$A$ radioactive sample has a half-life period of $10 \text{ days}$. If a sample originally has a mass of $1000 \text{ mg}$,then the mass remaining after $50 \text{ days}$ is:

The population $P = P(t)$ at time $t$ of a certain species follows the differential equation $\frac{dP}{dt} = 0.5P - 450$. If $P(0) = 850$,then the time at which the population becomes zero is:

$A$ body at an unknown temperature is placed in a room which is held at a constant temperature of $30^{\circ} F$. If after $10 \text{ minutes}$ the temperature of the body is $0^{\circ} F$ and after $20 \text{ minutes}$ the temperature of the body is $15^{\circ} F$,then the expression for the temperature of the body at any time $t$ is

$A$ spherical metal ball at $80^{\circ} C$ cools in $5 \text{ minutes}$ to $60^{\circ} C$ in a surrounding temperature of $20^{\circ} C$. The temperature of the ball after $20 \text{ minutes}$ is approximately: (in $^{\circ} C$)

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 $gm$)

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 will be $4N$ in (in $hours$)