Let x >1, y >1, z >1 be in GP. Then \(\rm \frac{1}{1+ln x}, \frac{1}{1+lny}, \frac{1}{1+\ln z}\) are

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. in AP
  2. in GP
  3. in HP
  4. neither in AP nor in GP nor in HP 

Answer (Detailed Solution Below)

Option 3 : in HP
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Detailed Solution

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Explanation:

Given,

x, y, z are in GP

Thus, 

⇒ y2 =xz

⇒ \(2lny = lnx + lnz\)

lnx, ln y and lnz are in AP

⇒ (1 + lnx), (1 + lny) and (1 + lnz) are in AP

⇒ \(\frac{1}{lnx}, \frac{1}{lny}, \frac{1}{lnz}\) are in HP

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