JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Permutations and Combinations

Letters of KANPUR in order: A, K, N, P, R, U.

Words starting with A, K, N each contribute $5!=120$, totaling $360$ words through N.

Among words starting with P, the remaining letters are A, K, N, R, U:

• PA-: $4!=24$ (positions $361$–$384$)
• PK-: $24$ (positions $385$–$408$)
• PN-: $24$ (positions $409$–$432$)

Remaining letters for P R _: A, K, N, U:

• PRA-: $3!=6$ (positions $433$–$438$)
• PRK-: $6$ (positions $439$–$444$)

Within PRK, the last three letters A, N, U in lexicographic order give the words ANU, AUN, NAU, NUA, UAN, UNA, occupying positions $439$–$444$. The $440$th word is the second one, AUN, so the full word is