List of top Mathematics Questions asked in BITSAT

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?
Evaluate the integral \( \int_0^1 \frac{\ln(1 + x)}{1 + x^2} \, dx \)
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 \( \vec{b} \).
If \( z = x + iy \) is a complex number such that \( |z - 1| = |z + 1| \), then the locus of \( z \) represents:
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?
Solve the inequality: \( \log_2(x^2 - 5x + 6) >1 \)
If \( A = \begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \\ \end{vmatrix} \), then the value of \( A \) is:
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 point $ P(x, y) $ satisfies the condition that its distance from the point $ (3, -2) $ is equal to its distance from the line $ y = 2x + 1 $, then the locus of point $ P $ is:
Let the function $ f(x) = \sqrt{\log_e(1 - x^2)} $. Then the domain of $ f(x) $ is:
Let $ f(x) = |x^2 - 4x + 3| + |x^2 - 5x + 6| $. The minimum value of $ f(x) $ is:
Let vectors $\mathbf{a}, \mathbf{b}, \mathbf{c}$ be such that $$ \mathbf{a} = \hat{i} + 2\hat{j} - \hat{k}, \quad \mathbf{b} = 2\hat{i} - \hat{j} + \hat{k}, \quad \mathbf{c} = \hat{i} + \hat{j} + \hat{k} $$ Then the volume of the parallelepiped formed by these vectors is:
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?
Evaluate: $$ \lim_{x \to 0} \frac{\sqrt{1 + x} - \sqrt{1 - x}}{x} $$
If $ f(x) = x^2 + 3x $, then $ f'(x) $ is:
Find the number of integers \(n\) such that \(1 \leq n \leq 100\) and \(n^2 + 3n + 2\) is divisible by 5.
Find the coordinates of the point which divides the line segment joining \((2, -3)\) and \((7, 9)\) in the ratio \(3:2\).
If \( z = 2(\cos 60^\circ + i \sin 60^\circ) \), find the value of \( z^3 \).
From a group of 10 men and 8 women, a committee of 5 is to be formed such that it contains at least 3 women. How many such committees are possible?
Two circles with centers $O_1$ and $O_2$ touch externally. The radius of the first circle is 4 cm and the second is 9 cm. The distance between their centers is 13 cm. Find the length of the direct common tangent.
Evaluate: \[ \lim_{x \to 0} \frac{\sin 3x - 3 \sin x}{x^3} \]
If $ x + \frac{1}{x} = 2 \cos \theta $, find the value of \[ x^5 + \frac{1}{x^5} \] in terms of $\theta$.
Maximize \( z = 5x + 2y \) subject to \( 2x + y \leq 8 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
If \( a>0, b>0, c>0 \) and \( a, b, c \) are distinct, then \( (a + b)(b + c)(c + a) \) is greater than:
A book contains 1000 pages. A page is chosen at random. The probability that the sum of the digits of the marked number on the page is equal to 9, is