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

The letters of the word UDAYPUR are written in all possible ways and arranged as in a dictionary

Q. 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

(A) 1579

(B) 1578

(D) 1581

Correct Answer: 1580

Explanation

The word UDAYPUR has 7 distinct letters.

Arrange the letters in alphabetical order:

A, D, P, R, U, U, Y

Since all letters are distinct, total permutations of remaining letters are calculated using factorials.

Now we count how many words come before UDAYPUR in dictionary order.

For the first letter U, letters before it are A, D, P, R.

Number of words starting with these letters:

4 × 6! = 4 × 720 = 2880

Now fix U and move to second letter D. Letters before D are A.

1 × 5! = 120

Fix UD, third letter is A. No letter before A, so contribution is 0.

Fix UDA, fourth letter is Y. Letters before Y are P and R.

2 × 3! = 12

Fix UDAY, fifth letter is P. No letter before P.

Fix UDAYP, sixth letter is U. No letter before U.

Fix UDAYPU, last letter is R.

Adding 1 for the word itself.

Total rank:

= 2880 + 120 + 12 + 1 = 1580

Hence, the rank of the word "UDAYPUR" is 1580.

Explanation

Related JEE Main Questions