$A$ container is filled with a liquid that cools from $100^{\circ}C$ to $70^{\circ}C$ in $5 \text{ min}$, when kept at a room temperature of $30^{\circ}C$. The time that it must have taken to cool down to $80^{\circ}C$ from its initial temperature is approximately: (in $\text{ min}$)

$A$ body cools in a surrounding which is at a constant temperature of $\theta_0$. Assume that it obeys Newton's law of cooling. Its temperature $\theta$ is plotted against time $t$. Tangents are drawn to the curve at the points $P(\theta = \theta_2)$ and $Q(\theta = \theta_1)$. These tangents meet the time axis at angles of $\varphi_2$ and $\varphi_1$,as shown in the figure.

$A$ solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature $120\ ^oC$,then:

Two spheres of the same metal have radii $r$ and $2r$. They are heated to the same temperature and placed in the same environment. The ratio of their rates of cooling will be:

$A$ body cools from $75 \, ^\circ \text{C}$ to $65 \, ^\circ \text{C}$ in $2 \, \text{min}$ in a room at $30 \, ^\circ \text{C}$. How long will it take to cool from $55 \, ^\circ \text{C}$ to $45 \, ^\circ \text{C}$ in the same room?

$A$ bowl filled with very hot water cools from $98^\circ C$ to $86^\circ C$ in $2$ minutes when the room temperature is $22^\circ C$. How long will it take to cool from $75^\circ C$ to $69^\circ C$?