NDA Mathematics Question (2025) — Solution

Step-by-step solution

The word DELHI consists of 5 letters: 3 consonants (D, L, H) and 2 vowels (E, I). The arrangement of letters in the word is Consonant-Vowel-Consonant-Consonant-Vowel. Since the positions of vowels and consonants must remain unchanged, the consonants can only be placed in the 1st, 3rd, and 4th positions, and the vowels can only be placed in the 2nd and 5th positions. The 3 consonants can be arranged in their 3 positions in 3! ways. The 2 vowels can be arranged in their 2 positions in 2! ways. Total number of arrangements = 3! 2! = 6 2 = 12. Answer: 12