Question
The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is
JEE Main
Mathematics
Permutation Combination
2026
JEE Main 2026 (24 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 1579
- B. 1581
- C. 1578
- D. 1580
Answer
D. 1580
Step-by-step solution
Letters of UDAYPUR: A, D, P, R, U, U, Y (U repeated twice). Words starting with a letter before U: letters A, D, P, R each give 6! 2! = 360 arrangements 4 360 = 1440. Fix U at position 1. Remaining: A, D, P, R, U, Y (all distinct). Words starting with UA: 5! = 120. Fix UD at positions 1-2. Remaining: A, P, R, U, Y. No letter before A, so fix UDA. Remaining: P, R, U, Y. Letters before Y: P, R, U give 3 3! = 18. Fix UDAY. Remaining: P, R, U. No letter before P, fix UDAYP. Remaining: R, U. Letter before U: R gives 1! = 1. Fix UDAYPU, last letter R: the word itself. Rank = 1440 + 120 + 18 + 1 + 1 = 1580.
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