For a shell of principal quantum number $\mathrm{n}=4$, which is incorrect?

Which of the above statement(s) is/are false?

I) Orbital angular momentum of the electron having $\mathrm{n}=5$ and having the value of the azimuthal quantum number as lowest for this principal quantum number is $\frac{\mathrm{h}}{\mathrm{\pi }}.$

II) If $\mathrm{n}=3, \mathrm{l}=0, \mathrm{m}=0$ for the last valence shell electron, then the possible atomic number maybe $12$ or $13$.

III) Total spin of electrons for the atom ${}_{25}\mathrm{Mn}$ is $\pm \frac{7}{2}.$

IV) The spin magnetic moment of inert gas is $0$.