The rate of reduction of a person's assets is proportional to the square root of the assets at that moment. If the assets at the beginning are $10000$ and they dwindle down to $5625$ in $2$ years, then in how many years will the person be bankrupt (in $years$)?

If $y = e^{-mx}$ is a solution of the differential equation $\frac{d^2y}{dx^2} + 4 \frac{dy}{dx} + 3y = 0$, then the values of $m$ are

The rate of growth of bacteria is proportional to the number present. If initially there were $1000$ bacteria and the number doubles in $1$ hour,then the number of bacteria after $2 \frac{1}{2}$ hours is (Given $\sqrt{2} = 1.414$):

If the population grows at the rate of $8 \%$ per year,then the time taken for the population to be doubled is $\quad$ (given $\log 2=0.6912$ ) (in $years$)

Let the curve $y = y(x)$ be the solution of the differential equation,$\frac{dy}{dx} = 2(x + 1)$. If the numerical value of the area bounded by the curve $y = y(x)$ and the $x-$axis is $\frac{4\sqrt{8}}{3}$,then the value of $y(1)$ is equal to

The rate of increase of the population of a city is proportional to the population present at that instant. In the period of $40$ years,the population increased from $30,000$ to $40,000$. At any time $t$,the population is given by $P(t) = (a)(b)^{\frac{t}{40}}$. Then the values of $a$ and $b$ are respectively: