List of top Mathematics Questions asked in BITSAT

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?
Maximize \( z = 3x + 4y \) subject to \( x + y \leq 4 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
Find the sum of the series \( 1 + 3 + 5 + \ldots + 99 \).
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 \( \vec{p} \cdot (\vec{q} \times \vec{r}) \).
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?
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.

If $ A = \left[\begin{array}{cc} 3 & 1 \\2 & 4 \end{array}\right] $, then the determinant of the adjoint of $ A^2 $ is:

If $ f(x) = \sin^{-1}(2x\sqrt{1 - x^2}) $, then $ f'(x) $ is:
If $ y = \tan^{-1}\left(\frac{2x}{1 - x^2}\right) $, then $ \frac{dy}{dx} $ is:
If the roots of the quadratic equation $ x^2 + 4x + k = 0 $ are real and equal, then the value of $ k $ is:
Find the slope of the line passing through the points $ (1, 2) $ and $ (3, 6) $:
Evaluate the integral \( \int x e^{x^2} dx \):
Evaluate the integral \( \int \frac{x}{x^2 + 1} dx \):
If the distance between the points \( (2, -1) \) and \( (k, 3) \) is 5, then the possible values of \( k \) are:
If \( \tan A + \cot A = 2 \), then the value of \( \tan^2 A + \cot^2 A \) is:
The sum of the first 20 terms of the arithmetic progression 7, 10, 13, ... is:
The quadratic equation $ x^2 - 5x + k = 0 $ has equal roots. Find the value of $ k $.
If the sum of the first $ n $ terms of an arithmetic progression is given by $ S_n = 3n^2 + 5n $, find the first term $ a $ and common difference $ d $.
If $\sin \theta = \frac{3}{5}$ and $\theta$ lies in the first quadrant, find $\cos \theta$.
Find the equation of the circle which passes through the points $ (1,2) $, $ (4,3) $ and has its center on the line $ x + y = 5 $.
Find the equation of the tangent to the curve $ y = x^3 - 3x + 1 $ at the point where $ x = 2 $.
If $\log_2 (x-1) + \log_2 (x-3) = 3$, find the value(s) of $ x $.
Two dice are rolled simultaneously. What is the probability that the sum of the numbers on the two dice is at least 10?
If $$ A = \begin{pmatrix} 2 & 3 \\ 1 & k \end{pmatrix} $$ and $\det(A) = 7$, find the value of $ k $.
Find the sum of the infinite geometric series: $$ S = 8 + 4 + 2 + \cdots $$ if it converges.