If a, x, b are in AP, a, y, b are in GP and a, z, b are in HP such that x = 9z and a > 0, b > 0 then

JEE Advanced Mathematics question

If are in AP, are in GP and are in HP such that and then

Answer: (A),(B)

(AM), (GM), (HM). Key fact: , and .

- **(b)** With : (as ), i.e. . **True.** - **(a)** With : (as $z >

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Question ID VK-107799