List of top Mathematics Questions asked in BITSAT

Number of solutions of equations $ \sin 9\theta = \sin \theta $ in the interval $ [0, 2\pi] $ is

If the 17th and the 18th terms in the expansion of $ (2 + a)^{50} $ are equal, then the coefficient of $ x^{35} $ in the expansion of $ (a + x)^{-2} $ is:

If $ a>0 $, $ b>0 $, $ c>0 $ and $ a, b, c $ are distinct, then $ (a + b)(b + c)(c + a) $ is greater than

The variance of 20 observations is 5. If each observation is multiplied by 2, then the new variance of the resulting observation is

Let $ f(x) = \sin x $, $ g(x) = \cos x $, $ h(x) = x^2 $ then
\[ \lim_{x \to 1} \frac{f(g(h(x))) - f(g(h(1)))}{x - 1} = \]

If $ A = 1 + r^a + r^{2a} + r^{3a} + \cdots \infty $ and $ B = 1 + r^b + r^{2b} + r^{3b} + \cdots \infty $, then $ a/b $ is equal to

If the system of linear equations $ 2x + y - z = 7 $, $ x - 3y + 2z = 1 $, $ x + 4y + \delta z = k $ (where $\delta, k \in \mathbb{R}$) has infinitely many solutions, then $\delta + k$ is equal to:

If $ A = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} $, $ P = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix} $ and $ X = A P A^T $, then $ A^T X^{50} A = $

The 5th term of an AP is 20 and the 12th term is 41. Find the first term.

The area enclosed between the curve $y = \log_e(x + e)$ and the coordinate axes is:

The equation of the line passing through the point $ (2, 3) $ and making equal intercepts on the coordinate axes is:

Find the determinant of the matrix $ A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} $.

Two dice are rolled simultaneously. What is the probability that the sum of the numbers on the two dice is at least 10?

Evaluate the integral: $$ \int_0^{\pi/4} \frac{\ln(1 + \tan x)}{\cos x \sin x} \, dx $$

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 $.

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 $.

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?

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 $.

What is the dot product of the vectors $ \mathbf{a} = (2, 3, 1) $ and $ \mathbf{b} = (1, -1, 4) $?

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: