List of top Mathematics Questions

If the foci and vertices of an ellipse are respectively $(\pm 2,0)$ and $(\pm 3,0)$ then its eccentricity is

The equation of a hyperbola is $9x^{2}-16y^{2}=144$. If $A$ and $S$ are, respectively, the focus and the vertex of one section of the hyperbola, then the length of $AS$ is

If the focus and vertex of a parabola are at a distance of 3 units and 6 units, respectively, from the origin on the positive x-axis, then the equation of the parabola is

The perpendicular distance between the lines $3x+4y-6=0$ and $6x+8y+18=0$ is

The x-intercept and y-intercept of a line are three times and four times of the x-intercept and y-intercept of the line $3x+2y=6$, respectively. Then the equation of the line is

The value of $\tan^{-1}\left(\frac{\cos x-\sqrt{3}\sin x}{\sqrt{3}\cos x+\sin x}\right)$ , where $0<x<\frac{\pi}{2}$ is

If the foot of the perpendicular drawn from the origin to the line $y=mx+c$ is $(1,1)$ then the value of $m$ and $c$ are, respectively,

The value of $\cos^{-1}\left(\cos\frac{2\pi}{3}\right)+\sin^{-1}\left(\sin\frac{2\pi}{3}\right)$ is equal to

The value of $\tan^{2}(\sec^{-1}(3))$ is

Let $f(x)=(8\sin x+15\cos x+3)^{2}-15$, $x\in\mathbb{R}.$ Then the maximum value of $f$ is

The value of $\frac{\tan 75^{\circ}+\tan 15^{\circ}}{\tan 75^{\circ}-\tan 15^{\circ}}$ is equal to

The value of $\frac{\sqrt{3}(\sin 40^{\circ}+\sin 20^{\circ})}{\cos 40^{\circ}+\cos 20^{\circ}}$ is

If $\sec^{2}\theta+\tan^{2}\theta=7, 0<\theta<\frac{\pi}{2}$, then $\tan 2\theta$ is equal to

If $|2x-3|<5, x\in\mathbb{R}$, then $x$ lies in the interval

The value of $4 \cos 36^{\circ}\cos 72^{\circ}$ is equal to

The value of $\begin{vmatrix} \sin 30^{\circ} & \cos 30^{\circ} & \sin(30^{\circ}+75^{\circ}) \\ \sin 45^{\circ} & \cos 45^{\circ} & \sin(45^{\circ}+75^{\circ}) \\ \sin 60^{\circ} & \cos 60^{\circ} & \sin(60^{\circ}+75^{\circ}) \end{vmatrix}$ is equal to

If $\frac{21x-6}{4}-9\le0$ and $\frac{x-1}{3}+1\ge0, x\in\mathbb{R}$ then $x$ lies in the interval

If the coefficient of $y^{3}$ in the binomial expansion of $\left(2\alpha-\frac{y}{2}\right)^{8}$ is -7, then the value of $\alpha$ is equal to

Let $(1+ax)(1-2x)^{3}=\sum_{n=0}^{4}a_{n}x^{n}$, where $a$ is a constant. If $a_{2}=0$, then the value of $a$ is

If $A$ is a square matrix of order $n$ such that $|\text{adj}(\text{adj} A)|=|A|^{25}$, then $n$ is equal to

If $A$ is a non-singular matrix of order $n$ satisfying the matrix equation $I+A+A^{2}+A^{3}+...+A^{10}=0$, where $I$ and $0$ are, respectively, unit and null matrices of order $n$, then $A^{10}=$

If $a, x, y, b$ are in G.P., then $(x+y)^{2}=$

The number of 3-digit even numbers that can be formed with the digits 0, 1, 2, 3, 4, 5, 6 are

If the $3^{\text{rd}}$, $7^{\text{th}}$, $11^{\text{th}}$ terms of a geometric progression are $a$, $b$, $c$ respectively, then $(ac)^{4} =$

A cricket team of 11 players from 16 players is to be selected. If three particular players are always included in the team, then the number of ways of selecting the team is