For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?

Velocity vector of a flow fields is given as $$\overrightarrow V = 2xy\widehat i - {x^2}z\widehat j.$$ The vorticity vector at $$(1,1,1)$$ is

A smooth pipe of diameter $$200$$ $$mm$$ carries water. The pressure in the pipe at section
$${S_1}\,\,$$ (elevation : $$10$$ $$m$$ ) is the $$50$$ $$kPa.$$ At section
$${S_2}\,\,$$ (elevation : $$12$$ $$m$$ ) the pressure is $$20$$ $$kPa$$ and velocity is $$2$$ $$m/s.$$
Density of water is $$1000$$ $$kg/{m^3}$$ and acceleration due to gravity is $$9.8$$ $$m{s^{ - 2}}.$$ Which of the following is TRUE?

Maximum velocity of a one-dimensional incompressible fully developed viscous flow, between two fixed parallel plates, is $$6\,\,m{s^{ - 1}}.$$ Then mean velocity (in $$m{s^{ - 1}}$$) of the flow is