JEE Mathematics 2026 Question with Solution

Given: The word is UDAYPUR.

Find: The dictionary rank of UDAYPUR among all arrangements of its letters.

Arrange the distinct letters alphabetically:

The solution states that we count all words occurring before UDAYPUR in dictionary order by checking, at each position, how many smaller letters can be placed first and then arranging the remaining letters.

Using the stated counting:

Then include the word itself:

Therefore, the correct option is C.

Given: The letters of UDAYPUR are all distinct.

Find: Its rank in dictionary order.

For dictionary ranking, compare the word from left to right. At each position, count arrangements beginning with letters smaller than the current letter and then sum all such counts. Finally, add $1$ to include the given word itself.

From the extracted solution:

1. Arrange letters alphabetically.
2. Count permutations starting with smaller letters at each position.
3. Total preceding permutations are $1579$.
4. Add $1$ for the word itself.

Hence,

So the rank of UDAYPUR is $1580$.