If the population grows at the rate of $8 \%$ per year,then the time taken for the population to be doubled is $\quad$ (given $\log 2=0.6912$ ) (in $years$)

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

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

The rate of disintegration of a radioactive element at any time is proportional to its mass at that time, where $k (k > 0)$ is the constant of proportionality. The time during which an original mass of $1.5 \text{ gm}$ will disintegrate to a mass of $0.5 \text{ gm}$ is ...

The slope of the tangent at any point $(x, y)$ on the curve is equal to the product of the coordinates of that point. If the equation of the normal to the curve at the point $(\sqrt{2}, e)$ is $ax + by = 1$,then $\frac{b}{a} =$

If the length of the sub-tangent at any point $P$ on a curve is proportional to the abscissa of the point $P$,then the equation of that curve is ($C$ is an arbitrary constant).