The bacteria increases at a rate proportional to the number of bacteria present. If the original number $N$ doubles in $4$ hours,then the number of bacteria in $12$ hours will be: (in $N$)

$A$ tangent to the curve $y = f(x)$ at $P(x, y)$ meets the $x-$axis at $A$ and the $y-$axis at $B$. If $AP : BP = 1 : 3$ and $f(1) = 1$,then the curve also passes through the point:

Number of straight lines which satisfy the differential equation $\frac{dy}{dx} + x \left( \frac{dy}{dx} \right)^2 - y = 0$ is:

If the tangent at a point $P(x, y)$ of a curve is perpendicular to the line that joins the origin with the point $P$,then the curve is

The microorganisms double themselves in $3$ hours. Assuming that the quantity increases at a rate proportional to itself,then the number of times it multiplies itself in $18$ hours is:

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?