Concept: The question tests on the basics of Counting/Combinations
Not changing the relative order means keeping the vowels and consonants in the same place as the original word.
In P A T A L I P U T R A, the consonants an vowels are C V C V C V C V C C V
We have 6 consonants of which P comes twice and T comes twice.
The number of arrangements for the consonants = 6! / 2!2! = 180
We have 5 vowels of which A is repeated thrice
The number of arrangements for the vowels = 5! / 3! = 20
Total number of words = 180 * 20 = 3600