JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Biomolecules

A cyclic tripeptide is a ring of three amino-acid residues joined head to tail, each residue being either $A$ or $B$. Because the ring may be turned round, only the pattern of residues matters, and with three places that pattern is fixed by how many are $A$: all three alike gives $A\text{-}A\text{-}A$ and $B\text{-}B\text{-}B$, two alike with one different gives the single ring $A\text{-}A\text{-}B$, and one alike with two different gives the single ring $A\text{-}B\text{-}B$. Counting these distinct rings gives four cyclic tripeptides.