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NDA 2 2024 Maths, question 15

Topic: Algebra

Q15

The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?

  1. (a) 240240
  2. (b) 720720
  3. (c) 14401440Correct answer
  4. (d) 16201620

Solution.

Answer: (c) 14401440

  1. E,U,A,I,O form one block and Q,T,N another.
  2. Order the two blocks in 2! ways, then arrange the vowels in 5! and consonants in 3! ways.
  3. The total is 2×120×6=1440.