List of top Mathematics Questions

The integral $ \int e^x \left[ \frac{x^2 + 1}{(x+1)^2} \right] \, dx $

The general solution of the differential equation $ (1 + \tan y)(dx - dy) + 2x \, dx \, dy = 0 $

The co-ordinate of the foot of the perpendicular from $ P(1, 8, 4) $ on the line joining $ R(0, -1, 3) $ and $ Q(2, -3, -1) $ is

The side of a cube is equal to the diameter of a sphere. If the side and radius increase at the same rate then the ratio of the increase of their surface area is

A coin is tossed until a head appears or until the coin has been tossed three times. Given that 'head' does not appear on the first toss, what is the probability that the coin is tossed thrice?

The value of $ \int \frac{dx}{\sqrt{2ax - x^2}} $

A number consists of three digits in geometric progression. The sum of the right hand and left hand digits exceeds twice the middle digit by 1 and the sum of left hand and middle digits is two third of the sum of the middle and right hand digits. Then the sum of digits of number is

If $ f(x) = \begin{cases} x, & 0 \leq x \leq 1 \\ 2x - 1, & x > 1 \end{cases} $, then:

The shaded region in the Venn diagram represents

The measure of the angle between the lines $ x = k + 1, \quad y = 2k - 1, \quad z = 2k + 3, \quad k \in \mathbb{R} $ and $ \frac{x-1}{2} = \frac{y+1}{1} = \frac{z-1}{2} $ is:

If $ y = \sqrt{\sin x + y} $, then find $ \frac{dy}{dx} $ at $ x = 0, y = 1 $.

Let A and B be two events such that $ P(A/B) = \frac{1}{2}, \quad P(B/A) = \frac{1}{3}, \quad \text{and} \quad P(A \cap B) = \frac{1}{6} $ Then, which one of the following is not true?

If $ y = f(x), \, p = \frac{dy}{dx}, \, q = \frac{d^2 y}{dx^2}, \text{ then } \frac{d^2 x}{dy^2} \text{ is equal to } $

If $ \frac{\cos x}{\cos(x - 2y)} = \lambda \quad \text{then} \quad \tan(x - y) \tan y = $

If $ \hat{i} + \hat{j} - \hat{k} $ and $ 2\hat{i} - 3\hat{j} + \hat{k} $ are adjacent sides of a parallelogram, then length of its diagonal is

Consider an infinite geometric series with first term $ a $ and common ratio $ r $. If the sum of infinite geometric series is 4 and the second term is $ \frac{3}{4} $, then:

The value of the integral $ \int_{1/3}^1 \frac{(x - x^3)^{\frac{1}{3}}}{x^4} \, dx $ is:

The area of the region enclosed by the curve $ \left\{ (x, y) : 4x^2 + 25y^2 = 100 \right\} $ is:

The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6, then the other two observations are:

If $3A + 4B^{t} = \left( \begin{array}{cc} 7 & -10 \\ 0 & 6 \end{array} \right) $ and $ 2B - 3A^{t} = \left( \begin{array}{cc} -1 & 18 \\ 4 & -6 \\ -5 & -7 \end{array} \right) $, then find $ (5B)^{t}$:
 

The area of the triangle whose vertices are $ (-2, a) $, $ (2, -6) $, and $ (5, 4) $ is 35 square units. Then the value of $ a $ is:

While shuffling a pack of cards, 3 cards were accidentally dropped, then find the probability that the missing cards belong to different suits?