Pronunciation of vowels and consonants

How many words can be formed with the letters of thw word 'PATALIPUTRA' without changing the relative positions of vowels and consonants?

The letters of the word LOGARITHM are arranged in all possible ways.The number of arrangements in which the relative positions of the vowels and consonants are not changed

The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is:

The number of ways in which the letters of the word 'PROPORTION ' be arranged with out changing the relative positions of vowels and consonants is

find the number of arrangements which can be made out of the letters of the word 'algebra', without altering the relative positions of vowels and consonants.

In how many ways can the letters of the word INTERMEDIATE be arranged so that: the vowels always occupy even places? the relative order of vowels and consonants do not alter?