What will be 55th word of SHUVANK in dictionary?

Answer: AHSNKUV

Key idea: List letters in alphabetical order and use permutation blocks to locate the 55th word.

Alphabetical order of letters: A, H, K, N, S, U, V.

1. First letter: Words starting with A account for 6! = 720 permutations, which contains the 55th word. So the first letter is A.

2. Second letter: Within A, consider second letters in order H, K, N, S, U, V. Each choice fixes 5! = 120 permutations. Since 55 ≤ 120, the second letter is H.

3. Third letter: With prefix AH, the remaining third-letter options K, N, S, U, V each fix 4! = 24 permutations. The blocks are: K (1–24), N (25–48), S (49–72). The 55th falls in the S-block, so the third letter is S. The position inside the AHS-block is 55 − 48 = 7.

4. Fourth letter: Within AHS, remaining letters K, N, U, V give blocks of 3! = 6 permutations each. K covers positions 1–6 of the AHS-block. Since our index is 7, subtract 6 and move to the next choice, so the fourth letter is N. The new index inside AHSN is 7 − 6 = 1.

5. Remaining letters: After A H S N the leftover letters are K, U, V. With index 1, arrange them in alphabetical order K, U, V.

6. Therefore the 55th word in dictionary order is AHSNKUV.