JEE MAIN - Mathematics (2024 - 6th April Evening Shift - No. 16)
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 :
NRAPUG
NRAGUP
NRAPGU
NRAGPU
Explanation
NAGPUR
Word at $$315^{\text {th }}$$ position
$$\begin{aligned} & \text { A...... }=5!=120 \\ & \text { G....... }=5!=120 \\ & \text { NA..... }=4!=24 \\ & \text { NG..... }=4!=24 \\ & \text { NP..... }=4!=24 \end{aligned}$$
..... Till 312 words
$$313^{\text {th }} \text { word }=\text { NRAGPU }$$
$$314^{\text {th }}$$ word $$=$$ $$\mathrm{NRAGUP}$$
$$315^{\text {th }} \text { word }=\text { NRAPGU }$$
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