \), where \( \lambda \) is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at \( D = 10d \) is \dots

• (A) \( I_o/4 \)
• (B) \( I_o/2 \)
• (C) \( I_o \)
• (D) \( 3I_o/4 \)

An electron is travelling with a velocity \( v \) in free space and when it enters a medium, its velocity is reduced by 20%. The de Broglie wavelength of electron in the medium is \( \alpha\lambda_o \), where \( \lambda_o \) is its de Broglie wavelength in free space. The value of \( \alpha \) is \dots

• (A) 1.20
• (B) 1.0
• (C) 1.25
• (D) 0.75

Assuming the experimental mass of \( {}^{12}_{6}C \) as 12 u, the mass defect of \( {}^{12}_{6}C \) atom is \dots MeV/\( c^2 \).

(Mass of proton = 1.00727 u, mass of neutron = 1.00866 u, 1 u = 931.5 MeV/\( c^2 \))

• (A) 127.5
• (B) 89.03
• (C) 272.0
• (D) 92.0

In a semiconductor p-n diode, the doping concentrations on p-side and n-side are \( 10^{15} atoms/cm^3 \) and \( 10^{18} atoms/cm^3 \), respectively. Which one of the following statements is true?

• (A) Widths of depletion region on either side of the interface are equal
• (B) The depletion region width is more on p-side compared to that in n-side
• (C) The depletion region width is more on n-side compared to that in p-side
• (D) No depletion region forms because of unequal doping concentrations

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is \( 600 \times 10^{-6} m^3 \). The elastic potential energy stored in the wire in stretched condition would be \dots J. (Given Young's modulus of copper = \( 1.1 \times 10^{11} N/m^2 \))

The heat extracted out of \( x \) gram of water initially at \( 50^\circC \) to cool it down to \( 0^\circC \) is sufficient to evaporate \( (1000-x) \) gram of water also initially at \( 50^\circC \). The value of \( x \) (closest integer) is \dots

(Take latent heat of water 2256 kJ/kg, specific heat capacity of water 4200 J/kg\(\cdot\)K)

A series LCR circuit with \( R = 20\ \Omega, L = 1.6 H and C = 40\ \muF \) is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is \dots \(\Omega\).

When an external resistance of 5 \(\Omega\) is connected across terminals of a cell, a current of 0.25 A flows through it. When the 5 \(\Omega\) resistor is replaced by a 2 \(\Omega\) resistor, a current of 0.5 A flows through it. The internal resistance of the cell is \dots \(\Omega\).

A circular loop of radius 20 cm and resistance 2 \(\Omega\) is placed in a time varying magnetic field \( \vec{B} = (2t^2 + 2t + 3) T \). At \( t=0 \), for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at \( t = 3 s \) is \( \alpha/50 A \). The value of \( \alpha \) is \dots (Take \( \pi = 22/7 \))