List of top Questions asked in Birla Institute of Technology & Science Admission Test- 2025

What is the major product when 1-bromopropane undergoes nucleophilic substitution with \(OH^-\)?
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
A box contains 5 red balls and 3 blue balls. If two balls are drawn randomly without replacement, what is the probability that one of the balls is red and the other is blue?
Find the determinant of the matrix \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \).
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?
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 gas expands isothermally and reversibly from a volume V to 2V. If the initial pressure is P, what is the final pressure?
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?
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
Find the angle between the vectors \( \mathbf{a} = (2, -1, 3) \) and \( \mathbf{b} = (1, 4, -2) \).
If \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \), find the determinant of \( A^2 \).
If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.
The equation of the line passing through the point $ (2, 3) $ and making equal intercepts on the coordinate axes is:
If $ \tan \theta + \cot \theta = 4 $, then find the value of $ \tan^3 \theta + \cot^3 \theta $.
If $ y = \ln(x^2 + 1) $, then find $ \frac{dy{dx} $ at $ x = 1 $.
If $ a, b $ are roots of the equation $ x^2 - 5x + 6 = 0 $, find the value of $ a^3 + b^3 $.
In triangle $ ABC $, the length of sides are $ AB = 7 $, $ BC = 10 $, and $ AC = 5 $. What is the length of the median drawn from vertex $ B $?
If $ f(x) = e^{2x} \sin x $, find $ f'(x) $.
The half-life of a radioactive substance is 4 hours. If initially there are 256 grams, how much remains after 10 hours?
A fluid flows through a pipe with varying cross-section. If the velocity at the narrow section is 3 m/s and the cross-sectional area is half of the wider section, what is the velocity in the wider section?
The escape velocity from the surface of a planet is 11.2 km/s. If the radius of the planet is doubled but the mass remains the same, what will be the new escape velocity?
Two identical charges $ q $ are placed 1 m apart. The electrostatic force between them is $ 9 \times 10^{-9} \, \text{N} $. What is the magnitude of each charge? (Take $ k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 $)
A charged particle moves in a magnetic field with velocity $ v $ perpendicular to the field $ B $. The radius of the circular path is $ r $. Which of the following expressions gives the charge $ q $ of the particle?
How much water must be added to 500 mL of 2 M $ \mathrm{H_2SO_4} $ solution to make it 0.5 M?
How many grams of $ \text{CO}_2 $ are produced when 10 g of $ \text{C}_2\text{H}_6 $ (ethane) is completely combusted? Reaction: $ 2\text{C}_2\text{H}_6 + 7\text{O}_2 \rightarrow 4\text{CO}_2 + 6\text{H}_2\text{O} $