List of top Mathematics Questions

Given $ tan\text{ }A $ and $ tan\text{ B} $ are the roots of $ {{x}^{2}}-ax+b=0 $ . The value of $ {{\sin }^{2}}(A+B) $ is

The probability of choosing a number divisible by $6$ or $8$ from among $1$ to $90$ is

On the set $N$ of all natural numbers define the relation $R$ by $a R b$ if and only if the $G.C.D.$ of $a$ and $b$ is $2$, then $R$ is

When three dice are thrown the probability of getting a $4$ or $5$ so on each of the dice simultaneously is

The condition that the roots of the equation $ {{x}^{3}}+3p{{x}^{2}}+3qx+r=0 $ are in the Arithmetic Progression is:

If a line makes angles $ \frac{\pi }{3} $ and $ \frac{\pi }{4} $ with the $x$ and $y$-axis respectively, then the angle made by the line and $Z$-axis is

If the circles $x^2 + y^2 - 2x - 2y - 7 = 0$ and $x^2 + y^2 + 4x + 2y + k = 0$ cut orthogenally, then the length of the common chord of the circles is

If $A =\begin{bmatrix} {1}&{-1} &{1}\\ {2}&{1}& {-3} \\ {1}&{1}&{1}\\ \end{bmatrix} ,10B \begin{bmatrix} {4}&{2} &{2}\\ {-5}&{0}& {\alpha} \\ {1}&{-2}&{3}\\ \end{bmatrix} $ and $B$ is the inverse of $A$, then the value of $\alpha$ is

The number of common tangents to the circles $x^2+y^2=4 $ and $ x^2+y^2-6x-8y-24=0 $ is

The $ x- $ axis, $ y- $ axis and a line passing through the point A (6, 0) form a triangle $ABC$. If $ \angle A=30{}^\circ , $ then the area of the triangle, in sunits is

The conjugate of the complex number $ \frac {(1+i)^2}{1-i}$ is

The area enclosed by the pair of lines $xy = 0$ , the line $x - 4 = 0$ and $y + 5 = 0$ is

The equation of the plane passing through the points $ (a,0,0),(0,b,0) $ and $ (0,0,c) $ is

The angle between the asymptotes of the hyperbola $x^2 - 3y^2 = 12$ is

The amplitude of $\sin \frac{\pi}{5} + i\left( 1 - \cos \frac{\pi}{5}\right) $

A set $A$ has $5$ elements. Then the maximum number of relations on $A$ (including empty relation) is

If $a= 5, b = 13 , c = 12$ in $\Delta ABC$, then $\tan \frac{B}{4}$ is

The derivative of $\cos^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) $ with respect to $\cot^{-1} \left(\frac{1-3x^{2}}{3x-x^{3}}\right)$ is

The function $f(x) = \begin{cases} x^2 & \quad \text{for } x < 1\\ 2 - x & \quad \text{for } x \geq 1 \end{cases}$ is

The maximum value of $ f(x) = \frac{\log x}{x} , 0 < x < \infty$ is

The vectors $\vec{a} = x \hat{i} + (x +1) \hat{j} + ( x +2 ) \hat{k} $ $\vec{b} = (x + 3) \hat{i} + (x +4) \hat{j} + ( x + 5 ) \hat{k} $ , and $\vec{c} = (x + 6) \hat{i} + (x + 7 ) \hat{j} + ( x + 8) \hat{k} $ are co-planar for

The value of $[ \vec{a} - \vec{b} \,\,\,\,\,\, \vec{b} - \vec{c} \,\,\,\,\,\, \vec{c} - \vec{a} ]$ where $|\vec{a}| = 1 , |\vec{b} | = 5 , |\vec{c}| = 3 $

If $x^y = \log x$ , then $\frac{dy}{dx} $ at the point where the curve cuts the $x-axis$ is

If $y = \tan^{-1} ( \sec x - \tan x) $, then $ \frac{dy}{dx} = $