List of top Mathematics Questions asked in COMEDK UGET

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
Which of the following is an empty set?
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 ?
The number of proper subsets of a set having $n + 1$ elements is
The value of $\int^2_{-2}(ax^3+bx +c)dx$ depends on the
Let $x$ be a number which exceeds its square by the greatest possible quantity, then $x$ =
If the coefficients of $x^5$ and $x^6$ in $\left(2+\frac{x}{3}\right)^{n}$ are equal, then $n$ is
$\int^{\frac{\pi}{2}}_0 \log(\tan\,x)dx=$
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?
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) = $
The solution of $\left(x+y\right)^{2} \left(x \frac{dy}{dx}+y\right)=xy \left(1 +\frac{dy}{dx}\right) $ is
$\int e^{x}\left(\cos x -\sin x\right)dx $ is equal to
If $y = \tan \: x $ then $ \frac{d^2 y}{dx^2} $ =
If $\vec{a}$ and $\vec{b}$ are two vectors of magnitude $2$, each inclined at an angle $60^\circ$, then angle between $\vec{a}$ and $\vec{a} +\vec{b}$ is
If $\sin(120 - A)= \sin(120 - B)$ and $0< A, B < \pi $ then all values of $A, B$ are given by.
Given that $P(A) = 0.1, P(B | A) = 0.6$ and $ P(B |A^c ) = 0.3$ what is $P(A | B)$ ?
If tan $ \theta$ + tan $4\theta$ + tan $7\theta$ = tan $\theta$ tan $4\theta$ tan $7\theta,$ then the general solution is
The area (in s units) bounded by the curves $y = \sqrt{x} , 2y - x + 3 = 0, x$-axis and lying in the first quadrant is
If $\int f\left(x\right) dx =\Psi\left(x\right)$ then $ \int x^{5} f\left(x^{3}\right)dx $ is equal to
At present, a firm is manufacturing $1000$ items. It is estimated that the rate of change of production $P$ with respect to additional number of workers $x$ is given by $\frac {dP}{dx}=100-12 \sqrt x$ If the firm employees $25$ more workers, then the new level of production of items is
If $x, y, z$ are in A.P. and $\tan^{-1}x, \tan^{-1}y$ and $\tan^{-1}z$ are also in A.P., then