List of top Questions asked in BITSAT

If $ x + \frac{1}{x} = 2 \cos \theta $, find the value of \[ x^5 + \frac{1}{x^5} \] in terms of $\theta$.

In the electrolysis of molten $ \mathrm{NaCl} $, what is produced at the cathode?

In the reaction $ \mathrm{N_2(g)} + 3\mathrm{H_2(g)} \leftrightarrow 2\mathrm{NH_3(g)} $, if the equilibrium constant $ K_c = 4 \times 10^{-3} $ at a certain temperature, which of the following is true about the reaction at equilibrium?

For the reaction $ A + B \to C $, the rate law is found to be $ \text{rate} = k[A]^2[B] $. If the concentration of $ A $ is doubled and $ B $ is halved, by what factor does the rate change?

Which of the following is the correct electronic configuration of $ \mathrm{Cr} $ (Chromium, atomic number 24)?

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 $)

A projectile is launched with an initial velocity of $ 20 \, \text{m/s} $ at an angle of $ 30^\circ $ with the horizontal. What is the maximum height reached by the projectile? (Take $ g = 10 \, \text{m/s}^2 $)

From the top of a 50 m tall building, the angles of depression to two points on the ground are $ 45^\circ $ and $ 30^\circ $. Find the distance between the two points.

Maximize $ z = 5x + 2y $ subject to $ 2x + y \leq 8 $, $ x \geq 0 $, $ y \geq 0 $. What is the maximum value of $ z $?

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?

If $ \vec{p} = 3\hat{i} - \hat{j} + 2\hat{k} $, $ \vec{q} = \hat{i} + 4\hat{j} - \hat{k} $, and $ \vec{r} = 2\hat{i} - 3\hat{j} + 5\hat{k} $, find $ \vec{p} \cdot (\vec{q} \times \vec{r}) $.

Find the sum of the series $ 1 + 3 + 5 + \ldots + 99 $.

Maximize $ z = 3x + 4y $ subject to $ x + y \leq 4 $, $ x \geq 0 $, $ y \geq 0 $. What is the maximum value of $ z $?

From the top of a 60 m high building, the angles of depression to two points on the ground on the same side of the building are $ 30^\circ $ and $ 60^\circ $. What is the distance between the two points?

If the word "GIFT" is coded using A=1, B=2, ..., Z=26, and each letter’s value is squared, what is the sum of the coded values?

If $ \vec{a} = \hat{i} + 2\hat{j} - \hat{k} $, $ \vec{b} = 2\hat{i} - \hat{j} + 3\hat{k} $, and $ \vec{c} = -\hat{i} + 3\hat{j} + 2\hat{k} $, find $ \vec{a} \cdot (\vec{b} \times \vec{c}) $.

In the given cycle ABCDA, the heat required for an ideal monoatomic gas will be:

If two charges $ q_1 $ and $ q_2 $ are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?

Evaluate the following limit: $ \lim_{n \to \infty} \prod_{r=3}^n \frac{r^3 - 8}{r^3 + 8} $.

What will be the acceleration due to gravity at a depth $ d $, where $ g $ is the acceleration due to gravity on the surface of the Earth?

For two events A and B, if $P(A) = P(A/B) = \frac{1}{4}$ and $P(B/A) = \frac{1}{2}$, then which of the following is not true?

A book contains 1000 pages. A page is chosen at random. The probability that the sum of the digits of the marked number on the page is equal to 9, is

Given below is the distribution of a random variable $X$:
\[ \begin{array}{|c|c|} \hline X = x & P(X = x) \\ \hline 1 & \lambda \\ 2 & 2\lambda \\ 3 & 3\lambda \\ \hline \end{array} \] If $\alpha = P(X<3)$ and $\beta = P(X>2)$, then $\alpha : \beta = $

The probability that certain electronic component fails when first used is 0.10. If it does not fail immediately, the probability that it lasts for one year is 0.99. The probability that a new component will last for one year is

In a binomial distribution, the mean is 4 and variance is 3. Then, its mode is: