List of top Mathematics Questions

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

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

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

The number of three digit numbers in which $9$ appears only in one place is

If the petrol burnt in driving a motor boat varies as the cube of the velocity, then the speed (in km hom ) of the boat going against a water flow of C kms hour so that the quantity of petrol burnt is minimum is

Let $z = x + iy$ and a point $P$ represent $z$ in the Argand plane. If the real part of $\frac{z - 1}{z + i}$ is 1. then a point that lies on the locus of $P$ is

If $z_{1} = 1 -2i ; z_{2} = 1 + i$ and $z_{3 } = 3 + 4i,$ then $ \left( \frac{1}{z_{1}} + \frac{3}{z_{2}}\right) \frac{z_{3}}{z_{2}} = $

If $1 , \omega , \omega^2$ are the cube roots of unity, then $\frac{1}{1+2\omega} + \frac{1}{2+\omega } - \frac{1}{1+\omega } = $

If A and B are the two real values of k for which the system of equations $x + 2y + z = 1,x + 3y + 4r = k.x + 5v + 10z = k^2 $ is consistent, then $A + B = $

The number of rational terms in the binomial expansion of $\left(\sqrt[4]{5} + \sqrt[5]{4}\right)^{100} $ is

If a circle touches the lines $3x - 4y - 10 = 0$ and $3x - 4y + 30 = 0$ and its centre lies on the line $x + 2y = 0$ then the equation of the equation of the circle is