The equation of the family of curves for which the length of the subnormal at any point $(x, y)$ is always a constant $(k)$ is

$A$ 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:

The rate of change of volume of a spherical balloon at any instant is directly proportional to its surface area. If initially its radius is $3 \ cm$,and after $2 \ minutes$ its radius becomes $9 \ cm$,then what is the radius of the balloon after $4 \ minutes$ (in $cm$)?

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 rate at which the population of a city increases varies as the population present. Within the period of $30$ years,the population grew from $20$ lakhs to $40$ lakhs. Then,the population after a further period of $15$ years will be (Take $\sqrt{2} = 1.41$) (in $lakhs$)

The number of differentiable functions $y: (-\infty, \infty) \rightarrow [0, \infty)$ satisfying $y^{\prime} = 2 \sqrt{y}$ and $y(0) = 0$ is