List of top Mathematics Questions asked in COMEDK UGET

The direction ratios of the line which is perpendicular to the lines $\frac{ x - 7}{2} = \frac{y +17}{-3}= \frac{z - 6}{1} $ and $\frac{ x + 5}{1} = \frac{y +3}{2}= \frac{z - 4}{-2} $ are
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
A bag contains $3$ white, $4$ black, $2$ red balls. If $2$ balls are drawn at random, then the probability that both the balls are white, is
A line making angles $45^\circ$. and $60^\circ$ with the positive directions of the axis of $x$ and $y$, makes with the positive direction of $z$-axis, an angle of
If a class of $175$ students the following data shows the number of students opting one or more subjects. Mathematics $100$, Physics $70$, Chemistry $40$, Mathematics and Physics $30$, Mathematics and Chemistry $28$, Physics and Chemistry $23$, Mathematics, Physics and Chemistry $18$. The number of students who have opted Mathematics alone is
If a set $A$ has $4$ elements, then the total number of proper subsets of set $A$, 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 differential equation of the family of parabolas $y^2 = 4ax$, where $a$ is parameter, 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
The number of bijective functions from the set $A$ to itself, if $A$ contains $108$ elements 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
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 $\Delta ABC, cosec\, A(\sin\, B \, \cos\, C + \cos \, B\, \sin\, C)$ =
$AB$ and $CD$ are $2$ line segments ; where $A(2,3,0),B (6, 9, 0), C(-6, -9, 0). P $ and $Q$ are midpoint of $AB$ and $CD$, respectively and $L$ is the midpoint of $PQ$. Find the distance of $L$ from the plane $3x + 4z + 25 = 0$
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 subtangent at $x = \pi/2$ on the curve $y = x \sin x $ is
If the line px + qy = 0 coincides with one of the lines given by $ax^2 + 2hxy + by^2 = 0$, then