CUET Mathematics - Algebra - Inequalities | Free Questions - Page 2

Q1:

2025: 21 May Shift 2

Algebra

>

Inequalities

Medium

Applied

If a, b, c are positive real numbers, then the least value of $(a+b+c)(ab+bc+ca)$ is:

1

abc

9abc

3abc

Correct Answer

Option 3

Correct Answer

Explanation

Q2:

2025: 21 May Shift 1

Algebra

>

Inequalities

Easy

Applied

The solution set of the inequation $|2x - 3| ≤ 4$ is

$\left[\frac{1}{2}, \frac{7}{2}\right]$

$\left[-\frac{1}{2}, \frac{7}{2}\right]$

$\left[-\frac{1}{2}, \frac{5}{2}\right]$

$\left[-\frac{7}{2}, \frac{7}{2}\right]$

Correct Answer

Option 2

Correct Answer

Explanation

Q3:

2025: 19 May Shift 1

Algebra

>

Inequalities

Medium

Applied

Match List-I with List-II

List-I	List-II
(Inequality)	(Solution Set)
---	---
(A) $2x - 3 < x + 2 \le 3x + 5, x \in \mathbb{R}$	(I) $x \in (-1, \infty)$
(B) $\vert 2x + 3\vert < 7, x \in \mathbb{R}$	(II) $x \in (-\infty, 120]$
(C) $\frac{1}{2}\left(\frac{3}{5}x + 4\right) \ge \frac{1}{3}(x - 6), x \in \mathbb{R}$	(III) $x \in (-5, 2)$
(D) $\frac{\vert x + 1\vert }{x + 1} > 0, x \in \mathbb{R} - \{-1\}$	(IV) $x \in \left[-\frac{3}{2}, 5\right)$

Choose the correct answer from the options given below:

(A) - (II), (B) - (I), (C) - (III), (D) - (IV)

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

Correct Answer

Option 4

Correct Answer

Explanation

Q4:

2025: 16 May Shift 1

Algebra

>

Inequalities

Medium

Applied

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:

Two

Three

Four

Five

Correct Answer

Option 4

Correct Answer

Explanation

Q5:

2025: 15 May Shift 2

Algebra

>

Inequalities

Medium

Applied

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

(0, 1]

[1, 0)

(0, 1)

[0, 1]

Correct Answer

Option 1

Correct Answer

Explanation

Q6:

2025: 15 May Shift 1

Algebra

>

Inequalities

Medium

Applied

The inequality $\frac{5x - 2}{3} - \frac{7x - 3}{5} > \frac{x}{4}$ holds when

$x \in (-4, \infty)$

$x \in (4, \infty)$

$x \in (-\infty, 2]$

$x \in (-\infty, 4]$

Correct Answer

Option 2

Correct Answer

Explanation

Q7:

2025: 14 May Shift 2

Algebra

>

Inequalities

Medium

Applied

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:

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

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

(C) and (D) only

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

Correct Answer

Option 2

Correct Answer

Explanation

Q8:

2025: 14 May Shift 1

Algebra

>

Inequalities

Medium

Applied

Which of the following inequalities holds true?

(A) $\sqrt{5} + \sqrt{3} > \sqrt{6} + \sqrt{2}$ .

(B) If $a > b$ and $c < 0$ , then $\frac{a}{c} < \frac{b}{c}$ .

(C) $\frac{1}{x^2} > \frac{1}{x} > 1$ , if $0 < x < 1$ .

(D) If $a$ and $b$ are positive integers and $\frac{a - b}{6.25} = \frac{4}{2.5}$ , then $b > a$ .

Choose the correct answer from the options given below:

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

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

(A) and (B) only

(B) and (C) only

Correct Answer

Option 2

Correct Answer

Explanation

Q9:

2025: 13 May Shift 2

Algebra

>

Inequalities

Medium

Applied

If $a > b$ and $c < 0$ , then which of the following is NOT correct?

(A) $ac < bc$

(B) $a + c < b + c$

(C) $a - c < b - c$

(D) $ac > bc$

Choose the correct answer from the options given below:

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

(B) and (C) only

(A), (C) and (D) only

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

Correct Answer

Option 4

Correct Answer

Explanation

Q10:

2025: 13 May Shift 1

Algebra

>

Inequalities

Hard

Applied

If $a, b$ and $c$ are positive real numbers, then

Match List-I with List-II

List-I	List-II
(Expression)	(The Least value of the expression)
(A) $(a + b)(b + c)(c + a)$	(I) $8abc$
(B) $(a + b + c)(ab + bc + ca)$	(II) $9a^2b^2c^2$
(C) $(a^2b + b^2c + c^2a)(ab^2 + bc^2 + ca^2)$	(III) $9abc$
(D) $(a + b)^2(b + c)^2(c + a)^2$	(IV) $64a^2b^2c^2$

Choose the correct answer from the options given below:

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (I), (B) - (III), (C) - (II), (D) - (IV)

(A) - (I), (B) - (II), (C) - (IV), (D) - (III)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Correct Answer

Option 2

Correct Answer

Explanation

Q11:

2024: 16 May Shift 1

Algebra

>

Inequalities

Medium

Applied

The solution set of the inequality $|3 x| \geq|6-3 x|$ is :

$(-\infty, 1]$

$[1, \infty)$

$(-\infty, 1) \cup(1, \infty)$

$(-\infty,-1) \cup(-1, \infty)$

Correct Answer

Option 2

Correct Answer

Explanation

Q12:

2023: 22 May Shift 3

Algebra

>

Inequalities

Medium

Common

All points lying inside the triangle formed by the points (5, 0), (-1, 2) and (1, 3) satisfy :

(A) $3x + 2y - 18 > 0$

(B) $3x + 2y > 0$

(C) $2x + y + 13 < 0$

(D) $2x - 3y - 12 < 0$

(E) $2x - 3y + 12 > 0$

Choose the correct answer from the options given below :

(A) and (B) Only

(B) and (C) Only

(D) and (E) Only

(B), (D) and (E) Only

Correct Answer

Option 4

Correct Answer

Explanation

Q13:

2023: 15 June Shift 2

Algebra

>

Inequalities

Easy

Applied

Match List - I with List - II.

List - I	List - II
(A) The solution set of the inequality $-5x > 3$ , $x \in R$ , is	(I) $\left[\frac{20}{7}, \infty\right)$
(B) The solution set of the inequality is, $\frac{-7x}{4} \leq -5$ , $x \in R$ is,	(II) $\left[\frac{4}{7}, \infty\right)$
(C) The solution set of the inequality $7x - 4 \geq 0$ , $x \in R$ is,	(III) $\left(-\infty, \frac{7}{5}\right)$
(D) The solution set of the inequality $9x - 4 < 4x + 3$ , $x \in R$ is,	(IV) $\left(-\infty, -\frac{3}{5}\right)$

Choose the correct answer from the options given below :

(A)-(IV), (B)-(I), (C)-(II), (D)-(III)

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

(A)-(IV), (B)-(I), (C)-(III), (D)-(II)

(A)-(I), (B)-(IV), (C)-(II), (D)-(III)

Correct Answer

Option 1

Correct Answer

Explanation

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