The differential equation obtained from the function $$y=a(x-a)^2$$ is

The differential equation of all lines perpendicular to the line $$5 x+2 y+7=0$$ is

The bacteria increases at the rate proportional to the number of bacteria present. If the original number '$$N$$' doubles in $$4 \mathrm{~h}$$, then the number of bacteria in $$12 \mathrm{~h}$$ will be

The rate of decay of certain substance is directly proportional to the amount present at that instant. Initially, there are $$27 \mathrm{~gm}$$ of certain substance and $$3 \mathrm{~h}$$ later it is found that $$8 \mathrm{~gm}$$ are left, then the amount left after one more hour is