BITSAT 2025 Question Paper June 22 Shift 1 (Available): Download Solutions with Answer Key

A block of mass 2 kg slides on a frictionless horizontal surface with a velocity of 3 m/s. It collides elastically with another block of mass 3 kg initially at rest. What is the velocity of the 2 kg block after the collision?

• (A) 1 m/s
• (B) 1.5 m/s
• (C) 2 m/s
• (D) 2.5 m/s

The electric field at a point on the axis of a uniformly charged ring of radius R at a distance x from its center is given by: \[ E = \frac{1}{4\pi\epsilon_0} \cdot \frac{2\pi kQx}{(x^2 + R^2)^{3/2}}. \]
If x = 2R, what is the magnitude of the electric field?

• (A) \( \frac{kQ}{R^2} \)
• (B) \( \frac{2kQ}{R^2} \)
• (C) \( \frac{3kQ}{R^2} \)
• (D) \( \frac{kQ}{2R^2} \)

A gas expands isothermally and reversibly from a volume V to 2V. If the initial pressure is P, what is the final pressure?

• (A) \( \frac{P}{2} \)
• (B) \( \frac{P}{4} \)
• (C) \( 2P \)
• (D) \( P \)

For a reaction A → B, the concentration of A decreases from 0.8 M to 0.2 M in 10 minutes. If the rate constant is 0.1 min⁻¹, what is the order of the reaction?

• (A) 0
• (B) 1
• (C) 2
• (D) 3

Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]

• (A) 0
• (B) \( \frac{\pi}{2} \)
• (C) \( \frac{\pi}{4} \)
• (D) \( \pi \)

A bag contains 5 red, 3 blue, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both are red?

• (A) \( \frac{1}{2} \)
• (B) \( \frac{1}{3} \)
• (C) \( \frac{5}{9} \)
• (D) \( \frac{1}{6} \)

Find the angle between the vectors \( \mathbf{a} = (2, -1, 3) \) and \( \mathbf{b} = (1, 4, -2) \).

• (A) \( 45^\circ \)
• (B) \( 60^\circ \)
• (C) \( 90^\circ \)
• (D) \( 120^\circ \)

If \( A = \begin{bmatrix} 2 & 3
4 & 5 \end{bmatrix} \), find the determinant of \( A^2 \).

• (A) 0
• (B) 4
• (C) 9
• (D) 25