List of top Mathematics Questions asked in BITSAT

Evaluate the integral \( \int_0^1 \frac{\ln(1 + x)}{1 + x^2} \, dx \)
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 $.
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 \( z = 5x + 2y \) subject to \( 2x + y \leq 8 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
Find the sum of the series \( 1 + 3 + 5 + \ldots + 99 \).
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 $.
If $ y = \ln(x^2 + 1) $, then find $ \frac{dy{dx} $ at $ x = 1 $.
Given the sets $ A = \{ x \mid |x - 2|<3 \} $ and $ B = \{ x \mid |x + 1| \leq 4 \} $, find $ A \cap B $.
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
Let the function $ f(x) = \sqrt{\log_e(1 - x^2)} $. Then the domain of $ f(x) $ is:
The roots of the equation \( x^2 + 5x + 6 = 0 \) are:
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 $?
Maximize \( z = 3x + 4y \) subject to \( x + y \leq 4 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
Evaluate the integral \( \int \frac{x}{x^2 + 1} dx \):
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?
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 $.
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 \( \sin \theta \cos \theta \)?