Step 1: Linkage isomers differ only in which atom of the same ligand is bonded to the metal, so the test is: does any coordinated ligand have two different donor atoms available?
Step 2: Scan the four complexes. \( Cl^- \), \( Br^- \) and \( NH_3 \) each have a single donor atom, so complexes (i) and (iv) are ruled out at once. A sulphate held by oxygen in (iii) does not switch donor atom in the linkage sense; instead its counter ion \( Br^- \) makes it an ionisation isomer example.
Step 3: The nitrite ion \( NO_2 \) in (ii) is the classic ambidentate ligand: coordinating through nitrogen gives the yellow nitro complex, while coordinating through oxygen gives the red nitrito complex. These two are linkage isomers.
Step 4: Hence the complex that displays linkage isomerism is \( [Co(NH_3)_5(NO_2)]Cl_2 \), i.e. option (ii).