List of top Mathematics Questions asked in BITSAT

The probability of getting a sum greater than 7 when a pair of dice are thrown is:
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
The number of solutions of the differential equation \[ \frac{dy}{dx} = \frac{y+1}{x-1} \] when \( y(1) = 2 \) is:

x=logp and y=1/p differential equation

The interval in which the function \( f(x) = 4x^2 + x \) is decreasing is:
Evaluate the integral: \[ I = \int \frac{x + 3}{(x + 4)^2} e^x \,dx \]
If \( P(B) = \frac{3}{5} \), \( P(A \mid B) = \frac{1}{2} \), and \( P(A \cup B) = \frac{4}{5} \), then the value of \( P(A \cup B)' + P(A' \cup B) \) is:
If \( \vec{a} = \hat{i} + \hat{j} + \hat{k} \), \( \vec{a} \cdot \vec{b} = 1 \) and \( \vec{a} \times \vec{b} = \hat{j} - \hat{k} \), then \( \vec{b} \) is:
The area enclosed between the curve \( y = \log_e(x + e) \) and the coordinate axes is:

If the coordinates of the points A and B are (3, 3)  and  (7, 6),  then the length of the portion of the line AB intercepted between the axes is:

If \( y = \sqrt{\frac{1 + \cos 2\theta}{1 - \cos 2\theta}} \), then \( \frac{dy}{d\theta} \) at \( \theta = \frac{3\pi}{4} \) is:
The curve given by \( x + y = e^{xy} \) has a tangent parallel to the Y-axis at the point:
Bag P contains 6 red and 4 blue balls, and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?
Find the value of \[ \tan^{-1}\left(\frac{1}{4}\right) + \tan^{-1}\left(\frac{2}{9}\right) \]
For all \( n \in \mathbb{N} \), the sum of \( \frac{n^5}{5} + \frac{n^3}{3} + \frac{7n}{15} \) is:
The maximum value of \( z = 5x + 2y \) subject to the constraints: \[ x + y \leq 7, \quad x + 2y \leq 10, \quad x, y \geq 0 \]
If the sum of an infinite GP \( a, ar, ar^2, ar^3, \dots \) is 15 and the sum of the squares of each term is 150, then the sum of the series \( ar^2, a r^4, ar^6, \dots \) is:
The shortest distance between the lines \[ \frac{x - 3}{2} = \frac{y - 2}{3} = \frac{z - 1}{-1} \] and \[ \frac{x + 3}{2} = \frac{y - 6}{1} = \frac{z - 5}{3} \] is:
The middle term in the expansion of \( \left(\frac{10}{x} + \frac{x}{10}\right)^{10} \) is:
The function \( f(x) = \tan^{-1}(\sin x + \cos x) \) is an increasing function in:
The derivative of \( e^{x^3} \) with respect to \( \log x \) is:
Find the mean deviation about the mean for the data: \( 4, 7, 8, 9, 10, 12, 13, 17 \)
If \[ A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix} \] and \[ kA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}, \] then the values of \( k \), \( a \), and \( b \) respectively are:

The ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and  (3, -5, 8)  is  2 : m.  
The value of m is:

Find: \( \lim_{x \to 0} \frac{| \sin x |}{x} \)