Which of the following complexes will show coordination isomerism?...

Coordination isomerism arises from the interchange of ligands between cationic and anionic entities of different metal ions present in a complex.

A. $[Ag(NH_3)_2][Ag(CN)_2]$: Both the complex cation and anion contain the same metal ion ($Ag^+$). Interchanging one ligand produces a neutral molecule $[Ag(NH_3)(CN)]$, and interchanging both ligands yields the identical compound. Thus, it does not show coordination isomerism.

B. $[Co(NH_3)_6][Cr(CN)_6]$: The complex contains different metal ions ($Co^{3+}$ and $Cr^{3+}$). Interchange of ligands gives the coordination isomer $[Cr(NH_3)_6][Co(CN)_6]$. Thus, it shows coordination isomerism.

C. $[Co(NH_3)_6][Co(CN)_6]$: Both the complex cation and anion contain the same metal ion ($Co^{3+}$). According to the strict definition requiring different metal ions, this is generally excluded from being a primary example of coordination isomerism in standard contexts.

D. $[Fe(NH_3)_6][Co(CN)_6]$: The complex contains different metal ions ($Fe^{3+}$ and $Co^{3+}$). Interchange of ligands gives the coordination isomer $[Co(NH_3)_6][Fe(CN)_6]$. Thus, it shows coordination isomerism.

E. $[Co(NH_3)_6][Fe(CN)_6]$: This is the coordination isomer of complex D. Since it contains different metal ions, it also shows coordination isomerism by interchanging ligands to form $[Fe(NH_3)_6][Co(CN)_6]$.

Since complexes D and E are coordination isomers of each other, they must both be included together. Therefore, the complexes that show coordination isomerism are B, D, and E.

Answer: B, D and E Only