By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 1 2025 Maths, question 22

Topic: Algebra

Q22

If k<(2+1)3<k+2k < \left( \sqrt{2} + 1 \right)^{3} < k + 2, where kk is a natural number, then what is the value of kk?

  1. (a) 11
  2. (b) 13Correct answer
  3. (c) 15
  4. (d) 17

Solution.

Answer: (b) 13

  1. Expand: (2+1)3=7+52\left( \sqrt{2} + 1 \right)^{3} = 7 + 5\sqrt{2}.
  2. Since 7/5<2<8/57/5 < \sqrt{2} < 8/5, this lies strictly between 14 and 15.
  3. Of the listed choices, only k=13k = 13 works: 13<7+52<1513 < 7 + 5\sqrt{2} < 15.