List of top Mathematics Questions

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

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

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

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

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

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 $A$ 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

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 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

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

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 $(ac)^{4} =$

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

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

The three geometric means between 4 and 324 are

The value of $\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^{3}+\left(\frac{\sqrt{3}}{2}-\frac{i}{2}\right)^{3}$ is equal to

The $3^{\text{rd}}$ and $6^{\text{th}}$ terms of a G.P. are, respectively 108 and -32. Then the first term is

The imaginary part of $\frac{\cos 50^{\circ}+i\sin 50^{\circ}}{\cos 50^{\circ}-i\sin 50^{\circ}}$ is equal to

The equation $\text{Im}(1-i)z=1$ represents the line

The inverse function of $f(x) = ax + 1$, $x \in \mathbb{R}$ is itself. Then the value of $a$ is

If $f(x)=x+1$, and $g(x)=x^{3}$, then $f^{-1}(g(x))$ is equal to

The range of $f(x)=[\cos x]$, where $[x]$ is the greatest integer less than or equal to $x$, is

The domain of the function $f(x)=\sin^{-1}(\sqrt{2-x})$ is