List of top Mathematics Questions asked in COMEDK UGET

If $\tan A - \tan B = x$ and $\cot B - \cot A = y$, then $\cot (A- B) =$

The subtangent at $x = \pi /2$ on the curve $y = x \sin x$ is

If $y =\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y}}}} +.....$ then $ \frac{dy}{dx} $

The function $f\left(x\right) = \left(\frac{\log_{e}\left(1+ax\right) - \log_{e}\left(1-bx\right)}{x}\right)$ is undefined at $x = 0$. The value which should be assigned to $f$ at $x = 0$ so that it is continuous at $x = 0$ is

The maximum value of $\left(\frac{1}{x}\right)^{2x^2}$ is

Let $x$ be a number which exceeds its square by the greatest possible quantity, then $x$ =

Which of the following functions is differentiable at $x = 0$ ?

If $x= a\left(\cos t+\log \tan \frac{t}{2}\right), y = a \sin t, $ then $ \frac{dy}{dx} $

If $\int \frac{1}{x+x^{5}}dx =f\left(x\right)+c , $ then $\int \frac{x^{4}}{x+x^{5}} dx = $

If a set $A$ has $n$ elements, then the number of relations on $A$ is

If $\vec{a} = \hat{i} + \lambda \hat{j} + 2 \hat{k}$ and $\vec{b} = \mu \hat{i} + \lambda \hat{j} + 2 \hat{k}$ are orthogonal and if $|\vec{a} | = |\vec{b}|$, then $(\lambda, \mu)$ =

If $y =\left(1+x\right)\left(1+x^{2}\right) ....\left(1+x^{100}\right),$ then $\frac{dx}{dy} $ at $x = 0$ is

If $\vec{a} , \vec{b} ,\vec{c}$ are unit vectors and $\theta$ is the angle between them, then $| \vec{a} - \vec{b}| = $

If $\log (x + z) + \log (x - 2y + z) = 2 \log (x - z),$ then $ x, y, z$ are in

If $C$ is the centre of the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1 $ and S is one of the foci, then the ratio of CS to semi-minor axis of the ellipse is

If $n$ is a non-negative integer and $A = \begin{bmatrix}1&0\\ 1&1\end{bmatrix} $ , then $A^n = $

The value of $x$ for which $f(x) = x^3 - 6x^2 - 36x + 7 $ is increasing, belong to

If $ y =\sin^{-1} \left(\frac{5x+12 \sqrt{1 -x^{2}}}{13}\right)$ , then $ \frac{dy}{dx} = $