Permutations & Combinations
Dictionary Rank — UDAYPUR
nta_pyq_2026_jan
Grade 11

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
1579
1581
1578
1580

Step-by-Step Solution

Key Concept: Letters: U(2), D, A, Y, P, R — 7 letters. Words starting before U (A,D,P,R): $4\times\tfrac{6!}{2!}=1440$. Fix U, words starting UA: $5!=120$. Fix UD then UDA: count words starting UDAP, UDAR: $3\times3!=18$. Fix UDAY, starting UDAYP then UDAYR: $1+1=...$
Rank $=1580$.
Correct Answer: 4

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