List of top Mathematics Questions asked in BITSAT

Evaluate the integral: $$ \int_0^{\pi/4} \frac{\ln(1 + \tan x)}{\cos x \sin x} \, dx $$

If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \), where \( A + B + C = \pi \), then what is the value of \( \tan A \tan B + \tan B \tan C + \tan C \tan A \)?

If \( A = \begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \\ \end{vmatrix} \), then the value of \( A \) is:

Solve the inequality: \( \log_2(x^2 - 5x + 6) >1 \)

Two numbers are selected at random (without replacement) from the first 6 natural numbers. What is the probability that the difference of the numbers is less than 3?

If \( z = x + iy \) is a complex number such that \( |z - 1| = |z + 1| \), then the locus of \( z \) represents:

If \( \vec{a} = \hat{i} + 2\hat{j} + \hat{k} \) and \( \vec{b} = 2\hat{i} - \hat{j} + 2\hat{k} \), then find the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \).

Evaluate the integral \( \int_0^1 \frac{\ln(1 + x)}{1 + x^2} \, dx \)

If one root of the quadratic equation \( ax^2 + bx + c = 0 \) is double the other, then what is the correct relation among the coefficients?

Find the sum of the infinite geometric series: $$ S = 8 + 4 + 2 + \cdots $$ if it converges.

If $$ A = \begin{pmatrix} 2 & 3 \\ 1 & k \end{pmatrix} $$ and $\det(A) = 7$, find the value of $ k $.

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?

Find the equation of the tangent to the curve $ y = x^3 - 3x + 1 $ at the point where $ x = 2 $.

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 $.

How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?

If $\sin \theta = \frac{3}{5}$ and $\theta$ lies in the first quadrant, find $\cos \theta$.

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 $.

The quadratic equation $ x^2 - 5x + k = 0 $ has equal roots. Find the value of $ k $.

The sum of the first 20 terms of the arithmetic progression 7, 10, 13, ... is:

If \( \tan A + \cot A = 2 \), then the value of \( \tan^2 A + \cot^2 A \) is:

If the distance between the points \( (2, -1) \) and \( (k, 3) \) is 5, then the possible values of \( k \) are:

Evaluate the integral \( \int \frac{x}{x^2 + 1} dx \):

The equation of the circle passing through the points (1,2), (4,3), and (2,–1) is:

Evaluate the integral \( \int x e^{x^2} dx \):