CUET Mathematics 2025 27 May Shift 1 PYQs

Which of the following inequalities are NOT correct?

(A) If $a > 1, b > 1,$ then $\log_b a + \log_a b \leq 2$

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

(C) If $a,b,c$ are non-zero real numbers of the same sign, then $\left(\frac{a}{b} + \frac{b}{c} + \frac{c}{a}\right) \leq 3$

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

Choose the correct answer from the options given below:

If, in a pair of consecutive positive integers, both numbers are greater than 5 and their sum is less than 23, then the number of such pairs are:

The solution set of $6 \leq -3(2x - 4) < 12$, $x \in R$ is: