List of top Questions asked in BITSAT- 2024

Number of subsets of set of letters of word 'MONOTONE' is:
The range of \(8\sin(\theta) + 6\cos(\theta) + 2\) is:

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

The function \[ f(x) = \frac{\cos x}{\left\lfloor \frac{2x}{\pi} \right\rfloor + \frac{1}{2}}, \] where \( x \) is not an integral multiple of \( \pi \) and \( \lfloor \cdot \rfloor \) denotes the greatest integer function, is:
Evaluate the integral: \[ \int \frac{x^3 - 1}{x^3 + x} dx \]
Evaluate the integral: \[ \int \frac{x^2 (x \sec^2 x + \tan x)}{(x \tan x + 1)^2} dx \]
Consider the function \( f(x) = \frac{|x - 1|}{x^2} \). Then \( f(x) \) is:
Evaluate the integral: \[ \int \sqrt{x + \sqrt{x^2 + 2}} \, dx. \]
The value of \( \int_0^\infty \frac{dx}{(x^2 + a^2)(x^2 + b^2)} \) is:
The value of \( \int e^{\tan \theta} (\sec \theta - \sin \theta) \, d\theta \) is:
The locus of the point of intersection of the lines \(x = a(1 - t^2)/(1 + t^2)\) and \(y = 2at/(1 + t^2)\) (t being a parameter) represents:
The distance from the origin to the image of $(1,1)$ with respect to the line $x + y + 5 = 0$ is:
The locus of the mid-point of a chord of the circle $x^2 + y^2 = 4$ which subtends a right angle at the origin 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:
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:
If a function \( f: \mathbb{R} \setminus \{1\} \rightarrow \mathbb{R} \setminus \{m\} \) is defined by \( f(x) = \frac{x+3}{x-2} \), then \( \frac{3}{l} + 2m = \)
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:

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 \( A = \frac{1}{3} \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix} \) is an orthogonal matrix, then
The function f: R\(\rightarrow\) R is defined by \[ f(x) = \frac{x}{\sqrt{1 + x^2}} \] is:
The coefficient of \(x^2\) term in the binomial expansion of \(\left(\frac{1}{3}x^{\frac{1}{3}} + x^{-\frac{1}{4}}\right)^{10}\) is:
The number of real solutions of
\[ \sqrt{5 - \log_2 |x|} = 3 - \log_2 |x| \] 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:}
The domain of the real-valued function
\[ f(x) = \sqrt{\frac{2x^2 - 7x + 5}{3x^2 - 5x - 2}} \] is:
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