b
\((I)\;\;\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\)

\(\mathrm{Cr}^{+2} \Rightarrow[\mathrm{Ar}] 3 \mathrm{d}^{4}\)

\(\mathrm{H}_{2} \mathrm{O} \rightarrow\) Weak field ligand

\(\text { Unpaired } \mathrm{e}^{-}=4\)

\(\text { Magnetic moment } =\sqrt{24} \mathrm{BM} =4.89 \mathrm{BM}\)

\((II)\;\;\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\)

\(\mathrm{Fe}^{+2} \Rightarrow[\mathrm{Ar}] 3 \mathrm{d}^{6}\)

\(\mathrm{CN}^{-} \rightarrow\) Strong field ligand

Unpaired \(\mathrm{e}^{-}=0\)

Magnetic moment \(=0 \mathrm{BM}\) \(=0 \mathrm{BM}\)

\(\mathrm{III}\;\;\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\)

\(\mathrm{Fe}^{+3} \Rightarrow[\mathrm{Ar}] 3 \mathrm{d}^{5}\)

As \(\Delta_{0}>P\)

Unpaired \(\mathrm{e}^{-}=1\)

\(\text { Magnetic moment } =\sqrt{3} \mathrm{BM}\)\(=1.73 \mathrm{BM}\)

\((IV)\;\;\left(\mathrm{Et}_{4} \mathrm{N}\right)^{+}\left[\mathrm{CoCl}_{4}\right]^{2-}\)

\(\mathrm{Co}^{+2} \Rightarrow[\mathrm{Ar}] 3 \mathrm{d}^{7}\)

Unpaired electrons \(=3\)

\(\begin{aligned} \text { Magnetic moment } &=\sqrt{15} \mathrm{BM} \\ &=3.87 \mathrm{BM} \end{aligned}\)

Hence order of magnetic moment is \(I>IV>III>II\)