List of top Mathematics Questions asked in COMEDK UGET

If $[x]$ denotes the greatest integer function, then $\int\limits_{1}^{4} \left(\left[x\right] -1\right)\left(\left[x\right] -2\right)\left(\left[x\right] -3\right)\left(\left[x\right] -4\right)dx = $
If $\log_2 \: \sin x - \log_2 \cos x -\log_2(1 - \tan^2x) = - 1$, then
If $u = f(x^2) , v = g(x^3) , f'(x) = \sin x $ and $g'(x) = \cos x,$ then $ \frac{du}{dv} = $
If $x= 3 \cos t - 2 \cos^{3} t , y = 3\sin t - 2 \sin^{3} t ,$ then $ \frac{d^{2}y}{dx^{2}} t = \frac{\pi}{6}$ is
If $\tan^{-1} \left(\frac{x}{y}\right) + \log \sqrt{x^{2} +y^{2}} = 0 $ , then $\frac{dx}{dy} = $
Let $f\left(x\right) = \frac{\log\left(1+ex\right)-\log\left(1-x\right)}{x} , x\ne0 $ . Then $f$ is continuous at $x = 0$ if $f(0)$ =
If $\sqrt{1-x^{2} } + \sqrt{1- y^{2}} =x -y $, then $\frac{dy}{dx} = $
A particular solution of $ \frac{dy}{dx} = (x+9y)^2$ when $ x = 0, y = \frac{1}{27}$ is
A set $A$ has $5$ elements. Then the maximum number of relations on $A$ (including empty relation) 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) $
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 $a$ 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 $x^y = \log x$ , 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 $A, B, C, D$ are four points and $\vec{AB} = \vec{DC}$ , then $\vec{AC} + \vec{BD} = $
$\tan\left[\frac{1}{2} \sin^{-1} \left(\frac{2x}{1+x^{2}}\right) + \frac{1}{2} \cos^{-1} \left(\frac{1-x^{2}}{1+x^{2}}\right)\right] = $
If $x = \log_a bc, y = \log_b ca, z = \log_c ab,$ then $\frac{x}{1+x} + \frac{y}{1+y} + \frac{z}{1+z } = $