List of top Mathematics Questions asked in BITSAT

Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
A box contains 5 red balls and 3 blue balls. If two balls are drawn randomly without replacement, what is the probability that one of the balls is red and the other is blue?
Find the angle between the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \).
Find the determinant of the matrix \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \).
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
Find the angle between the vectors \( \mathbf{a} = (2, -1, 3) \) and \( \mathbf{b} = (1, 4, -2) \).
If \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \), find the determinant of \( A^2 \).
Evaluate the sum: $$ \sum_{n=1}^{\infty} \frac{1}{n(n+1)(n+2)} $$
The equation of the circle passing through the points (1,2), (4,3), and (2,–1) is:
In triangle $ ABC $, the length of sides are $ AB = 7 $, $ BC = 10 $, and $ AC = 5 $. What is the length of the median drawn from vertex $ B $?
The equation of the line passing through the point $ (2, 3) $ and making equal intercepts on the coordinate axes is:
How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition such that the number is divisible by 5?
How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?
If $ f(x) = e^{2x} \sin x $, find $ f'(x) $.
If $ a, b $ are roots of the equation $ x^2 - 5x + 6 = 0 $, find the value of $ a^3 + b^3 $.
If $ y = \ln(x^2 + 1) $, then find $ \frac{dy{dx} $ at $ x = 1 $.
If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.
The 5th term of an AP is 20 and the 12th term is 41. Find the first term.
The value of $ \sin^2 30^\circ + \cos^2 60^\circ $ is:
The sum of the infinite geometric series $ S = \frac{a}{1-r} $ is 24, and the sum of the first three terms is 21. Find $ a $ and $ r $.
Find the value of $ \sin 75^\circ \cos 15^\circ + \cos 75^\circ \sin 15^\circ $.
Given the sets $ A = \{ x \mid |x - 2|<3 \} $ and $ B = \{ x \mid |x + 1| \leq 4 \} $, find $ A \cap B $.
The area of a triangle with vertices at points $ A(1,2) $, $ B(4,6) $, and $ C(k, 8) $ is 5. Find the value of $ k $.
If \( \vec{a} = \hat{i} + 2\hat{j} - \hat{k} \), \( \vec{b} = 2\hat{i} - \hat{j} + 3\hat{k} \), and \( \vec{c} = -\hat{i} + 3\hat{j} + 2\hat{k} \), find \( \vec{a} \cdot (\vec{b} \times \vec{c}) \).
If the word "GIFT" is coded using A=1, B=2, ..., Z=26, and each letter’s value is squared, what is the sum of the coded values?