Basic nature is directly proportional to electron releasing tendency. If lone pair is delocalised, electron density decreases and basic strength decreases.
So, there is delocalisation of electron in both options (a) and (c). But it option (c) there is delocalisation of electron with both carbonyl group. Hence, it is weakest base. There is a subtle interplay of the inductive effect, solvation effect and steric hinderance of the alkyl group, which decides the basic strength of alkyl amines in the aqueous state. The order of basic strength in case of ethyl substituted amines in aqueous solution is as follows (C2H5)2NH>(C2H5)3N>C2H5NH2>NH3 ∴(C2H5)2