List of top Questions asked in BITSAT- 2025

Two capacitors $ C_1 = 4\mu F $ and $ C_2 = 6\mu F $ are connected in series across a 60 V battery. The potential difference across $ C_2 $ is:
What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
Given the sets $ A = \{ x \mid |x - 2|<3 \} $ and $ B = \{ x \mid |x + 1| \leq 4 \} $, find $ A \cap B $.
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
Let the function $ f(x) = \sqrt{\log_e(1 - x^2)} $. Then the domain of $ f(x) $ is:
In a mixture of gases, the average number of degrees of freedom per molecule is 6. If the rms speed of the molecule is \(c\), what is the velocity of sound in the gas?
How much water must be added to 500 mL of 2 M $ \mathrm{H_2SO_4} $ solution to make it 0.5 M?
A proton enters a uniform magnetic field $\vec{B} = 0.5 \hat{k} \ \text{T}$ with velocity $\vec{v} = 10^6 \hat{i} \ \text{m/s}$. The magnitude of the magnetic force on the proton is:
The half-life of a radioactive substance is 4 hours. If initially there are 256 grams, how much remains after 10 hours?
A simple pendulum has a time period of 2 s on Earth's surface. What is its time period at a height equal to the Earth's radius (R)? (Acceleration due to gravity at height h is \( g_h = \frac{g}{(1 + h/R)^2} \)).
The escape velocity from the surface of a planet is \(v_e\). What will be the escape velocity from a planet whose mass and radius are twice that of the original planet?
A ball is thrown vertically upward with a speed of 49 m/s. How long will it take to return to the thrower’s hand?
The roots of the equation \( x^2 + 5x + 6 = 0 \) are:
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?
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 $?
Which of the following compounds will give a positive Iodoform test?
A convex lens has focal length 20 cm. An object is placed at a distance of 40 cm from the lens. What is the position of the image formed?
Maximize \( z = 3x + 4y \) subject to \( x + y \leq 4 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
Two identical bodies of mass 1 kg each are moving towards each other with velocities of 5 m/s and 3 m/s, respectively. They collide elastically. What will be the velocity of the body initially moving at 5 m/s after the collision?
A simple pendulum of length 1 m is oscillating with an amplitude of 0.1 m. What is the maximum tension in the string if the mass of the bob is 0.2 kg? (Assume \( g = 10 \, \text{m/s}^2 \))
Evaluate the integral \( \int \frac{x}{x^2 + 1} dx \):
If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.
If the word "BITS" is coded using \( A=1, B=2, \ldots, Z=26 \), and the code is the sum of the squares of each letter's value, what is the code for the word?

Which of the following is the correct electronic configuration for \( \text{Oxygen (O)} \)?

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?