Multiple choice

The number of words that can be formed using all the letters of the word "KANPUR" when the vowels are in even places is

  1. $144$
  2. $36$
  3. $24$
  4. $48$
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A Correct answer
Explanation

KANPUR has 6 letters: K, A, N, P, U, R. Vowels are A, U (2). Consonants are K, N, P, R (4). Even places are 2, 4, 6. We must place 2 vowels in 3 even slots: 3P2 = 6 ways. The remaining 4 letters can be arranged in 4! = 24 ways. Total = 6 * 24 = 144.

AI explanation

The word KANPUR has 6 distinct letters, comprising 2 vowels (A, U) and 4 consonants. For the vowels to occupy even places, they must be placed in 2 of the 3 available even positions (2nd, 4th, and 6th), which can be done in 3P2 = 6 ways. The remaining 4 positions are filled by the 4 consonants in 4! = 24 ways. Multiplying these gives 6 * 24 = 144.

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