List of top Mathematics Questions

If the circle $x^{2}+y^{2}-6x-12y-55=0$ intercepts the x-axis at two points $A$ and $B$, then $|AB|$ is equal to

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 angle between the vectors $\vec{a}=x\hat{i}+3\hat{j}+\hat{k}$ and $\vec{b}=x\hat{i}-x\hat{j}+2\hat{k}$ is acute, then $x$ lies 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 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

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

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

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

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

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

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

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 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

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

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 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 $(x+y)^{2}=$

If six persons are to be selected to form a committee from a group of seven women and four men so that at least three women are there on the committee, then the number of ways it can be done, is

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