List of top Mathematics Questions asked in COMEDK UGET

$\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 $\int f\left(x\right) dx =\Psi\left(x\right)$ then $ \int x^{5} f\left(x^{3}\right)dx $ is equal to

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

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

The intercepts on $x-axis$ made by tangents to the curve, $y = \displaystyle\int_0^x |t| dt, x \in R$, which are parallel to the line $y = 2x$, are equal to

Consider : Statement-I : $(p \wedge \sim q) \wedge ( \sim p\wedge q)$ is a fallacy. Statement-II : $(p\to q) \leftrightarrow (\sim q \to \sim p)$ is a tautology.

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

The expression $\frac{\tan A}{1-\cot A} + \frac{\cot A}{1 - \tan A} $ can be written as

If $y = \sin^{2} \left(\tan^{-1} \sqrt{\frac{1-x^{2}}{1+x^{2}}}\right), $ then $\frac{dy}{dx}$ =

$ y =\tan^{-1} \left( \frac{1}{1+x+x^{2}} \right) + \tan ^{-1} \left( \frac{1}{x^{2}+3x+3} \right) + \tan ^{-1} \left( \frac{1}{x^{2}+5x+7} \right) + ......+ $ upto $n$ terms, then $ \frac{dy}{dx} $ at $x = 0$ and $n = 1$ is equal to

If $(4)^{\log_9 3} + (9)^{\log_2 4} = (10)^{\log_x 83}$, then X is equal to

If $\omega$ is a cube root of unity, then the value of determinant $\begin{vmatrix}1+\omega&\omega^{2}&\omega \\ \omega^{2} + \omega &-\omega &\omega^{2} \\ 1+\omega^{2} &\omega &\omega^{2} \end{vmatrix}$

If $\alpha, \beta , \gamma$ are the roots of the equation $x^3 - 3x^2 + 2x - 1 = 0$ then the value of $[(1 - \alpha) (1 -\beta )(1 - \gamma)]$ is

If $\frac{2}{9!} + \frac{2}{3! \,7!}+\frac{1}{5! \,5!} =\frac{2^{a}}{b!}$ where $a,b \in \, N$ then theordered pair $(a, b)$ is

In the group $G = \{1, 5, 7, 11\}$ under $\otimes_{12}$ the value of $7 \otimes_{12} 11^{-1}$ is equal to