List of top Mathematics Questions asked in COMEDK UGET

In the group $\{1, 2, 3, 4, 5, 6\}$ under multiplication mod $7, 2^{-1} \times 4 =$
The argument of the complex number $\sin\left(\frac{6\pi}{5}\right) + i\left(1 +\cos \frac{6\pi}{5}\right) $ is
If $A= \begin{bmatrix}1&2\\ 0&1\end{bmatrix} $, then $A^n$ is
The number of distinct real roots of $\begin{vmatrix}\sin x&\cos x&\cos x\\ \cos x&\sin x&\cos x\\ \cos x &\cos x&\sin x\end{vmatrix}$ in the interval $ \left[\frac{-\pi}{4}, \frac{\pi}{4}\right] $ is
$\displaystyle\lim_{n\to\infty} \frac{\left(1^{2} +2^{2} + ....+n^{2}\right) \sqrt[n]{n}}{ \left(n+1\right)\left(n+10\right)\left(n+100\right)} = $
The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is
The volume of the tetrahedron formed by the points $(1, 1, 1 ), (2, 1, 3), (3, 2, 2)$ and $(3, 3, 4)$ in cubic units is
The value of $\left(0.2\right)^{\log_{\sqrt{5}}\left(\frac{1}{4} + \frac{1}{8} + \frac{1}{6} + .... to \, \infty\right)}$
$\int \frac{x^{2}+1}{x^{4}+1}dx $
$\int e^{x} \left\{\frac{1+\sin x \cos x}{\cos^{2} x}\right\} dx = $
If $\tan A - \tan B = x$ and $\cot B - \cot A = y$, then $\cot (A- B) =$
The subtangent at $x = \pi /2$ on the curve $y = x \sin x$ is
The maximum value of $\left(\frac{1}{x}\right)^{2x^2}$ is
Let $x$ be a number which exceeds its square by the greatest possible quantity, then $x$ =
If $y =\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y}}}} +.....$ then $ \frac{dy}{dx} $
The function $f\left(x\right) = \left(\frac{\log_{e}\left(1+ax\right) - \log_{e}\left(1-bx\right)}{x}\right)$ is undefined at $x = 0$. The value which should be assigned to $f$ at $x = 0$ so that it is continuous at $x = 0$ is
Which of the following functions is differentiable at $x = 0$ ?
If $x= a\left(\cos t+\log \tan \frac{t}{2}\right), y = a \sin t, $ then $ \frac{dy}{dx} $
If $C$ is the centre of the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1 $ and S is one of the foci, then the ratio of CS to semi-minor axis of the ellipse is
$\int \frac{2^{x+1} - 5^{x-1}}{10^{x}}dx = $
If a set $A$ has $n$ elements, then the number of relations on $A$ is
The acute angle between the hour hand and minute hand of a clock when the time is $5\, hours$ and $40\, minute$ is
If $\int \frac{1}{x+x^{5}}dx =f\left(x\right)+c , $ then $\int \frac{x^{4}}{x+x^{5}} dx = $
If $\vec{a} = \hat{i} + \lambda \hat{j} + 2 \hat{k}$ and $\vec{b} = \mu \hat{i} + \lambda \hat{j} + 2 \hat{k}$ are orthogonal and if $|\vec{a} | = |\vec{b}|$, then $(\lambda, \mu)$ =
If $\vec{a} , \vec{b} ,\vec{c}$ are unit vectors and $\theta$ is the angle between them, then $| \vec{a} - \vec{b}| = $