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, Pyrrole is an aromatic compound but both the lone pair electrons contribute to the `pi`-electron system. The lone pair, thus, takes part in resonance and is delocalized over the ring. Hence, it is less available for a proton and the basic character is the least.
Pyridine is an aromatic system with six-`pi`-electrons, so the ring is planar and lone pair is held `sp^2` hybridized orbital of nitrogen. The increased s character of this orbital as compared to the `sp^3` orbital in piperidine means that the lone pair electrons are held closer to the nitrogen and hence less available for protonation. Hence the basicity is less than that of piperidine.
, In piperidine, nitrogen is `sp^3` hybridized, so the lone pair is held in `sp^3` orbital. It is more basic than pyridine where the lone pair resides in `sp^2` orbital. Hence, the order is `III gt II gt I`