JEE Advanced 2026 · Paper 2

A metal wire of cross-sectional area 0.5 mm² and length 100 m is connected across a battery of e.m.f. 2 V and internal resistance 1 Ω. The density, atomic mass and electrical conductivity of the metal are 6.35 × 10³ kg m⁻³, 63.5 gm/mole and 2 × 10⁸ mho m⁻¹, respectively. Assuming one conduction electron per atom of the metal, the drift velocity (in mm s⁻¹) of the electrons in the wire is: [Take Avogadro’s number as 6 × 10²³ and charge of the electron as 1.6 × 10⁻¹⁹ C.]

1. A0.052
2. B0.104
3. C0.208
4. D0.156

A nuclear reactor starts producing a radioactive nuclide X from t = 0, at a constant rate of α per second. Each decay of X produces energy E₀, which is utilized to heat a liquid of mass m and specific heat s. Assuming no heat loss from the liquid and taking λ as the decay constant of X, the rate of increase in the temperature of the liquid is:

1. AαE₀/(ms)(1 − e⁻λᵗ)
2. BαE₀/(ms)(eλᵗ − 1)
3. CλE₀/(ms)(1 − e⁻λᵗ)
4. DE₀/(ms)(α − λe⁻λᵗ)

A beam of polychromatic light passes through a thin prism of prism angle 6°. The refractive index of the material of the prism varies with wavelength (λ) as n(λ) = αλ + β/λ², where α = 3 μm⁻¹ and β = 0.096 μm². If λmin is the wavelength at which the angle of minimum deviation Dₘ is smallest, then the correct value of Dₘ at λmin is

1. A6.4°
2. B4.8°
3. C3.2°
4. D2.4°

A particle of mass m, and angular momentum ℓ is moving in a circular orbit of radius r₀ under the influence of an attractive force F⃗(r) = −(k/r²)r̂. Keeping its angular momentum unchanged, the particle is displaced radially by a small distance δr ≪ r₀, due to which its radial distance varies periodically. The corresponding time period is:

1. A2πℓ³/(mk²)
2. B2π√(m/k)
3. C2πℓ³/(3mk²)
4. D2πℓ³/(5mk²)

In a vacuum chamber, a particle of charge 1 μC and mass 1 mg is projected with a velocity (î + 2ĵ) ms⁻¹ from the XZ plane at time t = 0 in an electric field of 1î Vm⁻¹. At t = 0.2 s, the electric field is switched off and a magnetic field of 6ĵ T is switched on. The acceleration due to gravity is −10ĵ ms⁻². Correct option(s) is/are:

1. AThe vertical distance of the particle from the XZ plane at t = 0.3 s is 15 cm.
2. BThe vertical distance of the particle from the XZ plane at t = 0.4 s is 10 cm.
3. CThe radius of the trajectory of the particle for t > 0.2 s is 20 cm.
4. DThe particle will be in the XZ plane at t = 0.35 s.

Consider an electric dipole comprising two charges +q and −q each with mass m, separated by a fixed distance d and initially at rest with its dipole moment pointing along î. A uniform electric field E ĵ is turned on at time t = 0 and it is turned off at t = t_f, when the dipole moment makes an angle θ_f with î. Neglecting any sources of energy loss, correct option(s) is/are:

1. AThe center of mass of the dipole is deflected towards ĵ in the presence of the field.
2. BIf the magnitude of the final angular velocity ω_f = √(2qE/(md)), then θ_f = π/6.
3. CIf θ_f = π/3, then the change in kinetic energy of the dipole is given by 2√3 qEd.
4. DFor θ_f = π/4, the dipole rotates around its center of mass with a constant angular velocity after t > t_f.