List of top Mathematics Questions asked in BITSAT

What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
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 $?
Evaluate the integral \( \int \frac{x}{x^2 + 1} dx \):
Evaluate the integral \( \int_0^1 \frac{\ln(1 + x)}{1 + x^2} \, dx \)
The equation of the line passing through the point $ (2, 3) $ and making equal intercepts on the coordinate axes is:
If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.
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?
A bag contains 5 red, 3 blue, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both are red?
Find the value of $ \sin 75^\circ \cos 15^\circ + \cos 75^\circ \sin 15^\circ $.
The 5th term of an AP is 20 and the 12th term is 41. Find the first term.
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 $.
Given the sets $ A = \{ x \mid |x - 2|<3 \} $ and $ B = \{ x \mid |x + 1| \leq 4 \} $, find $ A \cap B $.
Find the determinant of the matrix \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \).
The equation of a straight line is given by \( y = 3x + 4 \). What is the slope of the line?
What is the value of \( \sin 30^\circ \)?
The area enclosed between the curve \(y = \log_e(x + e)\) and the coordinate axes is:
If $ \tan \theta + \cot \theta = 4 $, then find the value of $ \tan^3 \theta + \cot^3 \theta $.
Evaluate the sum: $$ \sum_{n=1}^{\infty} \frac{1}{n(n+1)(n+2)} $$
What is the sum of the first 10 terms of the arithmetic progression with first term 3 and common difference 2?
If \( \sin \theta + \cos \theta = \sqrt{2} \), what is the value of \( \sin \theta \cos \theta \)?
What is the value of \( \int_0^{\pi/2} \sin x \cos x \, dx\)?
If the roots of the quadratic equation \( x^2 - 6x + k = 0 \) are real and distinct, what is the range of values for \( k\)?
If \( \sin \theta + \cos \theta = 1 \), what is the value of \( \sin^2 \theta + \cos^2 \theta \)?
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?
If log$_{10}$(x + 1) = 2, what is the value of x?