An enemy fighter jet is flying along the curve, given by $$y=x^2+2$$. A soldier is placed at $$(3,2)$$ wants to shoot down the jet when it is nearest to him. Then, the nearest distance is

A circular plate of radius $$5 \mathrm{~cm}$$ is heated. Due to expansion, its radius increase at the rate of $$0.05 \mathrm{~cm} / \mathrm{s}$$. The rate at which its area is increasing when the radius is $$5.2 \mathrm{~cm}$$ is

The function $$f(x)=\log (1+x)-\frac{2 x}{2+x}$$ is increasing on

The coordinates of the point on the $$\sqrt{x}+\sqrt{y}=6$$ at which the tangent is equally inclined to the axes is