Mathematics · Permutations and Combinations

JEE Main 2024 — 6 April, Shift 2 — Question 12

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 $315^{\text {th }}$ position in this arrangement is :

Option A:
NRAGUP
Option B:
NRAGPU
Option C:
NRAPGU
Correct
Option D:
NRAPUG

Answer: C

Step-by-step solution

NAGPUR $\mathrm{A} \rightarrow 5!=120$

$G{ }^{\circledR} 5!=120$ 240

$\mathrm{NA}{ }^{\circledR} 4!=24$ 264

$\mathrm{NG}{ }^{\circledR} 4!=24$ 288

$\mathrm{NP}{ }^{\circledR} 4!=24$ 312

NRAGPU $=1$ 313

NRAGUP 314

NRAPGU 315

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 6 April, Shift 2
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Applications of Permuations and Combination