In how many ways can we sort the letters of the word MANAGEMENT so that the comparative position of vowels and consonants remains the same as in MANAGEMENT.

Correct option is D

Given
Word: MANAGEMENT
Vowels: A, A, E, E (4 vowels)
Consonants: M, N, G, M, N, T (6 consonants)

Solution
The relative positions must remain the same, meaning vowels stay in vowel spots and consonants in consonant spots.
Arrangements of Vowels (A, A, E, E): $$\frac{4!}{2!2!} = \frac{24}{4} = 6$$​​
Arrangements of Consonants (M, N, G, M, N, T): $$\frac{6!}{2!2!} = \frac{720}{4} = 180$$​​
Total ways = $$6 \times 180 = 1080$$​​

Final Answer
So the correct answer is (d)