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NDA 2020 Maths · Mathematics · Sequences and Series · medium

For non-zero real numbers a,b,c: 1. If a,b,c are in GP, then a^2,b^2,c^2 are in GP. 2. If a,b,c are in AP, then a^2,b^2,c^2 are in AP.

Single correct option

Consider the following statements for non-zero real numbers a,b,ca,b,c:
1. If a,b,ca,b,c are in GP, then a2,b2,c2a^2,b^2,c^2 are in GP.
2. If a,b,ca,b,c are in AP, then a2,b2,c2a^2,b^2,c^2 are in AP.
Which of the statements is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (A) 1 only

If b2=acb^2=ac then (b2)2=a2c2(b^2)^2=a^2c^2, so statement 1 holds. For statement 2 take 1,2,31,2,3 in AP: their squares 1,4,91,4,9 have differences 3 and 5, so they are not in AP. Hence only statement 1 is correct.
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Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake