The particular solution of differential equation $$\mathrm{e}^{\frac{d y}{d x}}=(x+1), y(0)=3$$ is
A right circular cone has height $$9 \mathrm{~cm}$$ and radius of base $$5 \mathrm{~cm}$$. It is inverted and water is poured into it. If at any instant, the water level rises at the rate $$\frac{\pi}{\mathrm{A}} \mathrm{cm} / \mathrm{sec}$$. where $$\mathrm{A}$$ is area of the water surface at that instant, then cone is completely filled in
The solution of $$\mathrm{e}^{y-x} \frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{y(\sin x+\cos x)}{(1+y \log y)}$$ is
Water flows from the base of rectangular tank, of depth 16 meters. The rate of flow of the water is proportional to the square root of depth at any time $$\mathrm{t}$$. If depth is $$4 \mathrm{~m}$$ when $$\mathrm{t}=2$$ hours, then after 3.5 hours the depth (in meters) is