List of top Questions asked in BITSAT

Find out which part of the sentence has an error. If there is no error, mark part (d) as your answer.
The team a. / are planning to launch b. / the project next month. c. / No error d.
The sum of the infinite geometric series $ S = \frac{a}{1-r} $ is 24, and the sum of the first three terms is 21. Find $ a $ and $ r $.
If $ y = \ln(x^2 + 1) $, then find $ \frac{dy{dx} $ at $ x = 1 $.
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?
Identify the part of the sentence which contains a grammatical error:
"Each of the students have submitted their assignments on time."
A current of 3 A flows through a resistor of resistance 4 Ω for 2 minutes. The heat produced is:
Three resistors of $ 2\, \Omega $, $ 3\, \Omega $, and $ 6\, \Omega $ are connected in parallel. What is the equivalent resistance of the combination?
Two resistors, 4 $\Omega$ and 6 $\Omega$, are connected in parallel to a 12 V battery. What is the total current drawn from the battery?
The equivalent resistance between points A and B in a circuit with two resistors of 6 \(\Omega\) each connected in parallel is:
The rate constant $ k $ of a reaction doubles when the temperature is raised from 300 K to 310 K. Calculate the activation energy $ E_a $ of the reaction. (Use $ R = 8.314 \, J/mol\cdot K $)
A gas expands isothermally and reversibly from a volume V to 2V. If the initial pressure is P, what is the final pressure?
An ideal gas undergoes an adiabatic expansion from volume \( V \) to \( 2V \). If the initial temperature is \( T \), what is the final temperature? (Assume the ratio of specific heats \( \gamma = \frac{5}{3} \))
How much heat is required to raise the temperature of $ 2 \, kg $ of water from $ 20^\circ C $ to $ 80^\circ C $? (Specific heat capacity of water = $ 4200 \, J/kg^\circ C $)
In an isobaric process, 200 J of heat is supplied to a gas. The gas does 50 J of work. What is the change in internal energy?
How much heat is required to raise the temperature of \( 2 \, \text{kg} \) of water from \( 25^\circ C \) to \( 75^\circ C \)? (Specific heat capacity of water \( c = 4200 \, \text{J/kg}^\circ C \))
An ideal gas expands from 2 L to 6 L at a constant temperature of 300 K. Calculate the work done by the gas if pressure remains constant at 2 atm. (1 atm = $1.013 \times 10^5$ Pa)
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?