Permutations and Combinations – Dictionary Rank – JEE Main 24 Jan 2026 Shift 2

Question ID: #888
JEE Main24 January Shift 2, 2026Algebra

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:

  • (1) 1580
  • (2) 1578
  • (3) 1579
  • (4) 1581

Solution:


Letters: A, D, P, R, U, U, Y

Words starting with A: $\frac{6!}{2!} = 360$

Words starting with D: $\frac{6!}{2!} = 360$

Words starting with P: $\frac{6!}{2!} = 360$

Words starting with R: $\frac{6!}{2!} = 360$

Total so far: $360 \times 4 = 1440$

Now start with U:

Words starting with UA: $5! = 120$ (Remaining: D, P, R, U, Y)

Total so far: $1440 + 120 = 1560$

Now start with UD:

Words starting with UDAP: $3! = 6$

Words starting with UDAR: $3! = 6$

Words starting with UDAU: $3! = 6$

Total so far: $1560 + 6 + 6 + 6 = 1578$

Next word: UDAYPRU (1579)

Next word: UDAYPUR (1580)

Rank = 1580

Ans. (1)

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