JEE Main 2025 · 3 Apr 2025 Shift 2

A particle is projected with velocity u so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as nu²/25g, where value of n is: (Given, ‘g’ is the acceleration due to gravity.)

1. A6
2. B12
3. C18
4. D24

A particle moves along the x−axis and has its displacement x varying with time t according to the equation: x = c₀ (t² − 2) + c (t − 2)² where c₀ and c are constants of appropriate dimensions. Then, which of the following statements is correct?

1. Athe initial velocity of the particle is 4c
2. Bthe acceleration of the particle is 2c₀
3. Cthe acceleration of the particle is 2c
4. Dthe acceleration of the particle is 2 (c + c₀)

Two cylindrical vessels of equal cross sectional area of 2m² contain water upto heights 10m and 6m, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is (Density of water is 10³ kg/m³ and g = 10 m/s²)

1. A4 × 10⁴ J
2. B6 × 10⁴ J
3. C8 × 10⁴ J
4. D1 × 10⁵ J

A block of mass 1 kg, moving along x with speed vᵢ = 10 m/s enters a rough region ranging from x = 0.1 m to x = 1.9 m. The retarding force acting on the block in this range is Fᵣ = −kx N, with k = 10 N/m. Then the final speed of the block as it crosses rough region is.

1. A10 m/s
2. B8 m/s
3. C6 m/s
4. D4 m/s

A solid steel ball of diameter 3.6 mm acquired terminal velocity 2.45 × 10⁻² m/s while falling under gravity through an oil of density 925 kg m⁻³. Take density of steel as 7825 kg m⁻³ and g as 9.8 m/s². The viscosity of the oil in SI unit is

1. A1.68
2. B1.99
3. C2.18
4. D2.38

An ideal gas exists in a state with pressure P₀, volume V₀. It is isothermally expanded to 4 times of its initial volume(V₀), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

1. AP₀V₀ (2ln 2 − 0.75)
2. BP₀V₀ (ln 2 − 0.75)
3. CP₀V₀ (2ln 2 − 0.25)
4. DP₀V₀ (ln 2 − 0.25)

Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4% when heated by 1°C. Its initial temperature must be:

1. A250°C
2. B2500 K
3. C25°C
4. D250 K

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is:

1. A360 m/s
2. B340 m/s
3. C335 m/s
4. D370 m/s