The letters of the word LOGARITHM are arranged in all possible ways.The no.of arrangements in which the relative positions of vowels and consonants is not changed is:

a)4320 b)720 c)4200 d)3420

in the word LOGARITHM 

the position of vowels is 2,4,6

the position of consonants is 1,3,5,7,8,9

as their relative positions should be maintained 

the vowels can occupy only positions 2,4,6

and the consonants can only occupy positions 1,3,5,7,8,9

the permutation among vowels = 3!

the permutation among consonants =6!

thus total permutation = 6!*3!

=4320