List of top Mathematics Questions asked in COMEDK UGET

$\lim_{x\to0} \frac{\tan x -\sin x}{x^{3}} = $
If $y =\left(1+x\right)\left(1+x^{2}\right) ....\left(1+x^{100}\right),$ then $\frac{dx}{dy} $ at $x = 0$ is
If $\log (x + z) + \log (x - 2y + z) = 2 \log (x - z),$ then $ x, y, z$ are in
$\displaystyle\lim_{n\to\infty} \frac{1^{2}+2^{2} +...+n^{2}}{4n^{3}+6n^{2}-5n+1}=$
The modulus and amplitude of $\frac{ 1 + 2i}{1 - (1 - i)^2}$ are respectively
The derivative of $\sin x^{\circ} \, \, \cos x$ with respect to $x$ is
If $n$ is a non-negative integer and $A = \begin{bmatrix}1&0\\ 1&1\end{bmatrix} $ , then $A^n = $
The value of $x$ for which $f(x) = x^3 - 6x^2 - 36x + 7 $ is increasing, belong to
If $ y =\sin^{-1} \left(\frac{5x+12 \sqrt{1 -x^{2}}}{13}\right)$ , then $ \frac{dy}{dx} = $
The value of $\tan^{-1} \frac{\sqrt{2+\sqrt{3}} -\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3} } +\sqrt{2-\sqrt{3}}} $
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 $f(0)$ =
A set $A$ has $5$ elements. Then the maximum number of relations on $A$ (including empty relation) is
If $x^y = \log x$ , then $\frac{dy}{dx} $ at the point where the curve cuts the $x-axis$ 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 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
If $A, B, C, D$ are four points and $\vec{AB} = \vec{DC}$ , then $\vec{AC} + \vec{BD} = $
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 $a= 5, b = 13 , c = 12$ in $\Delta ABC$, then $\tan \frac{B}{4}$ is
If $y = \tan^{-1} ( \sec x - \tan x) $, then $ \frac{dy}{dx} = $
If $\sqrt{1-x^{2} } + \sqrt{1- y^{2}} =x -y $, then $\frac{dy}{dx} = $