List of top Mathematics Questions

The number of solutions of $\sin \, x + \sin \, 3x + \sin \, 5x = 0$ in the interval $\left[\frac{\pi}{2} , 3 \frac{\pi}{2}\right] $ is

Matrix $A = \begin{bmatrix}1&2&3\\ 1&1&5\\ 2&4&7\end{bmatrix}$then the value of $a_{31} A_{31} + a_{32} A_{32} + a_{33 } + A_{33} $ is

The sum of odd integers from $1$ to $2001$ is

Let $f : \bullet \to \bullet $ satisfy $f (x) f ( y) = f (xy) $ for all real numbers $x$ and $y$. If $f (2)= 4$, then $f \left( \frac{1}{2} \right) = $

The focus of the parabola $y^2 - 4y - x+3=0$ is

The focus of the parabola $( y + 1)^2 = -8(x +2)$ is

Eccentricity of the ellipse $4x^2 + y^2 -8x + 4y -8= 0$ is

Let $f (x) = px^2 + qx + r$ , where $p, q, r$ are constants and $p \neq 0$ . If $f (5) = -3 f (2)$ and $f (-4) = 0$ , then the other root of $f$ is

Everybody in a room shakes hands with everybody else. The total number of handshakes is 45. The total number of persons in the room is

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