The differential equation $\frac{dy}{dx} = \frac{\sqrt{1-y^2}}{y}$ determines a family of circles with

$A$ family of curves is such that the length intercepted on the $y$-axis between the origin and the tangent at any point $(x, y)$ is three times the ordinate of the point of contact. The family of curves is:

Water is drained from a vertical cylindrical tank by opening a valve at the base of the tank. It is known that the rate at which the water level drops is proportional to the square root of water depth $y$,where the constant of proportionality $k > 0$ depends on the acceleration due to gravity and the geometry of the hole. If $t$ is measured in minutes and $k = \frac{1}{15}$,then the time required to drain the tank if the water is $4 \text{ m}$ deep to start with is .......... $\text{min}$.

The rate of reduction of a person's assets is proportional to the square root of their existing assets at that moment. If the assets at the beginning are $10000$ and they dwindle down to $5625$ in $2$ years, then the person will be bankrupt in: (in $years$)

$A$ wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet,hung in the open air,loses half its moisture during the first hour,then $90 \%$ of the moisture will be lost in ...... hours.

The population $p$ of the city at time $t$ is given by $\frac{dp}{dt} = \frac{p}{2} - 100$. If the initial population at $t = 0$ is $100$,then $p$ is: