The slope of a curve passing through the point $(2, 0)$ at $(x, y)$ is $x^2 - 2x$. Find the value of $y$ at $x = 0$.

$A$ spherical raindrop evaporates at a rate proportional to its surface area. If its radius originally is $3 \text{ mm}$ and $1 \text{ hour}$ later has been reduced to $2 \text{ mm}$,then the expression of radius $r$ of the raindrop at any time $t$ is (where $0 \leq t < 3$):

In a certain culture of bacteria,the rate of increase is proportional to the number present. It is found that the number doubles in $4$ hours. Then the number of times the bacteria are increased in $12$ hours is

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

The solution of $\frac{dy}{dx} = \frac{ax + b}{cy + d}$ represents a parabola if

In a culture,the bacteria count is $1,00,000$. The number increases by $10 \%$ in $2$ 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?