We need to match the coordination compounds from Column I with their correct type of isomerism from Column II.
- (a) \([Pt(NH_3)_2Cl_2]\): This compound exhibits geometrical isomerism as it has two different ligands (\(NH_3\) and \(Cl_2\)) arranged in different positions. Hence, it is related to (iv) geometrical isomerism.
- (b) \([Co(en)_3]^{3+}\): The compound with ethylenediamine (\(en\)) as the ligand exhibits optical isomerism due to the possibility of non-superimposable mirror images. Hence, it matches with (iii) optical isomerism.
- (c) \([Cr(NH_3)_5(SO_4)]Br\): This compound exhibits linkage isomerism because the sulfate ion (\(SO_4\)) can bind through either the sulfur or oxygen atom. Hence, it corresponds to (ii) linkage isomerism.
- (d) \([Co(NH_3)_5(NO_2)]Cl_2\): This compound exhibits ionisation isomerism because it can form different ions when dissolved, depending on the position of the chloride and nitrate ions. Hence, it matches with (i) ionisation isomerism.
Thus, the correct matching is:
(a) \((iv)\), (b) \((iii)\), (c) \((ii)\), (d) \((i)\).
Thus, the correct answer is option (C), (a)-(iv), (b)-(iii), (c)-(ii), (d)-(ii).