The ratio of the wavelength of a photon of energy ' $E$ ' to that of the electron of same energy is ( $\mathrm{m}=$ mass of an electron, $\mathrm{c}=$ speed of light, $\mathrm{h}=$ Planck's constant)

The r.m.s. velocity of hydrogen at S.T.P. is ' $u$ ' $\mathrm{m} / \mathrm{s}$. If the gas is heated at constant pressure till its volume becomes three times, then the final temperature of the gas and the r.m.s. speed are respectively

The distance of the two planets A and B from the sun are $r_A$ and $r_B$ respectively. Also $r_B$ is equal to $100 r_A$. If the orbital speed of the planet $A$ is ' $v$ ' then the orbital speed of the planet B is

A tube of uniform bore of cross-sectional area ' $A$ ' has been set up vertically with open end facing up. Now ' $M$ ' gram of a liquid of density ' $d$ ' is poured into it. The column of liquid in this tube will oscillate with a period ' T ', which is equal to [ $g=$ acceleration due to gravity]