List of top Mathematics Questions asked in COMEDK UGET

In $Z$, the set of all integers, the inverse of $-7$ with respect to $*$ defined by $a * b = a + b + 7$ for all $a, b \in Z$ is
In $Z_7 - \{0\}$ under multiplication mod $7$, if $2^{-1} y \,3^{-1} = 5^{-1}$, then $y =$
If $x= a\left(\cos \theta +\theta \sin \theta\right)$ and $ y = a \left(\sin \theta- \theta \cos \theta \right) $ where $0 < \theta < \frac{\pi}{2}$ , then $ \frac{d^{2}y}{dx^{2}}$ at $ \theta = \frac{\pi}{4}$ is equal to
If $\log y= m \tan^{-1} x,$ then
The digit in the unit place of $2009! + 3^{7886}$ is
Let $y' = e^{-2x} $ and $ y = 0$ when $x =e$. Then the value of $x$ when $ y =\frac{1}{2}$ is
If $f\left(9\right)= 9 , f'\left(9\right) = 4 $ then $\lim_{x\to9} \frac{\sqrt{f\left(x\right)} -3}{\sqrt{x} - 3} = $
In the group $\{1, 2, 3, 4, 5, 6\}$ under multiplication modulo $7$, if $5x = 4$, then $x =$
The area bounded by the curve $y = \sin x$ between $x = 0$ and $x = 2\pi $ given by
If $a, b, c$ are in A.P., then $7^a, 7^b,$ and $7^c$ are in
$\displaystyle\lim_{x \to 0} \frac{6^{x} -3^{x} -2^{ x}+1}{x^{2}} = $
The locus of the centre of the circle of radius 3 which rolls on the outside of the circle $x^2+y^2 + 3x - 6y - 9 = 0$ is
$ \frac{1 -\tan^2 15^\circ}{1 + \tan^2 15^\circ} = $
The contrapositive of the statement "If $x^2 - 1 = 0$, then $x = -1$ or $x = + 1$ " is
The perpendicular distance between the lines $9x^2- 24xy + 16y^2 + 21x- 28y+ 10 = 0$ is
The length of the latus rectum of the parabola $bx^2 - 4ay + dx + e = 0$ is
If $|\vec{a} | = 15 , |\vec{b} | = 12$ and $|\vec{a} + \vec{b} | = 20 $ then $|\vec{a} - \vec{b} | = $
$ \sin^2 5^{\circ} + \sin^2 10^{\circ} + \sin^2 15^{\circ} +....+ \sin^2 90^{\circ} $ =
If $Z$ is a complex number with $I Z I = 1$ and $Z + \frac{1}{Z} = x + iy$, then $xy = $
If $^nC_1 + 2\, ^nC_2 + .... + n\, ^nC_n = 2n^2$, then $ n = $
The slopes of the tangent and normal at $(0, 1)$ for the curve $y = \sin x + e^x$ are respectively
$\int\limits_{1}^{e^{\frac{17}{2}}} \frac{\, \pi \cos (\pi \log x)}{x} dx =$
If $\frac{1}{2} \leq x \leq 1, $ then $\cos^{-1} x +\cos ^{-1}\left(\frac{x}{2} +\frac{\sqrt{3-3x^{2}}}{2}\right) =$
A stone is thrown up vertically and the height $'x'$ ft reached by it in time $'t'$ secs is given by $x = 80t - 16t^2$ . The stone reaches the maximum height in time ?
If for the curve $y = 1 + bx - x^2$, the tangent at $(1 - 2)$ is parallel to $x$-axis, then $b =$