List of top Mathematics Questions asked in BITSAT

What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
If the roots of the quadratic equation $ x^2 + 4x + k = 0 $ are real and equal, then the value of $ k $ is:
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?
Evaluate the sum: $$ \sum_{n=1}^{\infty} \frac{1}{n(n+1)(n+2)} $$
If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \), where \( A + B + C = \pi \), then what is the value of \( \tan A \tan B + \tan B \tan C + \tan C \tan A \)?
The area enclosed between the curve \(y = \log_e(x + e)\) and the coordinate axes is:
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 $ f(x) = x^2 + 3x $, then $ f'(x) $ is:
Find the derivative of \( y = \sin(x^2) \) with respect to \( x \).
If $\log_2 (x-1) + \log_2 (x-3) = 3$, find the value(s) of $ x $.
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?
If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.
Find the equation of the tangent to the curve $ y = x^3 - 3x + 1 $ at the point where $ x = 2 $.
A box contains 5 red balls and 4 green balls. Two balls are drawn one after another without replacement. What is the probability that the second ball is green, given that the first ball drawn was red?
What is the value of \(\int \frac{1}{x^2 + 1} \, dx\)?
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 $.
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 the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
Find the equation of the tangent to the curve \(y = x^2\) at the point (1,1).
If \( \sin \theta + \cos \theta = \sqrt{2} \), what is the value of \( \sin \theta \cos \theta \)?
Evaluate the integral: $$ \int_0^{\pi/4} \frac{\ln(1 + \tan x)}{\cos x \sin x} \, dx $$
The sum of the first 30 terms of an arithmetic progression is 930. If the first term is 2, what is the common difference of the progression?
The area enclosed between the curve \(y = \log_e(x + e)\) and the coordinate axes is:
What is the sum of the first 10 terms of the arithmetic progression with first term 3 and common difference 2?