List of top Mathematics Questions asked in COMEDK UGET

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 function $f(x) = \begin{cases} x^2 & \quad \text{for } x < 1\\ 2 - x & \quad \text{for } x \geq 1 \end{cases}$ is
A particular solution of $ \frac{dy}{dx} = (x+9y)^2$ when $ x = 0, y = \frac{1}{27}$ is
The amplitude of $\sin \frac{\pi}{5} + i\left( 1 - \cos \frac{\pi}{5}\right) $
The angle between the asymptotes of the hyperbola $x^2 - 3y^2 = 12$ is
The maximum value of $ f(x) = \frac{\log x}{x} , 0 < x < \infty$ is
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 $a$ and $ b$ are positive integers such that $a^2 - b^2$ is a prime number, then $a^2 - b^2$ is
$\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 } = $
If $\sin(\theta + \alpha) = \cos(\theta + \alpha),$ then the value of $\frac{1 - \tan \alpha}{1+ \tan \alpha}$ is
If $ \sqrt{x} + \frac{1}{\sqrt{x}} = 2 \, \cos \theta $, then $x^6 + x^6 = $
The number of points at which $f(x) = 3 + 2\, \, \, \sin x$ has maximum in the interval $\left( - \frac{11 \pi}{2} , 100 \pi \right)$ is
The projection of $\vec{a} = 5\hat{i} - \hat{j} + 3 \hat{k}$ on $\vec{b} = 2 \hat{i} + \hat{j} - \hat{k}$ is
In a triangle $ABC$ if $\begin{vmatrix}1&a&b\\ 1&c&a\\ 1&b&c\end{vmatrix} = 0$, then $\sin^2 A + \sin^2 B + \sin^2 C = $
If the area of triangle formed by the points $(\alpha, 0), (0, 1)$ and $(-1, 0)$ is 20 s units, then $\alpha$ is
The area of the triangle whose vertices are $A = (1, -1, 2), B = (2, 1, -1)$ and $C = (3, -1, 2)$ is
The coordinates of the circumcentre of the triangle with vertices $(2, 3), (4, -1) $ and $ (4, 3) $ are
The number of positive divisors of 67375 which are greater than 5 is
The differential equation whose general solution is $Ax^2 + By^2 = 1$, where $A$ and $B$ are arbitrary constants is of ?
If $a, b, c$ are in G.P and $x^a = y^b = z^c$, then
A point on the curve $2y^3 + x^2 = 12y$ at which the tangent to the curve is vertical is
If $g$ is the inverse function of $f$ and $f'(x) = \frac{1}{ 1+x^n} $ , then the value of $g'(x)$ is
$\displaystyle\lim_{x \to \infty} \left( \frac{x+6}{x+1}\right)^{x+4} =$
If $y= \sin^{-1} (3^{-x})$, then $\frac{dy}{dx} = $