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Which of the following inequalities are NOT correct? (A) If a > 1, b > 1, then log_b a + log_a b ≤ 2 (B) For any real number x, (9^x + 9^1-x) ≥ 9 (C)…

CUET UG 2025 — Mathematics Algebra

2025mcqmedium

Which of the following inequalities are NOT correct?

(A) If a>1,b>1,a > 1, b > 1,a>1,b>1, then log⁡ba+log⁡ab≤2\log_b a + \log_a b \leq 2logb​a+loga​b≤2

(B) For any real number x,(9x+91−x)≥9x, (9^x + 9^{1-x}) \geq 9x,(9x+91−x)≥9

(C) If a,b,ca,b,ca,b,c are non-zero real numbers of the same sign, then (ab+bc+ca)≤3\left(\frac{a}{b} + \frac{b}{c} + \frac{c}{a}\right) \leq 3(ba​+cb​+ac​)≤3

(D) If a,b,ca,b,ca,b,c are three distinct real numbers, then (a+b)(b+c)(c+a)≥8abc(a + b)(b + c)(c + a) \geq 8abc(a+b)(b+c)(c+a)≥8abc

Choose the correct answer from the options given below:

Official previous-year question

Held on 14 May 2025 · Verified 13 Jul 2026.

Options

  1. A

    (A), (B) and (D) only

  2. B

    (A), (B) and (C) only

  3. C

    (C) and (D) only

  4. D

    (B), (C) and (D) only

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