If surrounding air is kept at $20^{\circ} C$ and a body cools from $80^{\circ} C$ to $70^{\circ} C$ in $5$ minutes,then the temperature of the body after $15$ minutes will be: (in $^{\circ} C$)

In a bank,the principal increases continuously at the rate of $5 \%$ per year. In how many years will Rs $1000$ double itself?

The solution of the differential equation $y \frac{dy}{dx} + x = k$ represents . . . . . . .

$A$ spherical balloon expands at a rate proportional to its surface area. Initially, its radius is $2 \text{ cm}$ and $5 \text{ minutes}$ later it increases to $7 \text{ cm}$. What will be the surface area of the spherical balloon after $12 \text{ minutes}$ (in $\text{ cm}^2$)?

The population $P(t)$ of a certain mouse species at time $t$ satisfies the differential equation $\frac{dP(t)}{dt} = 0.5 P(t) - 450$. If $P(0) = 850$,then the time at which the population becomes zero is

The equation of the family of curves for which the length of the normal is equal to the radius vector is