List of top Mathematics Questions asked in COMEDK UGET

The shortest distance between the lines $\frac{ x - 3}{3} = \frac{y-8}{-1}= \frac{z - 3}{1} $ and $\frac{ x + 3}{-3} = \frac{y +7}{2}= \frac{z - 6}{4} $ is
The differential equation of the family of parabolas $y^2 = 4ax$, where $a$ is parameter, is
The value of $c$ in Lagrange's theorem for the function $f(x) = \log (\sin \, x)$ in the interval $\left[ \frac{\pi}{6} , \frac{5 \pi}{6} \right]$ is
The maximum area in square units of an isosceles triangle inscribed in an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with its vertex at one end of the major axis is
The medians $AD$ and $BE$ of a triangle with vertices $A(0, b), B(0, 0) $ & $C(a, 0)$ are perpendicular to each other, if
$\int\limits \frac{x^3 -1}{x^3 + x} dx = $
If $A = \begin{bmatrix}a&0&0\\ 0&a&0\\ 0&0&a\end{bmatrix}$, then det(adj A) is
A straight line meets the coordinates axes at $A$ and $B$, so that the centroid of the triangle $OAB\, is \, (1, 2)$. Then the equation of the line $AB$ is
The number of bijective functions from the set $A$ to itself, if $A$ contains $108$ elements is -
Given $5$ line segments of lengths $2, 3, 4, 5, 6 $ units. Then, the no. of triangles that can be formed by joining these segments is
Three dice are rolled once. The chance of getting a score of $5$ is
The number of solutions of the equation $\left|cot\,x\right|=cot\,x+\frac{1}{sin\,x}, \left(0 \le x \le 2\pi\right)$ is
$ \int\limits_1^e \log \, x \, dx = $
If $y = | \cos\, x | + | \sin\, x |$, then $\frac{dy}{dx}$ at $x = \frac{2 \pi}{3}$ is
If $f(x) = \log_{x^2} (\log \,x)$, then $f'(x)$ at $x = e$ is
$\frac{\sin x - \sin 3x}{\sin^{2} x -\cos^{2} x}$ is equal to
In a $\Delta ABC, cosec\, A(\sin\, B \, \cos\, C + \cos \, B\, \sin\, C)$ =
A spherical balloon is being inflated at the rate of $35\, cc$ per minute, When its radius is $7\, cm$, its surface area increases at the rate of
The interval I such that $\int^1_0\frac{dx}{\sqrt{1+x^4}}\in \,I$ is given by
The value of $\int^2_{-2}(ax^3+bx +c)dx$ depends on the
If the coefficients of $x^5$ and $x^6$ in $\left(2+\frac{x}{3}\right)^{n}$ are equal, then $n$ is
The value of $\frac{\tan 330^{\circ} \sec 420^{\circ} \sin 300^{\circ}}{\tan 135^{\circ} \sin 210^{\circ} \sec 315^{\circ} } $ is equal to
If the circle $x^2+y^2+2\,gx+2fy+=0,$ and $x^2+y^2+2g'x+2f'y$ touch each other, then
A card is picked at random from a pack of cards. Given that the picked card is a Queen, what is the probability that it is a spade ?
If the line px + qy = 0 coincides with one of the lines given by $ax^2 + 2hxy + by^2 = 0$, then