List of top Questions asked in BITSAT- 2024

The number of real solutions of
\[ \sqrt{5 - \log_2 |x|} = 3 - \log_2 |x| \] is:

If a function $ f: \mathbb{R} \setminus \{1\} \rightarrow \mathbb{R} \setminus \{m\} $ is defined by $ f(x) = \frac{x+3}{x-2} $, then $ \frac{3}{l} + 2m = $

If $ A = \frac{1}{3} \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix} $ is an orthogonal matrix, then

The coefficient of the highest power of $x$ in the expansion of $(x + \sqrt{x^2 - 1})^8 + (x - \sqrt{x^2 - 1})^8$ is:

Let $ [x] $ denote the greatest integer $ \leq x $. If $ f(x) = [x] $ and $ g(x) = |x| $, then the value of:
\[ f \left( g \left( \frac{8}{5} \right) \right) - g \left( f \left( \frac{-8}{5} \right) \right) \] is:

If $ \vec{a} = 2\hat{i} + \hat{j} + 2\hat{k} $, then the value of $ |\hat{i} \times (\vec{a} \times \hat{i})| + |\hat{j} \times (\vec{a} \times \hat{j})| + |\hat{k} \times (\vec{a} \times \hat{k})|^2 $ is equal to:}

In an examination, 62% of the candidates failed in English, 42% in Mathematics and 20% in both. The number of those who passed in both the subjects is:

If $ p $: 2 is an even number, $ q $: 2 is a prime number, and $ r $: $ 2 + 2 = 2^2 $, then the symbolic statement $ p \rightarrow (q \vee r) $ means:

If matrix $ A = \begin{bmatrix} 3 & -2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1 \end{bmatrix} $ and $ A^{-1} = \frac{1}{k} adj(A) $, then $ k $ is

If the variance of the data $ 2,3,5,8,12 $ is $ \sigma^2 $ and the mean deviation from the median for this data is $ M $, then $ \sigma^2 - M $ is:

One molar concentration of a solution represents:

From a point A(0,3) on the circle \[ (x + 2)^2 + (y - 3)^2 = 4 \] a chord AB is drawn and extended to a point Q such that AQ = 2AB. Then the locus of Q is:

In the following circuit diagram, when the $3\Omega$ resistor is removed, the equivalent resistance of the network:

From the top of a cliff 50 m high, the angles of depression of the top and bottom of a tower are observed to be $30^\circ$ and $45^\circ$. The height of the tower is:

The bond dissociation energy of X$_2$, Y$_2$ and XY are in the ratio of 1 : 0.5 : 1. $\Delta H$ for the formation of XY is -200 kJ/mol. The bond dissociation energy of X$_2$ will be

Choose the correct stability order of the given free radicals.

If the function $ f(x) $, defined below, is continuous on the interval $[0,8]$, then: \[ f(x) = \begin{cases} x^2 + ax + b, & 0 \leq x < 2 \\ 3x + 2, & 2 \leq x \leq 4 \\ 2ax + 5b, & 4 < x \leq 8 \end{cases} \]

The property of light which cannot be explained by Huygen's construction of a wavefront is:

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is:

The potential of a large liquid drop when eight liquid drops are combined is 20 V. Then, the potential of each single drop was:

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?

A plane progressive wave is given by y = 2 cos 2pi (330t - x) m. The frequency of the wave is:}

A particle is moving in a straight line. The variation of position $ x $ as a function of time $ t $ is given as:
$ x = t^3 - 6t^2 + 20t + 15 $.
The velocity of the body when its acceleration becomes zero is:

The distance between the Sun and Earth is $ R $. The duration of a year if the distance between the Sun and Earth becomes $ 3R $ will be:

The range of a projectile projected at an angle of $ 15^\circ $ with the horizontal is $ 50 $ m. If the projectile is projected with the same velocity at an angle of $ 45^\circ $, then its range will be: