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NDA 1 2024 Maths, question 10

Topic: Algebra

Q10

If 26!=n8k26!=n8^{k}, where kk and nn are positive integers, then what is the maximum value of kk ?

  1. (a) 66
  2. (b) 77Correct answer
  3. (c) 88
  4. (d) 99

Solution.

Answer: (b) 77

  1. The exponent of 2 in 26! is ⌊26/2⌋+⌊26/4⌋+⌊26/8⌋+⌊26/16⌋=13+6+3+1=23.
  2. Since 8ᵏ=2³ᵏ, the largest possible k is ⌊23/3⌋=7.