If is defined ∀ x ∈ R, then the set of values of 'a' is

Maths Fundamental of Mathematics General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

[9, ∞ )

[10, ∞ )

[15, ∞ )

[2, ∞ )

Text Solution

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The correct answer is:

for defined , log 4 log 3 log 2 (x 2 – 2x + a) ≥ 0

⇒ log 3 log 2 (x 2 – 2x + a) ≥ 1 ⇒ log 2 (x 2 – 2x + a) ≥ 3

⇒ x 2 – 2x + a ≥ 8 ⇒ x 2 – 2x + (a – 8) ≥ 0 ⇒ D ≤ 0

4 – 4(a – 8) ≤ 0 ⇒ 1 – a + 8 ≤ 0 ⇒ a ≥ 9

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