Water is running in a hemispherical bowl of radius $$180 \mathrm{~cm}$$ at the rate of 108 cubic decimeters per minute. How fast the water level is rising when depth of the water level in the bowl is $$120 \mathrm{~cm}$$ ? (1 decimeter $$=10 \mathrm{~m}$$)

If Rolle's theorem holds for the function $$f(x)=x^3+b x^2+a x+5$$ on $$[1,3]$$ with $$c=2+\frac{1}{\sqrt{3}}$$, then the values of $$a$$ and $$b$$ respectively are

If $$\mathrm{f}(x)=x^3+\mathrm{b} x^2+\mathrm{c} x+\mathrm{d}$$ and $$0<\mathrm{b}^2<\mathrm{c}$$, then in $$(-\infty, \infty)$$

The slope of the normal to the curve $$x=\sqrt{t}$$ and $$y=t-\frac{1}{\sqrt{t}}$$ at $$t=4$$ is