List of top Mathematics Questions

$20$ persons are invited for a party In how many different ways can they and the host be seated at circular table, if the two particular persons are to be seated on either side of the host?

What is the value of $\tan^{-1} \left(\frac{m}{n}\right) - \tan^{-1} \left(\frac{m-n}{m+n}\right) ? $

The number of positive integral solutions of the equation $\tan^{-1} x + \cot^{-1} y = \tan^{-1} 3 , $ is

The value of $\cos \left(\frac{1}{2} \cos^{-1} \frac{1}{8}\right) $ is equal to

In a $\Delta ABC$, if $A = tan^{-1}\, 2$ and $B = tan^{ -1}\, 3$ , then $C =$

$sin^{-1}\left(\frac{1}{\sqrt{e}}\right)> tan^{-1}\left(\frac{1}{\sqrt{\pi}}\right) $ $sin^{-1}\,x>tan^{-1}\,y$ for $x>y, \forall \,x, y \,\in\left(0, 1\right)$

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

$2^{\frac{1}{4}}, 4^{\frac{1}{8}}, 8^{\frac{1}{16}}, 16^{\frac{1}{32}}............ $ is equal to

If $x = a + b, y = a \omega +b \omega ^2$ and $z = a \omega^2 + b \omega$, then which one of the following is true.

If $b$ and $c$ are odd integers, then the equation $x^2 + bx + c = 0$ has

The principal value of the $arg (z)$ and $ | z |$ of the complex number $z=1+\cos\left(\frac{11\pi}{9}\right)+ i \, \sin\frac{11\pi}{9}$ are respectively

$\left(\frac{1}{1-2i} + \frac{3}{1+i}\right) \left(\frac{3+4i}{2-4i}\right)$ is equal to :

If $P$ is the affix of $z$ in the Argand diagram and $P$ moves so that $\frac{z-i}{z-1}$ is always purely imaginary, then locus of $z$ is

The value of $ \begin{vmatrix} b+c&a&a\\ b &c+a &b\\ c & c &a+b \end{vmatrix}$ is

If the three linear equations $x + 4ay + az = 0$ $x + 3 by + bz = 0$ and $x + 2cy + cz = 0$ have a non-trivial solution, then a, b, c are in

The matrix 'X' in the equation $AX = B$, such that $A = \begin{bmatrix}1&3\\ 0&1\end{bmatrix}$ and $ B = \begin{bmatrix}1&-1\\ 0&1\end{bmatrix}$ is given by

The only integral root of the equation $ \begin{vmatrix} 2-y &2&3\\ 2 &5-y &6\\ 3 & 4 & 10-y \end{vmatrix}$=0 is

$B$ is an extremity of the minor axis of an ellipse whose foci are $S$ and $S'$. If $?SBS'$ is a right angle, then the eccentricity of the ellipse is

Which of the following functions are one-one and onto ?

The value of $ \frac{\cos 30{}^\circ +i\sin 30{}^\circ }{\cos 60{}^\circ -i\sin 60{}^\circ } $ is equal to

Let $S(n)$ denote the sum of the digits of a positive integer n. e.g. $S(178)=1+$ $7+8=16 .$ Then, the value of $S(1)+S(2)+S(3)+\ldots+S(99)$ is

$ \int{(x+1){{(x+2)}^{7}}}(x+3)dx $ is equal to

$ \int{\frac{\sec x cosec x}{2\cot x-\sec x\cos ecx}}dx $ is equal to