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 [JEE Main 2026, 24 Jan (Shift 2)]

Question

YESPYQ · Accepted Answer

Correct answer: d) $1580$. Dictionary order is $A,D, P, R, U, Y$ number of words starting with $A\to \frac{6!}{2!}=360$ number of words starting with $D\to \frac{6!}{2!}=360$ number of words starting with $P\to \frac{6!}{2!}=360$ number of words starting with $R\to \frac{6!}{2!}=360$ number of words starting with $U A \rightarrow 5!=120$ number of words starting with $UDAP\to 3!=6$ number of words starting with $UDAR\to 3!=6$ number of words starting with $UDAU\to 3!=6$ number of words starting with $UDAYPRU\to 1$ number of words starting with $UDAYPUR\to 1$ Total $=1580$

The letters of the word "\(UDAYPUR\)" are written in all possible ways with or without meaning and these words are arran…

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