If the function $y = e^{4x} + 2e^{-x}$ is a solution of the differential equation $\frac{\frac{d^3y}{dx^3} - 13\frac{dy}{dx}}{y} = K$,then the value of $K$ is:

$A$ wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet,hung in the open air,loses half its moisture during the first hour,then $90 \%$ of the moisture will be lost in ...... hours.

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

The assets of a person are increasing at a rate proportional to the square root of the assets at a given time. His assets increase from Rupees $9$ crores to Rupees $16$ crores in $2$ years,then his assets at the end of $5$ more years will be

The rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance and that of air. The temperature of air is $290 \ K$ and the substance cools from $370 \ K$ to $330 \ K$ in $10 \ minutes$. Then the time to cool the substance up to $295 \ K$ is: (in $min$)

The latus rectum of the conic satisfying the differential equation $x dy + y dx = 0$ and passing through the point $(2, 8)$ is: