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 315th position in this arrangement is

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

Answer 1

Answer: (C)

NRAPGU

Answer 2

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.