List of top Mathematics Questions asked in COMEDK UGET

If $y =\frac{\sec x +\tan x}{\sec x - \tan x} $ , then $\frac{dy}{dx} = $
The surface area of a ball is increasing at the rate of $2 \pi \, s cm/sec$. The rate at which the radius is increasing when the surface area is $16 \pi \, s cm$ is
Let [ ?] denote the greatest integer function and $f (x) = [\tan^2 x]$. Then
If $\cos^{-1} x +\cos^{-1} y +\cos^{-1}z = 3\pi $, then $xy + yz + zx$ is
The sum of all the positive divisors less than $250$ of the number $484$ is
$\lim_{x\to\infty} x^{\frac{1}{x}} = $
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 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
$ \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 $^nC_1 + 2\, ^nC_2 + .... + n\, ^nC_n = 2n^2$, then $ n = $
The digit in the unit place of $2009! + 3^{7886}$ is
$ \sin^2 5^{\circ} + \sin^2 10^{\circ} + \sin^2 15^{\circ} +....+ \sin^2 90^{\circ} $ =
If $|\vec{a} | = 15 , |\vec{b} | = 12$ and $|\vec{a} + \vec{b} | = 20 $ then $|\vec{a} - \vec{b} | = $
$ \frac{1 -\tan^2 15^\circ}{1 + \tan^2 15^\circ} = $
If $\log y= m \tan^{-1} x,$ then
The slopes of the tangent and normal at $(0, 1)$ for the curve $y = \sin x + e^x$ are respectively
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} = $
Let $y' = e^{-2x} $ and $ y = 0$ when $x =e$. Then the value of $x$ when $ y =\frac{1}{2}$ is
The area bounded by the curve $y = \sin x$ between $x = 0$ and $x = 2\pi $ given by
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