JEE Main 2025 · 2 Apr 2025 Shift 1

The equation for real gas is given by (P + a/V²)(V − b) = RT, where P, V, T and R are the pressure, volume, temperature and gas constant, respectively. The dimension of ab⁻² is equivalent to that of :

1. ACompressibility
2. BEnergy density
3. CPlanck’s constant
4. DStrain

A river is flowing from west to east direction with speed of 9 km h⁻¹. If a boat capable of moving at a maximum speed of 27 km h⁻¹ in still water, crosses the river in half a minute, while moving with maximum speed at an angle of 150° to direction of river flow, then the width of the river is :

1. A112.5 m
2. B112.5 × √3 m
3. C75 m
4. D300 m

In an adiabatic process, which of the following statements is true ?

1. AWork done by the gas equals the increase in internal energy
2. BThe internal energy of the gas decreases as the temperature increases
3. CThe molar heat capacity is zero
4. DThe molar heat capacity is infinite

A particle is subjected to two simple harmonic motions as : x₁ = √7 sin 5t cm and x₂ = 2√7 sin (5t + π/3) cm where x is displacement and t is time in seconds. The maximum acceleration of the particle is x × 10⁻² m s⁻². The value of x is :

1. A25√7
2. B5√7
3. C125
4. D175

The battery of a mobile phone is rated as 4.2 V, 5800 mAh. How much energy is stored in it when fully charged?

1. A24.4 kJ
2. B87.7 kJ
3. C48.7 kJ
4. D43.8 kJ

The relationship between the magnetic susceptibility (χ) and the magnetic permeability (μ) is given by : (μ₀ is the permeability of free space and μᵣ is relative permeability)

1. Aχ = μᵣ + 1
2. Bχ = 1 − μ/μ₀
3. Cχ = μ/μ₀ − 1
4. Dχ = μᵣ/μ₀ + 1

Let B₁ be the magnitude of magnetic field at center of a circular coil of radius R carrying current I. Let B₂ be the magnitude of magnetic field at an axial distance ‘x’ from the center. For x : R = 3 : 4, B₂/B₁ is :

1. A25 : 16
2. B16 : 25
3. C4 : 5
4. D64 : 125

A point charge +q is placed at the origin. A second point charge +9q is placed at (d, 0, 0) in Cartesian coordinate system. The point in between them where the electric field vanishes is :

1. A(3d/4, 0, 0)
2. B(d/4, 0, 0)
3. C(d/3, 0, 0)
4. D(4d/3, 0, 0)