List of top Mathematics Questions asked in COMEDK UGET

Let $f (x)$ and $g(x)$ be differentiable functions on (0, 2] such that $f"(x) - g"(x) = 0, f'(1) = 2g'(1) = 4, f(2) = 3g(2) = 9.$ Then $f (x)- g(x)$ at $ x = 3/2$ is
If the area of a circle increases at a uniform rate, then its perimeter varies
If $x = 2y + 3$ is a focal chord of the ellipse with eccentricity 3/4, then the lengths of the major and minor axes are
$\begin{vmatrix}a&b&c&d\\ -a&b&c&d\\ -a&-b&c&d\\ -a&-b&-c&d\end{vmatrix} = $
$1 + 3 + 5 + 7 + ... + 29 + 30 +31 + 32 + ... + 60 =$
The length of the subtangent to the curv $x^2y^2 = a^4$ at $(-a, a)$ is
$\frac{1}{\sin\theta}- \frac{\sqrt{3}}{\cos \theta}=$
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
If $A = \begin{bmatrix}3&2\\ 4&5\end{bmatrix} $ and $AC = \begin{bmatrix}19&24\\ 37&46\end{bmatrix}$ then $C= $
$\sin10^{\circ} +\sin 20^{\circ }+\sin 30^{\circ }+...+\sin360^{\circ } =$
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 $y =$
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} $ =