$A$ spherical raindrop evaporates at a rate proportional to its surface area. The differential equation involving the rate of change of its radius $r$ with time $t$ is ... (where $k$ is a positive constant)

Statement $(A)$: When the temperature increases,the viscosity of gases increases and the viscosity of liquids decreases.
Statement $(B)$: Water does not wet an oily glass because the cohesive force of oil is less than that of water.
Statement $(C)$: $A$ liquid will wet a surface of a solid if the angle of contact is greater than $90^{\circ}$.

The heart of a man pumps $5 \, \text{litres}$ of blood through the arteries per minute at a pressure of $150 \, \text{mm}$ of mercury. If the density of mercury is $13.6 \times 10^3 \, \text{kg/m}^3$ and $g = 10 \, \text{m/s}^2$, then the power (in $\text{watt}$) is:

Two cylindrical vessels of equal cross-sectional area $16\,cm^{2}$ contain water up to heights $100\,cm$ and $150\,cm$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process is $......J$. [Take density of water $= 10^{3}\,kg/m^{3}$ and $g = 10\,m/s^{2}$]

The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section $A$ and height $h$. The upper part is a conical vessel of height $h$ with base area $A$ and top area $a$,and the walls of the vessel are inclined at an angle $30^o$ with the vertical. $A$ liquid of density $\rho$ fills both the sections up to a height $2h$. Neglecting atmospheric pressure:

Fill in the blanks:
$(i)$ The lines of flow and streamlines coincide with each other in ...... flow.
$(ii)$ The formula for the horizontal velocity of water coming from a hole at the bottom at a height $h$ from the surface of the water is ......
$(iii)$ $1 \ Pa = ...... \ dyne/cm^{2}$
$(iv)$ The relative velocity of two parallel layers of water is $6 \ cm/s$. If the perpendicular distance between the two layers is $0.1 \ mm$,then the velocity gradient will be ......