In which of the following circuits is the current maximum just after the switch $S$ is closed?

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

Two persons $A$ and $B$ are located in the $X-Y$ plane at the points $(0,0)$ and $(0,10)$ respectively. (The distances are measured in $MKS$ units). At time $t=0$,they start moving simultaneously with velocities $\overrightarrow{v}_A = 2\hat{j} \text{ m/s}$ and $\overrightarrow{v}_B = 2\hat{i} \text{ m/s}$ respectively. The time after which $A$ and $B$ are at their closest distance is

The set $\{x \in R: \cos 2x + 2 \cos^2 x = 2\}$ is equal to

The energy band diagrams for three semiconductor samples of silicon are as shown. We can then assert that

$A$ transformer works on the principle of