List of top Mathematics Questions asked in COMEDK UGET

The area of the parallelogram with $\vec{a}$ and $\vec{b}$ as adjacent sides is $20\, s \,units$. Then the area of the parallelogram having $7\vec{a} + 5\vec{b}$ and $8\vec{a} + 11\vec{b}$ as adjacent sides is
If the area of a circle increases at a uniform rate, then its perimeter varies
If $A = \begin{bmatrix}3&2\\ 4&5\end{bmatrix} $ and $AC = \begin{bmatrix}19&24\\ 37&46\end{bmatrix}$ then $C= $
$\int \frac{e^{x} \left(1 +\sin x\right)}{1+\cos x}dx= $
The length of the subtangent to the curv $x^2y^2 = a^4$ at $(-a, a)$ is
If the eccentricity of a hyperbola is 5/3, then the eccentricity of its conjugate is
The point of contact of the tangent $x + 2y + 2 = 0$ with the parabola $x^2 = 16y$ is
$\sin10^{\circ} +\sin 20^{\circ }+\sin 30^{\circ }+...+\sin360^{\circ } =$
$ \int\limits_0^{\pi /8} \tan^2 (2x) dx = $
$\tan^{-1} \left(\frac{1}{x+y} \right) +\tan ^{-1}\left(\frac{y}{x^{2} +xy +1}\right)= $
$\int\limits_{-1/2}^{1/2} \cos x\log\left(\frac{1+x}{1-x}\right) dx = $
In $Z$, the set of all integers, the inverse of $-7$ with respect to $*$ defined by $a * b = a + b + 7$ for all $a, b \in Z$ is
In $Z_7 - \{0\}$ under multiplication mod $7$, if $2^{-1} y \,3^{-1} = 5^{-1}$, then $y =$
If $\log y= m \tan^{-1} x,$ then
If $x= a\left(\cos \theta +\theta \sin \theta\right)$ and $ y = a \left(\sin \theta- \theta \cos \theta \right) $ where $0 < \theta < \frac{\pi}{2}$ , then $ \frac{d^{2}y}{dx^{2}}$ at $ \theta = \frac{\pi}{4}$ is equal to
The digit in the unit place of $2009! + 3^{7886}$ is
In the group $\{1, 2, 3, 4, 5, 6\}$ under multiplication modulo $7$, if $5x = 4$, then $x =$
The area bounded by the curve $y = \sin x$ between $x = 0$ and $x = 2\pi $ given by
Let $y' = e^{-2x} $ and $ y = 0$ when $x =e$. Then the value of $x$ when $ y =\frac{1}{2}$ is
If $f\left(9\right)= 9 , f'\left(9\right) = 4 $ then $\lim_{x\to9} \frac{\sqrt{f\left(x\right)} -3}{\sqrt{x} - 3} = $
If $a, b, c$ are in A.P., then $7^a, 7^b,$ and $7^c$ are in
$\displaystyle\lim_{x \to 0} \frac{6^{x} -3^{x} -2^{ x}+1}{x^{2}} = $
The locus of the centre of the circle of radius 3 which rolls on the outside of the circle $x^2+y^2 + 3x - 6y - 9 = 0$ is
$ \frac{1 -\tan^2 15^\circ}{1 + \tan^2 15^\circ} = $
The contrapositive of the statement "If $x^2 - 1 = 0$, then $x = -1$ or $x = + 1$ " is