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NDA 1 2024 Maths, question 13

Topic: Algebra

Q13

How many four-digit natural numbers are there such that all of the digits are even ?

  1. (a) 625625
  2. (b) 500500Correct answer
  3. (c) 400400
  4. (d) 256256

Solution.

Answer: (b) 500500

  1. The leading digit has four choices: 2,4,6,8.
  2. Each remaining digit has five choices including zero.
  3. Repetition is permitted, so the count is 4×5³=500.