Let a line perpendicular to the line $$2 x-y=10$$ touch the parabola $$y^2=4(x-9)$$ at the point P. The distance of the point P from the centre of the circle $$x^2+y^2-14 x-8 y+56=0$$ is __________.

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :

What is the dimensional formula of $$a b^{-1}$$ in the equation $$\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$$, where letters have their usual meaning.

A particle moves in $$x$$-$$y$$ plane under the influence of a force $$\vec{F}$$ such that its linear momentum is $$\overrightarrow{\mathrm{p}}(\mathrm{t})=\hat{i} \cos (\mathrm{kt})-\hat{j} \sin (\mathrm{kt})$$. If $$\mathrm{k}$$ is constant, the angle between $$\overrightarrow{\mathrm{F}}$$ and $$\overrightarrow{\mathrm{p}}$$ will be :