Circles: Relative positions

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

In how many ways the letters of the word “ARRANGE” can be arranged without altering the relative positions of vowels & consonants ?

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

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

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.