Correct order of basic strength of Pyrrole
, Pyridine
and Piperidine
is :

Solution

Chemistry ma’am · 4 steps

Ask where the nitrogen lone pair lives: free on sp3 N, held by sp2 N, or locked inside the aromatic ring.

1. What decides basicity. A base uses the lone pair on nitrogen to take up a proton. The more freely available that lone pair is, the stronger the base.

   Compound	Nitrogen	Where the lone pair is	Approx. pKₐ of conjugate acid
   Piperidine	sp³, saturated ring	In an sp³ orbital, free, pushed up by two alkyl groups	11.1
   Pyridine	sp², aromatic ring	In an sp² orbital in the ring plane, not part of the aromatic sextet, but held closer (more s character)	5.2
   Pyrrole	sp², aromatic ring	In the p orbital, part of the 6π aromatic sextet	about -3.8

2. Piperidine versus pyridine. An sp² orbital has 33% s character against 25% for sp³. More s character holds the lone pair closer to the nucleus, so pyridine gives it up less readily than piperidine.
3. Pyrrole is weakest. In pyrrole the lone pair is one of the six π electrons that make the ring aromatic. Protonating nitrogen would destroy aromaticity, so pyrrole is hardly basic at all.
4. So. The order is Piperidine > Pyridine > Pyrrole, which is option (d).

The idea to keep. For nitrogen bases, check the lone pair: sp³ and free beats sp², and a lone pair that is part of an aromatic sextet is almost not available at all.

Answer from the NTA final answer key. Solution by PrepWiser.