Question 38 — JEE Main 24 Jan 2026 S Ii

Question

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 24 Jan 2026 S II]
(1) 1580
(2) 1578
(3) 1579
(4) 1581

Solution

A, D, P, U,U,Y
A □ such words $=6!/ 2!=360$
D $\_\_\_\_$ such words $=6!/ 2!=360$
$\mathrm{P}----$ such words $=6!/ 2!=360$
R $\_\_\_\_$ such words $=6!/ 2!=360$
Till $\overline{\mathrm{n}} \overline{\mathrm{ow}} \overline{1} 4 \overline{4} 0$ words

U

U A □ such words $=5!=120$
left → D, P, R, U, Y
Till now 1560 words
U D A P $\_\_\_\_$ such words $=3!=6$
left R,V,Y
U D A R $\_\_\_\_$ such words $=3!=6$
left P,U,Y
U D A U $\_\_\_\_$ such words $=3!=6$
left R,P,Y
Till now 1578 words
UDAYPRU $\rightarrow 1579{ }^{\text {th }}$ word
UDA Y P U R $\rightarrow 1580{ }^{\text {th }}$ word Answer(1)