(i) \([\text{Co(NH}_3)_5(\text{NO}_2)](\text{NO}_3)_2\) — Linkage isomerism.
Step 1: The \(\text{NO}_2\) group is an ambidentate ligand: it can bind to the metal either through the nitrogen atom (nitro, \(-\text{NO}_2\)) or through an oxygen atom (nitrito, \(-\text{ONO}\)).
Step 2: Structures of the two isomers:
Nitro form: \([\text{Co(NH}_3)_5(\text{NO}_2)]^{2+}\) (Co–N bond), yellow.
Nitrito form: \([\text{Co(NH}_3)_5(\text{ONO})]^{2+}\) (Co–O bond), red.
Both are octahedral with five \(\text{NH}_3\) and one ambidentate ligand, and both have \((\text{NO}_3)_2\) as counter ions.
(ii) \([\text{Cr(NH}_3)_6][\text{Co(CN)}_6]\) — Coordination isomerism.
Step 1: Here both the cation and the anion are complex ions, so the ligands can be interchanged between the two metal centres.
Step 2: The isomer is \([\text{Co(NH}_3)_6][\text{Cr(CN)}_6]\), in which \(\text{NH}_3\) ligands are now on cobalt and \(\text{CN}^-\) ligands on chromium. Both metals stay octahedrally coordinated.
(iii) \([\text{Fe(NH}_3)_2(\text{CN})_4]^-\) — Geometrical (cis–trans) isomerism.
Step 1: This is an octahedral complex of the \(\text{MA}_2\text{B}_4\) type.
Step 2: The two isomers are:
cis isomer: the two \(\text{NH}_3\) ligands occupy adjacent (\(90^\circ\)) positions.
trans isomer: the two \(\text{NH}_3\) ligands occupy opposite (\(180^\circ\)) positions, with the four \(\text{CN}^-\) filling the remaining sites.
\[\boxed{\text{(i) Linkage, (ii) Coordination, (iii) Geometrical (cis/trans)}}\]