List of top Mathematics Questions

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
If $\log (x + z) + \log (x - 2y + z) = 2 \log (x - z),$ then $ x, y, z$ are in
$\displaystyle\lim_{n\to\infty} \frac{1^{2}+2^{2} +...+n^{2}}{4n^{3}+6n^{2}-5n+1}=$
The modulus and amplitude of $\frac{ 1 + 2i}{1 - (1 - i)^2}$ are respectively
The derivative of $\sin x^{\circ} \, \, \cos x$ with respect to $x$ is
The angles $A, B$ and $C$ of a triangle $ABC$ are in A.P. If $b : c =\sqrt {3} : \sqrt {2}$ then the angle $A$ is
If $n$ is a non-negative integer and $A = \begin{bmatrix}1&0\\ 1&1\end{bmatrix} $ , then $A^n = $
$R $ is a relation on $N$ given by $R =\{(x, y ) | 4x +3y = 20\}$. Which of the following belongs to $R$ ?
$\begin{bmatrix}0&a\\ b&0\end{bmatrix}^{^4}=I$, then
A spherical balloon is expanding. If the radius is increasing at the rate of $2$ centimeters per minute, the rate at which the volume increases (in cubic centimeters per minute) when the radius is $5$ centimetres is
If the $m^{th}$ term and the nth term of an $AP$ are respectively $\frac{1}{n}$ and $\frac{1}{m}$, then the $(mn )^{th}$ term of the $AP$ is
The coefficient of $ x^{-10}$ in $\left(x^{2} - \frac{1}{x^{3}}\right)^{10}$ is
The value of $\left(1-\omega+\omega^{2}\right)^{5} + \left(1+\omega -\omega^{2}\right)^{5}, $ where $\omega$ and $\omega^2$ are the complex cube roots of unity, is
The number of ways four boys can be seated around a round-table in four chairs of different colours is
The function $f(x ) = xe^{1-x}$ is
Area enclosed by the curve $\pi\left[4\left(x-\sqrt{2}\right)^{2} +y^{2}\right]=8$ is