Let $\mathrm{f}: \mathbb{R}-\{2\} \rightarrow \mathbb{R}-\{1\}$ defined by $\mathrm{f}(x)=\frac{x-3}{x-2}$ and $\mathrm{g}: \mathbb{R} \rightarrow \mathbb{R}$ defined by $\mathrm{g}(x)=3 x-2$, then sum of all values of $x$ for which $\mathrm{f}^{-1}(x)+\mathrm{g}^{-1}(x)=\frac{19}{6}$ is

There are 11 points in a plane of which 5 points are collinear. Then the total number of distinct quadrilaterals with vertices at these points is

$\int \frac{x^4 \cos \left(\tan ^{-1} x^5\right)}{1+x^{10}} d x$ equals

The length of the perpendicular drawn from the origin on the normal to the curve $x^2+2 x y-3 y^2=0$ at the point $(2,2)$ is