(A) Linkage isomerism arises in a coordination compound containing an ambidentate ligand. In $[Co(NH_3)_5NO_2]Cl_2$ and $[Co(NH_3)_5ONO]Cl_2$, the nitrite ligand binds either through nitrogen or oxygen. (A $\rightarrow$ III) (B) Coordination isomerism arises from the interchange of ligands between cationic and anionic entities of different metal ions present in a complex. (B $\rightarrow$ II) (C) Ionisation isomerism arises when the counter ion in a complex salt is itself a potential ligand and can displace a ligand which can then become the counter ion. Here, $SO_4^{2-}$ and $Br^-$ interchange. (C $\rightarrow$ I) (D) Solvate (hydrate) isomerism differs by whether or not a solvent (water) molecule is directly bonded to the metal ion or merely present as free solvent molecules in the crystal lattice. (D $\rightarrow$ IV) Therefore, the correct match is (A)-(III), (B)-(II), (C)-(I), (D)-(IV).