List of top Mathematics Questions asked in COMEDK UGET

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
If the circle $x^2+y^2+2\,gx+2fy+=0,$ and $x^2+y^2+2g'x+2f'y$ touch each other, then
The value of $\sin \left[\cot^{-1}\{{\cos(tan^{-1}\,x)\}}\right]$ is
If the line px + qy = 0 coincides with one of the lines given by $ax^2 + 2hxy + by^2 = 0$, then
The subtangent at $x = \pi/2$ on the curve $y = x \sin x $ is
Which of the following is an empty set?
The number of proper subsets of a set having $n + 1$ elements is
The curve $x^2 - xy + y^2 =27$ has tangents parallel to $x-axis$ at
The interval I such that $\int^1_0\frac{dx}{\sqrt{1+x^4}}\in \,I$ is given by
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 ?
Let $x$ be a number which exceeds its square by the greatest possible quantity, then $x$ =
The value of $\int^2_{-2}(ax^3+bx +c)dx$ depends on the
$\int^{\frac{\pi}{2}}_0 \log(\tan\,x)dx=$
Consider an experiment $E$ in which a box contains $10$ identical tickets numbered $1$ to $10$ and $2$ tickets are drawn at random from the box. What is the probability that both the tickets have even numbers on them?
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 $f\left(x\right) = \frac{2x -3}{3x+4} $ then $f^{-1} \left(\frac{-4}{3}\right) = $