A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

A thin rod of length $$'L'$$ is lying along the $$x$$-axis with its ends at $$x=0$$ and $$x=L$$. Its linear density (mass/length) varies with $$x$$ as $$k{\left( {{x \over L}} \right)^n},$$ where $$n$$ can be zero or any positive number. If the position $${X_{CM}}$$ of the center of mass of the rod is plotted against $$'n',$$ which of the following graphs best approximates the dependence of $${X_{CM}}$$ on $$n$$?

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $${V_1}$$ and contains ideal gas at pressure $${P_1}$$ and temperature $${T_1}$$. The other chamber has volume $${V_2}$$ and contains ideal gas at pressure $${P_2}$$ and temperature $${T_2}$$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

The speed of sound in oxygen $$\left( {{O_2}} \right)$$ at a certain temperature is $$460\,\,m{s^{ - 1}}.$$ The speed of sound in helium $$(He)$$ at the same temperature will be (assume both gases to be ideal)