If the half-life of a substance is $5$ years,then the total amount of the substance left after $15$ years,when the initial amount is $64$ gms,is: (in $gm$)

$A$ radioactive substance has a half-life of $h \ days$. Its initial decay rate is given by (Note that at $t = 0, M = m_0$):

Number of values of $m \in N$ for which $y = e^{mx}$ is a solution of the differential equation $D^3y - 3D^2y - 4Dy + 12y = 0$ is

If $y = At^2 + \frac{B}{t}$ ($A, B$ are parameters) is the general solution of the differential equation $f(t) y''(t) + g(t) y'(t) + h(t) y = 0$,then $2 f(t) + t^2 h(t) =$

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

In a culture,the bacteria count is $1,00,000$ initially. The number increases by $10 \%$ in the first $2$ hours. In how many hours will the count reach $2,00,000$,if the rate of growth of bacteria is proportional to the number present?