List of top Mathematics Questions asked in COMEDK UGET

If $f\left(x\right)= \cos^{-1} \left(\frac{1-\left(\log _{e} x\right)^{2}}{1+\left(\log _{e} x\right)^{2}}\right)$ , then $ f'\left(\frac{1}{e}\right) =$
The value of $\int \frac{10^{x/2}}{\sqrt{10^{-x} - 10^{x}}}dx$ is
$\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} \cos^2 \frac{5 \pi}{12} = $
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 $\alpha , \beta , \gamma$ are the roots of the equation $x^3 + px + q = 0$, then the value of the determinant $\begin{vmatrix}\alpha&\beta&\gamma\\ \beta&\gamma&\alpha\\ \gamma&\alpha&\beta\end{vmatrix} = $
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
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
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 $x$ =
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} $
$\int \frac{2^{x+1} - 5^{x-1}}{10^{x}}dx = $
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 $(\lambda, \mu)$ =