Number of cyclic tripeptides formed with 2 amino acids A and B is:
- A.2
- B.4
- C.5
- D.3
Show answer and solution
Correct option: A
Solution
A cyclic tripeptide with 2 amino acids A and B must use all 3 positions, so the possible compositions are AAB (2 A's, 1 B) or ABB (1 A, 2 B's).
For a cyclic tripeptide, rotations of the same sequence are identical. For AAB: the distinct cyclic arrangement is only one — A-A-B (since rotating A-A-B gives A-B-A and B-A-A, but these are all the same cyclic sequence). Similarly for ABB, there is only one distinct cyclic arrangement.
So total = 1 (from AAB) + 1 (from ABB) = 2 distinct cyclic tripeptides.
For a cyclic tripeptide, rotations of the same sequence are identical. For AAB: the distinct cyclic arrangement is only one — A-A-B (since rotating A-A-B gives A-B-A and B-A-A, but these are all the same cyclic sequence). Similarly for ABB, there is only one distinct cyclic arrangement.
So total = 1 (from AAB) + 1 (from ABB) = 2 distinct cyclic tripeptides.
[JEE Main 2023 · 29 Jan · Shift 1]