If the curves $$2 x=y^2$$ and $$2 x y=K$$ intersect perpendicularly, then the value of $$K^2$$ is

If the side of a cube is increased by $$5 \%$$, then the surface area of a cube is increased by

The maximum value of $$\frac{\log _e x}{x}$$, if $$x>0$$ is

The interval in which the function $$f(x)=x^3-6 x^2+9 x+10$$ is increasing in