$A$ spherical rain drop evaporates at a rate proportional to its surface area. If initially its radius is $3 \ mm$ and after $1 \ second$ it is reduced to $2 \ mm$,then at any time $t$ its radius is (where $0 \leq t < 3$)

$A$ 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 the time $t$,in which $99 \%$ of the moisture will be lost,is

$A$ population $P$ grows at the rate given by the equation $\frac{dP}{dt} = 0.05 P$. In how many years will the population double?

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is $290 \ K$ and the metal temperature drops from $370 \ K$ to $330 \ K$ in $10 \ \text{minutes}$,then the time required to drop the temperature up to $295 \ K$ is

The rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance and that of air. The temperature of air is $290 \ K$ and the substance cools from $370 \ K$ to $330 \ K$ in $10 \ minutes$. Then the time to cool the substance up to $295 \ K$ is: (in $min$)

The solution of the differential equation $x \frac{d^2y}{dx^2} = 1$,given that $y = 1$ and $\frac{dy}{dx} = 0$ when $x = 1$,is