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

NDA 2 2024 Maths, question 11

Topic: Algebra

Q11

Let x>1,y>1,z>1x>1,y>1,z>1 be in GP. Then

11+ln⁡x, 11+ln⁡y, 11+ln⁡z\frac{1}{1+\ln x},\ \frac{1}{1+\ln y},\ \frac{1}{1+\ln z}

are

  1. (a) in AP
  2. (b) in GP
  3. (c) in HPCorrect answer
  4. (d) neither in AP nor in GP nor in HP

Solution.

Answer: (c) in HP

  1. The GP condition is y²=xz.
  2. Taking logarithms gives 2ln y=ln x+ln z, so 1+ln x, 1+ln y and 1+ln z form an AP.
  3. Their reciprocals therefore form an HP.
  4. The denominators are positive since x,y,z>1.