List of top Mathematics Questions

The area bounded by the parabola $y^2 = 4ax$ and its latus-rectum $x = a$ is

If $x = a\left(t - \frac{1}{t}\right)$ and $y = b\left(t + \frac{1}{t}\right)$, then $\frac{dy}{dx} =$

Out of 7 consonants and 4 vowels, the number of words consisting of 3 consonants and 2 vowels are

If $y = \log \sqrt{\tan x}$, then the value of $\frac{dy}{dx}$ at $x = \frac{\pi}{4}$ is

Equation of planes parallel to the plane $x - 2y + 2z + 4 = 0$ which are at a distance of one unit from the point $(1, 2, 3)$ are

In a triangle ABC, with usual notations $a = 2$, $b = 3$, $c = 5$, then $\frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} =$

Given that the total of 16 values is 528 and the sum of the squares of deviation from 33 is 9158. The variance is

Rooms in a hotel are numbered from 1 to 19. Rooms are allocated at random as guests arrive. The first guest to arrive is given a room which is a prime number. The probability that the second guest to arrive is given a room which is a prime number is

If the surrounding air is kept at 25$^\circ$C and a body cools from 80$^\circ$C to 50$^\circ$C in 30 minutes, then temperature of the body after one hour will be

If $f(x) = \frac{1 - \sin x + \cos x}{1 + \sin x + \cos x}$, for $x \neq \pi$ is continuous at $x = \pi$, then the value of $f(\pi)$ is

Evaluate the limit: $\lim_{x \to 1} \left[ \frac{\sqrt{x} - 1}{\log x} \right] =$

Negation of the statement : $3 + 6 > 8$ and $2 + 3 < 6$ is

Evaluate the integral: $\int e^{(e^x + x)} dx$

If $3\hat{j}$, $4\hat{k}$ and $3\hat{j} + 4\hat{k}$ are the position vectors of the vertices $A, B, C$ respectively of $\Delta ABC$, then the position vector of the point in which the bisector of $\angle A$ meets $BC$ is

If $z = x + iy$ satisfies the condition $|z + 1| = 1$, then $z$ lies on the

Range of the function $f(x) = 3 + 2^x + 4^x$ is

The combined equation of a pair of lines passing through the origin and inclined at $60^\circ$ and $30^\circ$ respectively with X-axis is

10 is divided into two parts such that the sum of double of the first and square of the other is minimum, then the numbers are respectively

The general solution of the differential equation $\frac{dy}{dx} = 2^{y - x}$ is

If two lines represented by $ax^2 + 2hxy + by^2 = 0$ make angles $\alpha$ and $\beta$ with the positive direction of X-axis, then $\tan(\alpha + \beta) =$

If $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$, $\vec{b} = -\hat{i} + 2\hat{j} + \hat{k}$, $\vec{c} = 3\hat{i} + \hat{j}$ and $\vec{a} + \lambda \vec{b}$ is perpendicular to $\vec{c}$, then the value of $\lambda =$

The vector equation of the line passing through $\text{P}(1,2,3)$ and $\text{Q}(2,3,4)$ is

If $\tan^{-1} \left[ \frac{\sqrt{1+x^2} - \sqrt{1-x^2}}{\sqrt{1+x^2} + \sqrt{1-x^2}} \right] = \alpha$, then the value of $\sin 2\alpha$ is

If $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4\end{array}\right]$, $B=\left[\begin{array}{l}1 \\ 1 \\ 2\end{array}\right]$ and $X=\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]$ such that $AX = B$, then the value of $x_1 + x_2 + x_3 =$

If $A=\left[\begin{array}{rr}2 & 3 \\ 5 & -2\end{array}\right]$ and $A^{-1}=K A$, then $K$ is