The correct option is
B (c) > (a) > (b)
Comparing the given compounds (a), (b) and (c) all the compound has +I effect of
CH3 group but only compound (c) has ortho effect. In (c), due to presence of
−NR2 group and
−OCH3 group at ortho position they show SIR effect. The steric hindrance between
−NR2 and
−OCH3 will make the methyl groups in
−NR2 goes out of the plane. This reduce the steric hindrance hence SIR effect will dominates over SIP effect and makes the lone pair of electrons on N readily available for donation and also it experience +R effect of
−OCH3 which makes the overall compound more basic than others.
In compound (a), +R effect of
−OCH3 will increase the electron density on N atom and makes the lone pair of electrons on N readily available for donation of electron.
In compound (b),
−OCH3 present at meta position so +R effect is absent and it has only -I effect.
Comparing (a) and (b), (a) is more basic because resonance effect dominates over inductive effect.
Therefore, the order of decreasing basic strength is
(c) > (a) > (b)