$A$ 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 of decay of mass of a certain substance at time $t$ is proportional to the mass at that instant. The time during which the original mass of $m_{0} \text{ gm}$ will be reduced to $m_{1} \text{ gm}$ is (where $K$ is the constant of proportionality).

$A$ body cools according to Newton's law of cooling from $100^{\circ} C$ to $60^{\circ} C$ in $15$ minutes. If the temperature of the surrounding is $20^{\circ} C$,then the temperature of the body after cooling down for one hour is (in $^{\circ} C$)

The population of towns $A$ and $B$ increases at a rate proportional to their population present at that time. At the end of the year $1984$,the population of both the towns was $20,000$. At the end of the year $1989$,the population of town $A$ was $25,000$ and that of town $B$ was $28,000$. The difference of populations of towns $A$ and $B$ at the end of $1994$ was

$A$ body is heated to $110^{\circ} C$ and placed in air at $10^{\circ} C$. After $1$ hour,its temperature is $60^{\circ} C$. The additional time required for it to cool to $30^{\circ} C$ is

The area enclosed by the closed curve $C$ given by the differential equation $\frac{dy}{dx} + \frac{x+a}{y-2} = 0, y(1) = 0$ is $4\pi$. Let $P$ and $Q$ be the points of intersection of the curve $C$ and the $y$-axis. If normals at $P$ and $Q$ on the curve $C$ intersect the $x$-axis at points $R$ and $S$ respectively,then the length of the line segment $RS$ is