The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

The particular solution of the differential equation $$y(1+\log x) \frac{d x}{d y}-x \log x=0$$ when $$x=e, y=e^2$$ is

If $$\mathrm{G}(\overline{\mathrm{g}}), \mathrm{H}(\overline{\mathrm{h}})$$ and $$\mathrm{P}(\overline{\mathrm{p}})$$ are respectively centroid, orthocenter and circumcentre of a triangle and $$\mathrm{x} \overline{\mathrm{p}}+\mathrm{y} \overline{\mathrm{h}}+z \overline{\mathrm{g}}=\overline{0}$$, then $$\mathrm{x}, \mathrm{y}, \mathrm{z}$$ are respectively.

The co-ordinates of the foot of the perpendicular drawn from the point $$2 \hat{i}-\hat{j}+5 \hat{k}$$ to the line $$\vec{r}=(11 \hat{i}-2 \hat{j}-8 \hat{k})+\lambda(10 \hat{i}-4 \hat{j}-11 \hat{k})$$ are