CUET Mathematics - Algebra - Inequalities | Free Questions

Q1:

2026: 31 May Shift 2

Algebra

>

Inequalities

Easy

Applied

The solution set $\{x: x \in R, 3x-2 < x+2 \le 2x+6\}$ (Where $R$ is set of real numbers) is :

[-4,2)

[-4,-2)

[-4,2]

(-4,2)

Correct Answer

Option 1

Correct Answer

Explanation

Q2:

2026: 31 May Shift 2

Algebra

>

Inequalities

Medium

Applied

Which of the following facts are not true ?( Where $R$ is set of real numbers)

A. $|x+y| \le |x|+|y|, x,y \in R$

B. $|x-y| \ge |x|+|y|, x,y \in R$

C. $|x+y| \ge |x|+|y|, x,y \in R$

D. $|x-y| \le |x|+|y|, x,y \in R$

Choose the correct answer from the options given below:

A and B only

C and D only

B and C only

A and C only

Correct Answer

Option 3

Correct Answer

Explanation

Q3:

2026: 30 May Shift 2

Algebra

>

Inequalities

Easy

Core

The solution set of the inequality $3x+4y<12$ is

An open half-plane not containing the origin

An open half plane containing the origin

The whole xy-plane not containing the line $3x+4y=12$

A closed half-plane containing the origin

Correct Answer

Option 2

Correct Answer

Explanation

Q4:

2026: 30 May Shift 2

Algebra

>

Inequalities

Easy

Applied

Match List-I with List-II

List-I	List-II
(A) The solution set of the inequation $3x-6\le 0$ is	(I) $(3,\infty)$
(B) The solution set of the inequation $-5x+20<0$ is	(II) $[3,\infty)$
(C) The solution set of the inequation $3x-9\ge 0$ is	(III) $(-\infty,2]$
(D) The solution set of the inequation $8x+11>35$ is	(IV) $(4,\infty)$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 4

Correct Answer

Explanation

Q5:

2026: 30 May Shift 1

Algebra

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Inequalities

Medium

Applied

Match the LIST-I with LIST-II

	LIST-I (Inequality)		LIST-II (Solution Set)
A.	$\vert 3x-5 \vert \geq 4$	I.	$(-\infty,-1] \cup \left[\dfrac{7}{3},\infty\right)$
B.	$\vert 3x \vert \geq \vert 6-3x \vert$	II.	$(-\infty,-4] \cup [2,\infty)$
C.	$\vert x+1 \vert \geq 3$	III.	$[1,\infty)$
D.	$\vert 2-3x \vert \geq 5$	IV.	$\left(-\infty,\dfrac{1}{3}\right] \cup [3,\infty)$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 4

Correct Answer

Explanation

Q6:

2026: 29 May Shift 2

Algebra

>

Inequalities

Easy

Applied

The solution to the inequality $-12 < \frac{2x-1}{3} < 12$ is

$\left(\frac{-35}{2},\frac{37}{2}\right)$

$\left[\frac{-35}{2},\frac{37}{2}\right]$

$\left(\frac{-37}{2},\frac{35}{2}\right)$

$\left[\frac{-37}{2},\frac{35}{2}\right]$

Correct Answer

Option 1

Correct Answer

Explanation

Q7:

2026: 29 May Shift 2

Algebra

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Inequalities

Medium

Applied

Which of the following shaded regions represents the solution to the inequation $|x|+|y| \leq 1$ ?

Correct Answer

Option 3

Correct Answer

Explanation

Q8:

2026: 29 May Shift 1

Algebra

>

Inequalities

Easy

Applied

Which of the following are correct? (Where $R$ is set of real numbers)

(A) If $x \le 8$ , then $-x \ge -8$

(B) If $x \in R, |x| \le 3$ , then $-3 \le x \le 3$

(C) If $x \in R, |x|<-4$ , then $x \in \phi$

(D) $x=|x|$ iff $x \ge 0$

Choose the correct answer from the options given below:

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

(A), (B), (C) and (D)

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

(A) and (D) only

Correct Answer

Option 2

Correct Answer

Explanation

Q9:

2026: 25 May Shift 1

Algebra

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Inequalities

Medium

Applied

If $\dfrac{x+3}{2x-1} < 1$ , then the solution set contains :

A. $(-\infty,1/2)$

B. $(-\infty,4)$

C. $(-4,4)$

D. $(4,\infty)$

Choose the correct answer from the options given below:

A and D only

A and B only

B and C only

C and D only

Correct Answer

Option 1

Correct Answer

Explanation

Q10:

2026: 22 May Shift 2

Algebra

>

Inequalities

Medium

Applied

Match List-I with List-II

List-I: Inequation	List-II: Solution set
(A) $2(2x+3)-10<6(x-2)$	(I) $x\in(-\infty,3.9)$
(B) $\frac{2x-1}{12}-\frac{x-1}{3}<\frac{3x+1}{4}$	(II) $x\in\left(-\infty,\frac{-1}{2}\right)\cup\left[\frac{1}{2},\infty\right)$
(C) $\frac{x}{2x+1}\ge \frac{1}{4}$	(III) $x\in(0,\infty)$
(D) $\frac{2x-3}{4}+6>2+\frac{4x}{3}$	(IV) $x\in(4,\infty)$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 3

Correct Answer

Explanation

Q11:

2026: 22 May Shift 1

Algebra

>

Inequalities

Medium

Applied

Match List-I with List-II

List-I	List-II
Inequalities	Solution set
(A) If $\left\vert 3 - 5x \right\vert < 7$ , then $x \in$	(I) $\left[-\dfrac{5}{2}, \infty\right)$
(B) If $3x - 7 > 5x - 1$ , then $x \in$	(II) $(-\infty, -3)$
(C) If $\dfrac{x}{3} > \dfrac{x}{2} + 1$ , then $x \in$	(III) $\left(-\dfrac{4}{5}, 2\right)$
(D) If $5x + 4 \leq 7x + 9$ , then $x \in$	(IV) $(-\infty, -6)$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 2

Correct Answer

Explanation

Q12:

2026: 21 May Shift 2

Algebra

>

Inequalities

Easy

Applied

The solution set for the inequality $|5x-3| \le \dfrac{1}{5}$ is:

$\left[\dfrac{7}{5}, \dfrac{8}{5}\right]$

$\left[\dfrac{14}{25}, \dfrac{16}{25}\right]$

$\left[\dfrac{1}{16}, \dfrac{7}{16}\right]$

$\left[\dfrac{2}{15}, \dfrac{6}{15}\right]$

Correct Answer

Option 2

Correct Answer

Explanation

Q13:

2026: 21 May Shift 1

Algebra

>

Inequalities

Easy

Applied

Which one of the following inequalities are satisfied by $x = 10$ ?

$\frac{2x-5}{4} > 10, x \in \mathbb{R}$

$\frac{5x-2}{4} < 10, x \in \mathbb{R}$

$\frac{2x-5}{4} < 10, x \in \mathbb{R}$

$\frac{2-5x}{4} > 10, x \in \mathbb{R}$

Correct Answer

Option 3

Correct Answer

Explanation

Q14:

2026: 19 May Shift 2

Algebra

>

Inequalities

Easy

Applied

Match the LIST-I with LIST-II

LIST-I Inequality		LIST-II Solution set
A.	$4x + 3 \le 6x + 7$	I.	$x \in (-\infty, -2)$
B.	$5x - 5 > 3x - 1$	II.	$x \in (-\infty, 2]$
C.	$4x - 9 > 6x - 5$	III.	$x \in [-2, \infty)$
D.	$3x - 1 \le 5$	IV.	$x \in (2, \infty)$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 2

Correct Answer

Explanation

Q15:

2026: 19 May Shift 1

Algebra

>

Inequalities

Medium

Applied

The number that satisfies the inequality $\frac{29}{4} < \frac{x+20}{4} < 8$ is

$\frac{\pi}{2}$

$\pi$

$2\pi$

$3\pi$

Correct Answer

Option 4

Correct Answer

Explanation

Q16:

2026: 18 May Shift 2

Algebra

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Inequalities

Medium

Applied

Match the LIST-I with LIST-II

	LIST-I (Inequality)		LIST-II (Solution set)
A.	$\vert x-3 \vert < 1$	I.	$x \in \left(-\dfrac{2}{5}, \dfrac{8}{5}\right)$
B.	$\vert 3-5x \vert < 5$	II.	$x \in \left(-\infty, -\dfrac{1}{2}\right)$
C.	$2x+1 < \vert 2x+1 \vert$	III.	$x \in \left(-\dfrac{1}{3}, 5\right)$
D.	$\vert 7-3x \vert < 8$	IV.	$x \in (2,4)$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 4

Correct Answer

Explanation

Q17:

2026: 18 May Shift 1

Algebra

>

Inequalities

Easy

Applied

For the inequality $3-2x \geq x-32$ , which of the following are true?

(A) When $x \in N$ (set of natural numbers), the solution set is $\{1,2,3,\dots,11\}$ .

(B) When $x \in I$ (set of integers), the solution set is $\{-\infty,\dots,-3,-2,-1,0,1,2,3,\dots 10,11\}$ .

(C) When $x \in W$ (set of whole numbers), the solution set is $\{0,1,2,3,\dots,11\}$ .

(D) When $x \in R$ (set of real numbers), the solution set is $(-\infty,\infty)$ .

Choose the correct answer from the options given below:

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

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

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

(C) and (D) only

Correct Answer

Option 1

Correct Answer

Explanation

Q18:

2026: 15 May Shift 1

Algebra

>

Inequalities

Easy

Applied

Which of the following are correct?

A. If $|x-5|<2$ , then $x \in (3,7)$

B. If $|x-1|<4$ , then $x \in (-3,5)$

C. If $|x-2|<6$ , then $x \in (4,8)$

D. If $|x-4|<1$ , then $x \in (-3,5)$

Choose the correct answer from the options given below:

A and B only

A, B, and C only

A, B, C, and D

B, C, and D only

Correct Answer

Option 1

Correct Answer

Explanation

Q19:

2026: 12 May Shift 2

Algebra

>

Inequalities

Easy

Applied

The solution set of the inequation $|8x-7|\le\dfrac{2}{3}$ is

$\left(\dfrac{19}{24},\dfrac{23}{24}\right]$

$\left(\dfrac{19}{24},\dfrac{23}{24}\right)$

$\left[\dfrac{19}{24},\dfrac{23}{24}\right]$

$\left[\dfrac{19}{24},\dfrac{23}{24}\right)$

Correct Answer

Option 3

Correct Answer

Explanation

Q20:

2025: 3 June Shift 2

Algebra

>

Inequalities

Medium

Applied

If $\frac{3x - 5}{6} + 8 \geq 4 + \frac{2x}{3}$ , then

$x \in (-\infty, 19]$

$x \in (-\infty, -19]$

$x \in [19, \infty)$

$x \in [-19, \infty)$

Correct Answer

Option 1

Correct Answer

Explanation

Q21:

2025: 3 June Shift 1

Algebra

>

Inequalities

Easy

Applied

The solution set of the linear inequation $|4x - 3| \leq \frac{3}{4}$ is:

$(\frac{9}{16}, \frac{15}{16})$

$(-\frac{15}{16}, \frac{9}{16})$

$[\frac{9}{16}, \frac{15}{16}]$

$[-\frac{15}{16}, \frac{9}{16}]$

Correct Answer

Option 3

Correct Answer

Explanation

Q22:

2025: 2 June Shift 1

Algebra

>

Inequalities

Medium

Applied

Solution of the inequality $\frac{2x+3}{4x-5} \geq 0$ is

$\left(-\frac{3}{2}, \frac{5}{4}\right)$

$\left(-\infty, -\frac{3}{2}\right] \cup \left[\frac{5}{4}, \infty\right)$

$\left[-\frac{3}{2}, \frac{5}{4}\right)$

$\left(-\infty, -\frac{3}{2}\right] \cup \left(\frac{5}{4}, \infty\right)$

Correct Answer

Option 4

Correct Answer

Explanation

Q23:

2025: 30 May Shift 2

Algebra

>

Inequalities

Medium

Applied

The solution set of the inequality $\frac{2x+3}{x-1} < 0$ is:

$x \in (-\infty, 1)$

$x \in \left(-\infty, \frac{3}{2}\right)$

$x \in \left(-\frac{3}{2}, 1\right)$

$x \in \left(-\infty, \frac{2}{3}\right)$

Correct Answer

Option 3

Correct Answer

Explanation

Q24:

2025: 30 May Shift 1

Algebra

>

Inequalities

Medium

Applied

If $\mathbb{Z}$ and $\mathbb{R}$ denote set of integers and set of real numbers respectively, then match List I with List II.

List-I	List-II
(A) $5x - 3 \leq 3x + 1$ , $x \in \mathbb{Z}$	(I) $x \in (-\infty, -3]$
(B) $3x + 17 \leq 2(1 - x)$ , $x \in \mathbb{R}$	(II) $x \in (-\infty, -1)$
(C) $13x + 17 \leq 2(1 - x)$ , $x \in \mathbb{R}$	(III) $\{......, -4, -3, .......,0,1\}$
(D) $\frac{2x + 3}{5} - 2 > \frac{3(x - 2)}{5}$ , $x \in \mathbb{Z}$	(IV) $\{......, -4, -3, -2\}$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 3

Correct Answer

Explanation

Q25:

2025: 29 May Shift 2

Algebra

>

Inequalities

Medium

Applied

If $\frac{1}{|x| - 3} \leq \frac{1}{2}$ , then value of $x$ :

$x \in (-\infty, -6) \cup (-3,3) \cup (5, \infty)$

$x \in (-\infty, 5) \cup (5, \infty)$

$x \in (-\infty, -3) \cup [3, \infty)$

$x \in (-\infty, -5] \cup (-3,3) \cup [5, \infty)$

Correct Answer

Option 4

Correct Answer

Explanation

Q26:

2025: 27 May Shift 1

Algebra

>

Inequalities

Medium

Applied

If $x, y \in \mathbb{R}$ then match List-I with List-II

List-I	List-II
(A) $\vert x\vert < \vert y\vert$	(I) iff $x^2 > y^2$
(B) $\vert x\vert > \vert y\vert$	(II) iff $x^2 \le y^2$
(C) $\vert x\vert \le \vert y\vert$	(III) iff $x^2 < y^2$
(D) $\vert x\vert \ge \vert y\vert$	(IV) iff $x^2 \ge y^2$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 2

Correct Answer

Explanation

Q27:

2025: 26 May Shift 2

Algebra

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Inequalities

Medium

Applied

The solution of $\frac{7x+12}{x-9} < 4$ ; $\neq 9$ is:

$\{x: 9 < x < 16; x \in \mathbb{R}\}$

$\{x: -9 < x < -16; x \in \mathbb{R}\}$

$\{x: -16 < x < 9; x \in \mathbb{R}\}$

$\{x: -16 < x < -9; x \in \mathbb{R}\}$

Correct Answer

Option 3

Correct Answer

Explanation

Q28:

2025: 22 May Shift 2

Algebra

>

Inequalities

Medium

Common

The solution set of inequality $3x + 5y < 4$ is

an open half plane not containing the origin

an open half plane containing the origin

the whole $xy$ - plane not containing the line $3x+5y = 4$

a closed half plane containing the origin

Correct Answer

Option 2

Correct Answer

Explanation

Q29:

2025: 22 May Shift 1

Algebra

>

Inequalities

Easy

Applied

The solution set of the inequation $4x + 3y > 5$ is

half plane that contains the origin

open half plane not containing the origin

whole xy-plane except the points lying on the line $4x + 3y = 5$

lying only on first quadrant

Correct Answer

Option 2

Correct Answer

Explanation

Q30:

2025: 22 May Shift 1

Algebra

>

Inequalities

Medium

Applied

If $\frac{1}{x^2} - \frac{1}{x} > 0$ , then $x$ lies in the interval

$(-\infty, 0)$

$(-\infty, 0) \cup (0, 1)$

$(-\infty, 1)$

$(1, \infty)$

Correct Answer

Option 2

Correct Answer

Explanation

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