List of top Mathematics Questions

Evaluate the integral \( \int \frac{e^{\tan^{-1} x}}{1 + x^2} \, dx \)
Evaluate the limit \( \lim_{\theta \to \frac{\pi}{2}} \frac{1 - \sin \theta}{\left(\frac{\pi}{2} - \theta\right)\cos \theta} \)
If for two events \( A \) and \( B \), \( P(A - B) = \frac{1}{5} \) and \( P(A) = \frac{3}{5} \), then \( P(B/A) = \)
If the mean of 4, 7, 2, 8, 6 and \( k \) is 7. Then the mean deviation from the mean of these observations is
Evaluate the value of \( (1.02)^8 \) using binomial theorem up to two decimal places.
If \[ \int \frac{\sin x + \cos x}{\sqrt{1 + 2 \sin x \cos x}} \, dx = \varphi(x) + C, \text{ then } \varphi(x) = \]
Evaluate the integral \[ \int_0^{\frac{\pi}{2}} \log \left( \frac{5 + 4 \sin x}{5 + 4 \cos x} \right) \, dx \]
In a kabaddi league, two matches are being played between Jaipur and Delhi. It is assumed that the outcomes of the two games are independent. The probability of Jaipur winning, drawing and losing the game against Delhi are \( \frac{1}{2} \), \( \frac{3}{10} \), and \( \frac{1}{5} \) respectively. Each team gets 5 points for win, 3 points for draw and 0 points for loss in a game. After two games, find the probability that Jaipur has more points than Delhi.
The degree of the differential equation \[ \left( 1 + \left( \frac{dy}{dx} \right)^2 \right)^{\frac{3}{4}} = \left( \frac{d^2y}{dx^2} \right)^{\frac{1}{3}} \]
The point on the line \( x + y = 4 \) that lie at a unit distance from the line \( 4x + 3y = 10 \) is
Simplified expression of \[ 1 - \frac{\sin^2 y}{1 + \cos y} + \frac{1 + \cos y}{\sin y} - \frac{\sin y}{1 - \cos y} \]
The length of the perpendicular from the point \( P(1, -1, 2) \) to the given line \[ \frac{x + 1}{2} = \frac{y - 2}{-3} = \frac{z + 2}{4} \]
If \( A(\text{adj} A) = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix} \), then the value of \( |A| + |\text{adj} A| \) is equal to :
The area of the region bounded by the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) is
If \[ A = \begin{bmatrix} 0 & -1 & 2 1 & 0 & 3 -2 & -3 & 0 \end{bmatrix} \] then \( A + 2A^T = \)
Differentiate \( \log_a x \) with respect to \( a^x \)
A bag contains \( (n + 1) \) coins. It is known that one of these coins has a head on both sides, whereas the other coins are fair. One of these coins is selected at random and tossed. If the probability that the toss results in heads is \( \frac{7}{12} \), then the value of \( n \) is :
On each working day of a school there are six periods. The number of ways in which five subjects are arranged if each subject is allotted at least one period and no period remains vacant is
Quadrilateral PQRS is inscribed inside a rectangle of dimensions \( 10 \, \text{cm} \times 8 \, \text{cm} \). The value of \( x \), if the area of the quadrilateral is minimum, is

Integrating factor of the differential equation \[ \frac{dy}{dx} + y = \frac{x^3 + y}{x} \]
If \[ \binom{n+2}{8} : \, \binom{n-2}{4} = 57 : 16, \text{ then } n \text{ is } \]
The equations \( x = a(\theta + \sin \theta) \) and \( y = a(1 - \cos \theta) \) represent the equation of a curve. If \( \theta \) changes at a constant rate \( k \), then the rate of change of the slope of the tangent to the curve at \( \theta = \frac{\pi}{3} \) is
If \[ y = (\sin^{-1} x)^2 + (\cos^{-1} x)^2, \] then \[ (1 - x^2) \frac{d^2y}{dx^2} - x \frac{dy}{dx} = \]
The function \( f(x) = \left\{ \begin{array}{ll} \frac{|x|}{x} & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{array} \right. \) is discontinuous at
The curve \( 4y = 3x^4 - 2x^2 \) attains