List of top Questions asked in BITSAT- 2023

In an LC oscillator, if the values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of the oscillator becomes \( x \) times its initial resonant frequency \( \omega_0 \). The value of \( x \) is:
For all \( n \in \mathbb{N} \), the sum of \( \frac{n^5}{5} + \frac{n^3}{3} + \frac{7n}{15} \) is:
If the sum of an infinite GP \( a, ar, ar^2, ar^3, \dots \) is 15 and the sum of the squares of each term is 150, then the sum of the series \( ar^2, a r^4, ar^6, \dots \) is:

If the coordinates of the points A and B are (3, 3)  and  (7, 6),  then the length of the portion of the line AB intercepted between the axes is:

Find the mean deviation about the mean for the data: \( 4, 7, 8, 9, 10, 12, 13, 17 \)

How much ethyl alcohol must be added to 1 litre of water so that the solution will freeze at \(-14^\circ \text{C}\)? 

(Kf for water = 1.86 °C/mol)

If enthalpies of formation of \( {C}_2{H}_4(g) \), \( {CO}_2(g) \) and \( {H}_2{O}(l) \) at 25°C and 1 atm pressure are 52, 394 and -286 kJ/mol respectively, the change in enthalpy for combustion of \( {C}_2{H}_4 \) is equal to:
The middle term in the expansion of \( \left(\frac{10}{x} + \frac{x}{10}\right)^{10} \) is:
If \[ A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix} \] and \[ kA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}, \] then the values of \( k \), \( a \), and \( b \) respectively are:
Find the value of \[ \tan^{-1}\left(\frac{1}{4}\right) + \tan^{-1}\left(\frac{2}{9}\right) \]
If \( y = \sqrt{\frac{1 + \cos 2\theta}{1 - \cos 2\theta}} \), then \( \frac{dy}{d\theta} \) at \( \theta = \frac{3\pi}{4} \) is:

The ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and  (3, -5, 8)  is  2 : m.  
The value of m is:

The curve given by \( x + y = e^{xy} \) has a tangent parallel to the Y-axis at the point:
If \( \vec{a} = \hat{i} + \hat{j} + \hat{k} \), \( \vec{a} \cdot \vec{b} = 1 \) and \( \vec{a} \times \vec{b} = \hat{j} - \hat{k} \), then \( \vec{b} \) is:
Which of the following will precipitate first when an aqueous solution containing sulphate ions is added?
Find: \( \lim_{x \to 0} \frac{| \sin x |}{x} \)
The lines \[ \frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{-k} \] and \[ \frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z - 5}{1} \] are coplanar if:
The maximum value of \( z = 5x + 2y \) subject to the constraints: \[ x + y \leq 7, \quad x + 2y \leq 10, \quad x, y \geq 0 \]

Among the given halides, which one will give the same product in both S\(_N1\) and S\(_N2\) reactions? 

The equation of a common tangent to the parabolas \( y = x^2 \) and \( y = -(x - 2)^2 \) is:
The function \( f(x) = \tan^{-1}(\sin x + \cos x) \) is an increasing function in:
What is \( x \) in the following reaction? \[ {Al} (s) + {NaOH} (aq) + {H}_2O (l) \rightarrow x + {H}_2 (g) \]
The ratio of the speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:
What is the angle between the two straight lines \( y = (2 - \sqrt{3})x + 5 \) and \( y = (2 + \sqrt{3})x - 7 \)?
The shortest distance between the lines \[ \frac{x - 3}{2} = \frac{y - 2}{3} = \frac{z - 1}{-1} \] and \[ \frac{x + 3}{2} = \frac{y - 6}{1} = \frac{z - 5}{3} \] is: