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

• A. 1578
• B. 1579
• C. 1580
• D. 1581

Hint:

In dictionary ranking problems, always add 1 at the end to include the given word itself.

Answer 1

The Correct Option is C

Step 1: Arrange letters alphabetically. 
Alphabetical order: \[ A, D, P, R, U, Y \] Step 2: Count permutations before each letter. 
Compute permutations starting with letters smaller than the current letter at each position. 
Step 3: Sum all preceding permutations. 
Total number of words before ``UDAYPUR'' is \[ 1579 \] Step 4: Add 1 for the word itself. 
\[ \text{Rank}=1579+1=1580 \]