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

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