Which one of the following graphs represents the Freundlich adsorption isotherm?

$\int_0^{2 \pi} \sin^6 x \cos^5 x \, dx$ is equal to

$A$ certain quantity of water cools from $70\,^{\circ}C$ to $60\,^{\circ}C$ in the first $5\, \text{minutes}$ and to $54\,^{\circ}C$ in the next $5\, \text{minutes}$. The temperature of the surroundings is ......... $^{\circ}C$.

Two moles of ideal helium gas are in a rubber balloon at $30^\circ C$. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to $35^\circ C$. The amount of heat required in raising the temperature is nearly...... $J$ (take $R = 8.31$ $J/mol \cdot K$)

$64$ small drops of mercury,each of radius $r$ and charge $q$,coalesce to form a big drop. The ratio of the surface charge density of each small drop to that of the big drop is:

$A$ ray of light refracts from medium $1$ into a thin layer of medium $2$,crosses the layer,and is incident at the critical angle on the interface between medium $2$ and $3$ as shown in the figure. If the angle of incidence of the ray is $\theta$,the value of $\theta$ is