The amount of work done in blowing a soap bubble such that its diameter increases from $d$ to $D$ is ($T$ = surface tension of solution).

$A$ mixture of $2$ moles of helium gas (atomic mass $= 4$ $amu$) and $1$ mole of argon gas (atomic mass $= 40$ $amu$) is kept at $300$ $K$ in a container. The ratio of the rms speeds $(\frac{V_{rms}(helium)}{V_{rms}(argon)})$ is

Which one of the following transitions of an electron in a hydrogen atom emits radiation of the lowest wavelength?

During the change of $O_2$ to $O_2^-$ ion,the electron adds to which one of the following orbitals?

Alternating current of peak value $\left(\frac{2}{\pi}\right) \text{ A}$ flows through the primary coil of a transformer. The coefficient of mutual inductance between the primary and secondary coil is $1 \text{ H}$. The peak $EMF$ induced in the secondary coil is (Frequency of $AC = 50 \text{ Hz}$): (in $\text{ V}$)

Two particles of equal mass have velocities $\overrightarrow{v}_1=4 \hat{i} \text{ ms}^{-1}$ and $\overrightarrow{v}_2=4 \hat{j} \text{ ms}^{-1}$. The first particle has an acceleration $\overrightarrow{a}_1=(5 \hat{i}+5 \hat{j}) \text{ ms}^{-2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of