b
The order of basicity is \(I > III > II > IV.\) The lone pair of electrons on \(N\) is more readily available for protonation in \(I\) and \(III\) then in \(II.\) \(III\) contains an oxygen atom which has \(-I\) effect due to which it is less basic than \(I.\) In compound \(IV\) lone pair of \(e^-s\) on \(N-\) atom is contributed towards the aromatic sextet formation and hence is not at all available for protonation. Hence option \((b)\) is correct.