Question:-How many words can be formed with the letters of the word 'PATALIPUTRA' without changing the relative order of the vowels and consonants?Choices:- 3600 3200 3400 3000

The word 'PATALIPUTRA' has 10 letters in total, with 5 vowels (A, A, I, U, A) and 5 consonants (P, T, L, P, T, R).

The vowels must remain in the same relative order, as must the consonants. This means that we can treat the vowels as a single entity, and the consonants as another single entity.

So, we have 2 entities (Vowels and Consonants) to arrange in 10 places, which can be done in 10P2 = 90 ways.

Within the vowels, there are 5 vowels where 'A' is repeated 3 times. So, they can be arranged among themselves in 5!/3! = 20 ways.

Similarly, within the consonants, there are 5 consonants where 'P' and 'T' are repeated 2 times each. So, they can be arranged among themselves in 5!/(2!*2!) = 30 ways.

Therefore, the total number of words that can be formed is 90 * 20 * 30 = 54000.

However, none of the given choices match this answer. There might be a mistake in the question or the choices provided.