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NDA 1 2025 Maths, question 18

Topic: Algebra

Q18

In how many ways can the letters of the word DELHI be arranged keeping the positions of vowels and consonants unchanged?

  1. (a) 6
  2. (b) 9
  3. (c) 12Correct answer
  4. (d) 24

Solution.

Answer: (c) 12

  1. The vowels E and I occupy the two vowel positions and can be interchanged in 2!2! ways.
  2. The consonants D, L and H occupy the remaining three positions in 3!3! ways.
  3. The independent choices give 2!×3!=122! \times 3! = 12 arrangements.