List of top Mathematics Questions asked in COMEDK UGET

The perpendicular distance between the lines $9x^2- 24xy + 16y^2 + 21x- 28y+ 10 = 0$ is
The length of the latus rectum of the parabola $bx^2 - 4ay + dx + e = 0$ is
If $^nC_1 + 2\, ^nC_2 + .... + n\, ^nC_n = 2n^2$, then $ n = $
If $|\vec{a} | = 15 , |\vec{b} | = 12$ and $|\vec{a} + \vec{b} | = 20 $ then $|\vec{a} - \vec{b} | = $
$ \sin^2 5^{\circ} + \sin^2 10^{\circ} + \sin^2 15^{\circ} +....+ \sin^2 90^{\circ} $ =
If $Z$ is a complex number with $I Z I = 1$ and $Z + \frac{1}{Z} = x + iy$, then $xy = $
The slopes of the tangent and normal at $(0, 1)$ for the curve $y = \sin x + e^x$ are respectively
$\int\limits_{1}^{e^{\frac{17}{2}}} \frac{\, \pi \cos (\pi \log x)}{x} dx =$
If $\frac{1}{2} \leq x \leq 1, $ then $\cos^{-1} x +\cos ^{-1}\left(\frac{x}{2} +\frac{\sqrt{3-3x^{2}}}{2}\right) =$
A stone is thrown up vertically and the height $'x'$ ft reached by it in time $'t'$ secs is given by $x = 80t - 16t^2$ . The stone reaches the maximum height in time ?
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) =$
If for the curve $y = 1 + bx - x^2$, the tangent at $(1 - 2)$ is parallel to $x$-axis, then $b =$
The value of $\int \frac{10^{x/2}}{\sqrt{10^{-x} - 10^{x}}}dx$ is
In the group $\{1, 2, 3, 4, 5, 6\}$ under multiplication mod $7, 2^{-1} \times 4 =$
$\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} \cos^2 \frac{5 \pi}{12} = $
The argument of the complex number $\sin\left(\frac{6\pi}{5}\right) + i\left(1 +\cos \frac{6\pi}{5}\right) $ 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
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
$\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 = $