List of top Mathematics Questions

The amplitude of $\sin \frac{\pi}{5} + i\left( 1 - \cos \frac{\pi}{5}\right) $
The angle between the asymptotes of the hyperbola $x^2 - 3y^2 = 12$ is
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 the medians $AD$ and $BE$ of the triangle with vertices $A(0, b), B(0, 0), C(a, 0)$ are mutually perpendicular, then
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 $A, B, C, D$ are four points and $\vec{AB} = \vec{DC}$ , then $\vec{AC} + \vec{BD} = $
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
$Sin^2 \; 17.5^{\circ} + Sin^2 \; 72.5^{\circ}$ is equal to
The value of $\int \frac{x^2+1}{x^2-1}dx$ is
The value of $\int e^x(x^5+5x^4+1).dx $ is
If $x > 0$ and $\log_{3} x+\log_{3}\left(\sqrt{x}\right)+\log_{3}\left(\sqrt[4]{x}\right)+\log_{3}\sqrt[8]{x}+\log_{3}\left(\sqrt[16]{x}\right)+....=4,$ then x equals

The orthocentre of the triangle with vertices $O(0, 0), A(0,3/2)$ and $B(-5, 0)$ is

If $\frac {x^2}{36}-\frac{y^2} {k^2} = 1$ is a hyperbola, then which of the following statements can be true ?
If a and b are vectors such that $|a+b|=|a-b|$ then the angle between a and b is