List of top Mathematics Questions asked in COMEDK UGET

If $\sin(\theta + \alpha) = \cos(\theta + \alpha),$ then the value of $\frac{1 - \tan \alpha}{1+ \tan \alpha}$ is
The number of points at which $f(x) = 3 + 2\, \, \, \sin x$ has maximum in the interval $\left( - \frac{11 \pi}{2} , 100 \pi \right)$ is
The projection of $\vec{a} = 5\hat{i} - \hat{j} + 3 \hat{k}$ on $\vec{b} = 2 \hat{i} + \hat{j} - \hat{k}$ is
In a triangle $ABC$ if $\begin{vmatrix}1&a&b\\ 1&c&a\\ 1&b&c\end{vmatrix} = 0$, then $\sin^2 A + \sin^2 B + \sin^2 C = $
If the area of triangle formed by the points $(\alpha, 0), (0, 1)$ and $(-1, 0)$ is 20 s units, then $\alpha$ is
The area of the triangle whose vertices are $A = (1, -1, 2), B = (2, 1, -1)$ and $C = (3, -1, 2)$ is
The coordinates of the circumcentre of the triangle with vertices $(2, 3), (4, -1) $ and $ (4, 3) $ are
The number of positive divisors of 67375 which are greater than 5 is
If $ \sqrt{x} + \frac{1}{\sqrt{x}} = 2 \, \cos \theta $, then $x^6 + x^6 = $
The differential equation whose general solution is $Ax^2 + By^2 = 1$, where $A$ and $B$ are arbitrary constants is of ?
If $a, b, c$ are in G.P and $x^a = y^b = z^c$, then
A point on the curve $2y^3 + x^2 = 12y$ at which the tangent to the curve is vertical is
If $g$ is the inverse function of $f$ and $f'(x) = \frac{1}{ 1+x^n} $ , then the value of $g'(x)$ is
$\displaystyle\lim_{x \to \infty} \left( \frac{x+6}{x+1}\right)^{x+4} =$
If $y= \sin^{-1} (3^{-x})$, then $\frac{dy}{dx} = $
If $ f(x) = x^m$, where $m$ is a positive integer then the value of $m$ for which $f'(\alpha + \beta) = f'(\alpha ) + f'(\beta)$ for all $ \alpha , \beta > 0$ is
The points of discontinuities of $f(x) = \left(\frac{\pi x}{x+1} \right)$ other than $x = -1$ are
$f(x) = \begin{cases} x , \text{if } x \text{ is rational}\\ 0, \text{if } x \text{ is rational} \end{cases}$ then $f$ is
The value of the integral $\int\limits_{0}^{\pi/ 4} \frac{1+\sin^{2} }{ \cos^{3} x} dx $ is
If $\lambda_1 , \lambda_2$ and $\lambda_3$ are the eigen values (i.e. characteristic values) of the matrix $\begin{vmatrix}1&2&15\\ 3&4&11\\ 5&6&7\end{vmatrix}$ then $ \left(1 -\lambda_{1}\right)\left(1+\lambda _{2}\right)\left(1+\lambda _{3}\right)$ equals
If $p, q , r$ are the roots of the equation $\begin{vmatrix}x&1&2\\ 1&x&2\\ 1&2&x\end{vmatrix} = 0$ , then $\frac{p^{4} +q^{4}+r^{4}}{p^{2}+q^{2} +r^{2}}$ is equal to
Define $f (x) = min{x^2 + 1, x + 1]$ for.$x e\in R$. Then $ \int\limits_{-1}^1f (x)dx $ is
If $A$ is a square matrix.such that $A^3 = 0$, then $(I + A)^{-1}$ is
If $n$ is a positive integer which is relatively prime to $6,$ and if $n$ has $8$ divisors, then $12n$ has
If $\sin(\pi \cos \theta) = \cos(\pi \sin \theta),$ then $\sin 2 \theta$ equals