Question

If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at 315^th position in this arrangement is

• A. NRAGUP
• B. NRAGPU
• C. NRAPGU
• D. NRAPUG

Answer 1

The Correct Option is C

Arranging the letters in alphabetical order: NAGPUR

Starting with \( A \): \( 5! = 120 \) positions

Starting with \( G \): \( 5! = 120 \) positions, cumulative: 240

Starting with \( N \) and \( A \): \( 4! = 24 \) positions, cumulative: 264

Starting with \( N \) and \( G \): \( 4! = 24 \) positions, cumulative: 288

Starting with \( N \) and \( P \): \( 4! = 24 \) positions, cumulative: 312

Now, starting with \( N \), \( R \), and \( A \):

\[ \text{NRAGUP} = 1, \text{ cumulative: 313} \]

\[ \text{NRAGPU} = 1, \text{ cumulative: 314} \]

\[ \text{NRAPGU} = 1, \text{ cumulative: 315} \]

Thus, the word at the \( 315^{\text{th}} \) position is NRAPGU.