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NDA 1 2025 Maths, question 15

Topic: Algebra

Q15

How many 7-letter words (with or without meaning) can be constructed using all the letters of the word CAPITAL so that all consonants come together in each word?

  1. (a) 360
  2. (b) 300
  3. (c) 288Correct answer
  4. (d) 240

Solution.

Answer: (c) 288

  1. Treat the four consonants C, P, T, L as one block.
  2. The outer arrangement consists of this block and vowels A, A, I: 4!/2!=124!/2! = 12 arrangements.
  3. The four distinct consonants can be arranged inside their block in 4!=244! = 24 ways.
  4. Total 12×24=28812 \times 24 = 288.