List of top Mathematics Questions asked in COMEDK UGET

If $\frac{2}{9!} + \frac{2}{3! \,7!}+\frac{1}{5! \,5!} =\frac{2^{a}}{b!}$ where $a,b \in \, N$ then theordered pair $(a, b)$ is
$\displaystyle\lim_{x\to0} \left(\frac{1+5x^{2}}{1+3x^{2}}\right)^{\frac{1}{x^{2}}} = $
The multiplicative inverse of $ \frac{3 + 4i}{4 - 5 i}$ is
Identify the false statement
In the group $G = \{1, 5, 7, 11\}$ under $\otimes_{12}$ the value of $7 \otimes_{12} 11^{-1}$ is equal to
The parametric equation of a parabola is $x = t^2 + 1, y = 2t + 1$. The cartesian equation of its directrix is
If $ \int \frac{xe^{x}}{\left(1+x\right)^{2}} dx = e^{x} f\left(x\right) +c, $ then $f(x)$ is equal to
If $x= \frac{1-t}{1+t} ; y= \frac{2t}{1+t}, $ then $\frac{d^{2}y}{dx^{2}} = $
If $f(x) = \begin{cases} \frac{e^{3x} - 1}{4x} & \quad \text{for} x \neq 0 \\ \frac{k + x}{4} & \quad \text{for } x= 0 \end{cases}$ is continuous at $x = 0$, then $k =$
If the tangent to the curve $2y^3 = ax^2 + x^3$ at the point $(a, a)$ cuts off intercepts $\alpha$ and $\beta$ on the coordinate axes where $\alpha^2 + \beta^2 = 61$, then the value of $a$ is
Lengthof the subtangent at $(a, a)$ on the curve $y^2 = \frac{x^2}{2a +x}$ is equal to
If $\sqrt{\frac{x}{y}} + \sqrt{ \frac{y}{x}} = \sqrt{a}$ , then $ \frac{dy}{dx} = $
If $y=\log \tan\left(\frac{\pi}{4} + \frac{x}{2}\right) ,$ then $ \frac{dy}{dx} = $
If $|\vec{a} | = 2 , |\vec{b}| = 7$ and $\vec{a} \times \vec{b} = 3 \hat{i} + 2 \hat{j} + 6\hat{k}$ then the angle between $\vec{a}$ and $\vec{b}$ is
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
$\int \frac{e^{x} \left(1 +\sin x\right)}{1+\cos x}dx= $
If $f\left(x\right) = \frac{x^{2} -1}{x^{2} +1} ,x\in R$ then the minimum value of $f$ 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} = $
$1 + 3 + 5 + 7 + ... + 29 + 30 +31 + 32 + ... + 60 =$
$\frac{1}{\sin\theta}- \frac{\sqrt{3}}{\cos \theta}=$
The length of the subtangent to the curv $x^2y^2 = a^4$ at $(-a, a)$ is
If $A = \begin{bmatrix}3&2\\ 4&5\end{bmatrix} $ and $AC = \begin{bmatrix}19&24\\ 37&46\end{bmatrix}$ then $C= $
$\sin10^{\circ} +\sin 20^{\circ }+\sin 30^{\circ }+...+\sin360^{\circ } =$