List of top Mathematics Questions

If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\int\limits^{{2}}_{{0}}x^2 [x] dx$

If the matrix $A=\begin{pmatrix}2&0&0\\ 0&2&0\\ 2&0&2\end{pmatrix},$ then $A^{n}=\begin{pmatrix}a&0&0\\ 0&a&0\\ b&0&a\end{pmatrix}, n\,\in\,N$ where

For non-zero vectors $\vec{a} $ and $\vec{b} $ if $\left|\vec{a}+\vec{b}\right|

The letters of the word COCHIN are permuted and all permutation are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is

The value of $\sin^{-1}\left ( \cos\, \frac { 53 \pi}{5}\right)$ is

The derivative of $y = x^{\sin\,x}$ is

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

Value of $\left[\left(\log_{b}\,a\right)\left(\log_{c}\,b\right)\left(\log_{a}\,c\right)\right]$ is

$\sin^{2}\,\theta\, \cos^{3}\,\theta-\sin^{4}\,\theta\, \cos\,\theta$ is equal

$\log_3\,2, \log_6\,2, \log_{12}\,2$ are in

Let $ P $ and $ Q $ be any two points on the curve $ x=acos\theta $ , $ y=bsin\theta $ , where $ a > \, b, 0 \le \,\theta

If $r.v. X \sim B \left(n = 5, P=\frac{1}{3}\right)$ then $P(2 < X < 4) =$ ______________

General solution of $y \frac{dy}{dx}+by^{2}=a\,cos\,x, 0 < x< 1$ is

If function $f(x) = \begin{cases} x\, \sin\left(\frac{1}{x} \right) ; & \text{x $\ne$ 0} \\[2ex] a \,;& \text{x = 0} \end{cases}$ is continuous at $x = 0$, then value of $a$ is

The tangents to curve $y=x^{3}-2x^2+x-2$ which are parallel to straight line $y = x$ are

The Solution of the differential equation $\left(x+2y^{3}\right) \frac{dy}{dx}=y$ is

Value of the following expression is $\displaystyle \lim_{n \to \infty}$$\frac{1}{n^{3}}\left(1^{2}+2^{2}+3^{2}+ ..... +n^{2}\right)$

Two vectors $A = 3$ and $B = 4$ are perpendicular. Resultant of both these vectors is $R$. The projection of the vector $B$ on the vector $R$ is

A normal is drawn at a point $(x_1, y_1)$ of the parabola $y^2 = 16x$ and this normal makes equal angle with both $x$ and $y$ axes. Then point $(x_1, y_1)$ is

The Solution of the differential equation $\frac{dy}{dx}=2e^{x-y}+x^{2}e^{-y}$ is

Four men and three women are standing in a line for railway ticket. The probability of standing them in alternate manner is

The value of cos $15^{\circ}\, cos 7 \frac{1^{\circ}}{2}\, sin 7 \frac{1^{\circ}}{2}$ is

If the equation $x^2 + y^2 -10x + 21 = 0$ has real roots $x = a$ and $y=\beta$ then

If $r. v. x :$ waiting time in minutes for bus and $p.d.f.$ of $x$ is given by $f(x) = \begin{cases} \frac{1}{5} , & 0\le x\le5 \\[2ex] 0, & \text{otherwise} \end{cases}$ then probability of waiting time not more than $4$ minutes is = _______