List of top Mathematics Questions

The sides of a rectangle are given by $x = \pm \, a$ and $y = \pm \, b$. The equation of the circle passing through the vertices of the rectangle is

The sum of the four digit even numbers that can be formed with the digits 0,3,5,4 with out repetition is

The negation of the statement: "Getting above 95% marks is necessary condition for Hema to get the admission is good college"

If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 4x + 5 = 0$. then the quadratic equation whose roots are $\alpha^2 + \beta$ and $\alpha + \beta^2 $ is

If $\vec{a} , \vec{b} , \vec{c}$ are mutually perpendicular vectors having magnitudes 1, 2, 3 respectively, then $[\vec{a} + \vec{b} + \vec{c} \, \, \vec{b} - \vec{a} - \vec{c}] = ?$

If $2 \sin \left( \theta + \frac{\pi}{3}\right) = \cos \left( \theta -\frac{\pi}{6}\right) , $ then $\tan \, \theta = $

On $R$, a relation $\rho$ is defined by $x \rho y$ if and only if $x - y$ is zero or irrational. Then

The value of the integral $I = \int\limits^{2014}_{1/2014} \frac{\tan^{-1} x}{x} dx $ is

If $f : R \to R$ be defined by $f(x) = e^x $ and $g : R \to R $ be defined by $g(x) = x^2$. The mapping $g of : R \to R $ be defined by $(g o f ) (x) = g[f(x)] \forall x \in R$ , Then

If $z_1$ and $z_2$ be two non zero complex numbers such that $\frac{z_1 }{z_2 } + \frac{z_2}{z_1} = 1 $, then the origin and the points represented by $z_1$ and $z_2$

If $\int \, f(x) \, \sin \, x \, \cos \, x \, dx = \frac{1}{2(b^2 - a^2)} \log f(x) + c$, where c is the constant of integration , then f(x) =

Let $\vec{\alpha } = \hat{i} + \hat{j} + \hat{k} , \vec{\beta} = \hat{i} - \hat{j} - \hat{k}$ and $\vec{\gamma} = - \hat{i} + \hat{j} - \hat{k}$ be three vectors. A vector $\vec{\delta} $, in the plane of $\vec{\alpha}$ and $\vec{\beta}$, whose projection on $\vec{\gamma}$ is $\frac{1}{\sqrt{3}}$, is given by

On the set $R$ of real numbers, the relation $\rho$ is defined by $x \rho y, (x, y) \in R$

The approximate value of $\sin \, 31^{\circ}$ is

The value of $\displaystyle\lim_{n \to \infty} \frac{1}{n} \left\{ \sec^2 \frac{\pi}{4 n} + \sec^2 \frac{2 \pi }{4n} + ..... \sec^2 \frac{n \pi}{4n} \right\}$ is

For the LPP; maximise $z =x + 4y$ subject to the constraints $x + 2y \leq 2, x +2 y \ge 8, x, y \ge 0$

A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of 0.02 cm/s. The rate of increase of its volume when the radius is 10 cm is ___________$\pi$ cm/s

If $\sin^{-1} \,x + \cos^{-1} \,y = \frac{2 \pi}{5}$ , then $\cos^{-1} \,x + \sin^{-1}\, y$ is

The number of ways in which 5 girls and 3 boys can be seated in a row so the no two boys are together is

The value of $\displaystyle\lim_{x\to0} \frac{\left|x\right|}{x} $ is

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

If $|x + 5| \ge \,10 $ , then

Three players A, B and C play a game. The probability that A, B and C will finish the game are respectively $\frac{1}{2} , \frac{1}{3}$ and $\frac{1}{4}$ . The probability that the game is finished is