List of top Mathematics Questions

If A and B are mutually exclusive events , given that $P(A) = \frac{3}{5} , P(B) = \frac{1}{5}$, then P(A or B) is

The distance between the foci of a hyperbola is 16 and its eccentricity is $\sqrt{2}$. Its equation is

The angle between the lines $2x = 3y = - z$ and $6x = - y = - 4z$ is

Which of the following is the equation of a hyperbola?

The feasible region of an LPP is shown in the figure . If $z = 3x + 9y ,$ then the minimum value of z occurs at

A die is thrown four times. The probability of getting perfect square in at least one throw is

For the probability distribution given by $X=x_{i}$ 0 1 2 $p_{i}$ $\frac{25}{36}$ $\frac{5}{18}$ $\frac{1}{36}$ the standard deviation $(\sigma)$ is

The maximum value of $2x + y$ subject to $3x + 5y \leq 26$ and $5x + 3y \leq 30, x \geq 0, y \geq 0$ is

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 $x + 2y \leq 2, x +2 y \ge 8, x, y \ge 0$