The probability that a number selected at random from the set of numbers ${1, 2, 3, \ldots, 100}$ is a cube,is

Hot water cools from $60\,^{\circ}C$ to $50\,^{\circ}C$ in the first $10\,min$ and to $42\,^{\circ}C$ in the next $10\,min$. The temperature of the surrounding is ......... $^{\circ}C$.

Match the thermodynamic processes taking place in a system with the correct conditions. In the table: $\Delta Q$ is the heat supplied,$\Delta W$ is the work done,and $\Delta U$ is the change in internal energy of the system.

Process	Condition
$(I)$ Adiabatic	$(A) \Delta W = 0$
$(II)$ Isothermal	$(B) \Delta Q = 0$
$(III)$ Isochoric	$(C) \Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$
$(IV)$ Isobaric	$(D) \Delta U = 0$

Half-life of a radioactive substance is $20 \, min$. The difference between the points of time when it is $33 \%$ disintegrated and $67 \%$ disintegrated is approximately .......... $min$.

The approximate value of $(1.0002)^{3000}$ is

Which is the largest flower?