The volume of a spherical balloon being inflated changes at a constant rate. If initially its radius is $3$ units and after $3$ seconds it is $6$ units,find the radius of the balloon after $t$ seconds.

The assets of a person are reduced in his business such that the rate of reduction is proportional to the square root of the existing assets. If the assets were initially ₹ $10,00,000$ and due to loss they reduce to ₹ $10,000$ after $3$ years,then the number of years required for the person to go bankrupt will be

The curve passing through $(3, 0)$ and satisfying the differential equation $(9 - x^2)(\frac{dy}{dx})^2 = 9 - y^2$ represents:

The temperature $T(t)$ of a body at time $t=0$ is $160^{\circ} F$ and it decreases continuously as per the differential equation $\frac{dT}{dt}=-K(T-80)$,where $K$ is a positive constant. If $T(15)=120^{\circ} F$,then $T(45)$ is equal to . . . . . . . . (in $^{\circ} F$)

$A$ 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 a certain substance is directly proportional to the amount present at that instant. Initially,there are $27 \text{ gms}$ of the substance and $3 \text{ hours}$ later it is found that $8 \text{ gms}$ are left. The amount left after one more hour is: