$A$ piece of steel is heated to $100^{\circ}C$ and allowed to cool in a room. Which graph correctly represents the cooling process?

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:

Water is drained from a vertical cylindrical tank by opening a valve at the base of the tank. It is known that the rate at which the water level drops is proportional to the square root of water depth $y$,where the constant of proportionality $k > 0$ depends on the acceleration due to gravity and the geometry of the hole. If $t$ is measured in minutes and $k = \frac{1}{15}$,then the time required to drain the tank if the water is $4 \text{ m}$ deep to start with is .......... $\text{min}$.

At any point $(x, y)$ of a curve,the slope of the tangent is twice the slope of the line segment joining the point of contact to the point $(-4, -3)$. Find the equation of the curve given that it passes through $(-2, 1)$.

The rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance and that of air. The temperature of air is $290 \ K$ and the substance cools from $370 \ K$ to $330 \ K$ in $10 \ minutes$. Then the time to cool the substance up to $295 \ K$ is: (in $min$)

The number of solutions of $\frac{dy}{dx} = \frac{y+1}{x-1}$,when $y(1) = 2$ is