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If f(2x) = 4x2 + 1, then for how many real values of x will f(2x) be the GM of f(x) and f(4x)?  

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. Four
  2. Two
  3. One
  4. None

Answer (Detailed Solution Below)

Option 3 : One
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Detailed Solution

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Explanation:

f(2x) = 4x2 + 1

⇒f(x) = x2 + 1

⇒ f(4x) = 16x2 + 1

⇒ (4x2 + 1)2 = (x2 + 1) × (16x2 + 1)      [f(2x) is GM of f(x) & f(4x)]

⇒ x2 = 0

⇒x = 0

Thus One real value of x is possible

∴ Option (c) is correct.

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