List of top Mathematics Questions

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
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 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 $
The maximum value of $ f(x) = \frac{\log x}{x} , 0 < x < \infty$ is
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} = $
If $a$ and $ b$ are positive integers such that $a^2 - b^2$ is a prime number, then $a^2 - b^2$ is
Let $f(x) = \begin{cases} -2 \sin x, &x \leq - \pi /2 \\ a \sin x +b, & - \pi /2 < x < \pi /2 \\ \cos \, x , & x \geq \pi /2 \end{cases}$ then the? values of a and b so that $f(x)$ is continuous are
If the medians $AD$ and $BE$ of the triangle with vertices $A(0, b), B(0, 0), C(a, 0)$ are mutually perpendicular, then
If $A, B, C, D$ are four points and $\vec{AB} = \vec{DC}$ , then $\vec{AC} + \vec{BD} = $
$\frac{1+\tan ^{2} x}{1-\tan ^{2} x} d x$ is equal to
The ninth term of the expansion $\left(3x-\frac {1}{2x}\right)^8$ is
A vector perpendicular to the plane containing the points $A (1, -1, 2), B (2, 0, -1), C (0,2,1)$ is
The solution of $Tan^{-1}x+ 2cot^{-1}x=\frac {2\pi}{3}$ is