List of top Mathematics Questions

$ 3a{{\int_{0}^{1}{\left( \frac{ax-1}{a-1} \right)}}^{2}}\,\,dx $ is equal to
The number of solutions of $ \sin x=\sin 2x $ between $ \frac{-\pi }{2} $ and $ \frac{\pi }{2} $ is
If $A$ is a square matrix. $A'$ its transpose, then $ \frac{1}{2}(A-A') $ is
The foot of the perpendicular from $ (2,4,-1) $ to the line $ x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6) $
If $p^{th}$ term of an arithmetic progression is $q$ and the $q^{th}$ term is $p$, then $10^{th}$ term is
If $ y={{\sec }^{-1}}\left( \frac{1}{\sqrt{1-{{x}^{2}}}} \right), $ then $ \frac{dy}{dx} $ is equal to
If $ \alpha ,\beta $ are the roots of the equation $ {{x}^{2}}+ax+b=0, $ then $ \frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}} $ is equal to
The distance between the planes $ 2x-2y+z+3=0 $ and $ 4x-4y+2z+5=0 $ is
If $ |a|<1, $ then $ 1+2a+3{{a}^{2}}+4{{a}^{3}}+..... $ is equal to
$ \left| \begin{matrix} 1 & x & y+z \\ 1 & y & z+x \\ 1 & z & x+y \\ \end{matrix} \right| $ is equal to
The standard deviation of the first n natural numbers is
$ \frac{1}{3!}+\frac{2}{5!}+\frac{3}{7!}+... $ is equal to
The standard deviation for the scores $1, 2, 3, 4, 5, 6$ and $7$ is $2$. Then, the standard deviation of $12, 23, 34, 45, 56, 67$ and $78$ is
The maximum value of $\frac{Log \, x}{x} $ in $(2, \infty)$ is
If $Log_{10}7=0.8451$ then the position of the first significant figure of $7^{-20}$ is
A unit vector perpendicular to both the vectors $\hat {i} +\hat { j} $ and $ \hat {j} +\hat {k}$ is
If $\vec{a} $ and $\vec{b}$ are unit vectors and $|\vec{a} + \vec{b}|=1$ then $|\vec{a} -\vec{b}|$ is equal to
The acute angle between the hour hand and minute hand of a clock when the time is $5\, hours$ and $40\, minute$ is
If $\int \frac{1}{x+x^{5}}dx =f\left(x\right)+c , $ then $\int \frac{x^{4}}{x+x^{5}} dx = $
If $\vec{a} = \hat{i} + \lambda \hat{j} + 2 \hat{k}$ and $\vec{b} = \mu \hat{i} + \lambda \hat{j} + 2 \hat{k}$ are orthogonal and if $|\vec{a} | = |\vec{b}|$, then $(\lambda, \mu)$ =
If $\vec{a} , \vec{b} ,\vec{c}$ are unit vectors and $\theta$ is the angle between them, then $| \vec{a} - \vec{b}| = $
$\lim_{x\to0} \frac{\tan x -\sin x}{x^{3}} = $
If $y =\left(1+x\right)\left(1+x^{2}\right) ....\left(1+x^{100}\right),$ then $\frac{dx}{dy} $ at $x = 0$ is
If a set $A$ has $n$ elements, then the number of relations on $A$ is
If $C$ is the centre of the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1 $ and S is one of the foci, then the ratio of CS to semi-minor axis of the ellipse is