$A$ 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

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 $\text{ V}$)

The rate of disintegration of a fixed quantity of a radioactive element can be increased by

If $z_1, z_2$ are two complex numbers satisfying $\left|\frac{z_1-3 z_2}{3-z_1 \bar{z}_2}\right|=1$ and $\left|z_1\right| \neq 3$,then $\left|z_2\right|$ is equal to

$\tanh ^{-1}\left(\frac{1}{2}\right)+\operatorname{coth}^{-1}(2)$ is equal to

$A$ molecule $(X)$ has $(i)$ four sigma bonds formed by the overlap of $sp^2$ and $s$ orbitals,$(ii)$ one sigma bond formed by $sp^2$ and $sp^2$ orbitals,and $(iii)$ one $\pi$ bond formed by $p_z$ and $p_z$ orbitals. Which of the following is $X$?