List of top Mathematics Questions asked in COMEDK UGET

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

If $y= \sin^{-1} (3^{-x})$, then $\frac{dy}{dx} = $

If $ f(x) = x^m$, where $m$ is a positive integer then the value of $m$ for which $f'(\alpha + \beta) = f'(\alpha ) + f'(\beta)$ for all $ \alpha , \beta > 0$ is

The points of discontinuities of $f(x) = \left(\frac{\pi x}{x+1} \right)$ other than $x = -1$ are

$f(x) = \begin{cases} x , \text{if } x \text{ is rational}\\ 0, \text{if } x \text{ is rational} \end{cases}$ then $f$ is

If $\lambda_1 , \lambda_2$ and $\lambda_3$ are the eigen values (i.e. characteristic values) of the matrix $\begin{vmatrix}1&2&15\\ 3&4&11\\ 5&6&7\end{vmatrix}$ then $ \left(1 -\lambda_{1}\right)\left(1+\lambda _{2}\right)\left(1+\lambda _{3}\right)$ equals

If $p, q , r$ are the roots of the equation $\begin{vmatrix}x&1&2\\ 1&x&2\\ 1&2&x\end{vmatrix} = 0$ , then $\frac{p^{4} +q^{4}+r^{4}}{p^{2}+q^{2} +r^{2}}$ is equal to

Define $f (x) = min{x^2 + 1, x + 1]$ for.$x e\in R$. Then $ \int\limits_{-1}^1f (x)dx $ is

The value of the integral $\int\limits_{0}^{\pi/ 4} \frac{1+\sin^{2} }{ \cos^{3} x} dx $ is

If $A$ is a square matrix.such that $A^3 = 0$, then $(I + A)^{-1}$ is

If $n$ is a positive integer which is relatively prime to $6,$ and if $n$ has $8$ divisors, then $12n$ has

If $\sin(\pi \cos \theta) = \cos(\pi \sin \theta),$ then $\sin 2 \theta$ equals

The shortest distance from the point $(3, 0)$ to the parabola $y = x^2$ is.

If $x$ and $y$ are two real numbers such that $x + y = 1$ and $x^3 + y^3 = 4,$ then $x^5 + y^5$ is

Of all open tanks in the form of a rectangular parallelopiped with a square.base having a fixed volume, the one that has the least inner surface area has the property that its

If the greatest angle of a cyclic quadrilateral is 3 times the least angle, then the radian measure of the least angle is

If $x$ and $y$ are related by the relation$x^2 - ax+ y^2 = 0$, then $d^2y/dx^2$ is equal to

The maximum area of a rectangle which can be inscribed in an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is