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Chapter 5 · Class XI Mathematics · MCQ Practice

MCQ Practice Arena

Linear Inequalities

Solve Faster, Score Higher — Master the Sign-Flip Rule

📋 50 MCQs ⭐ 0 PYQs ⏱ 75 sec/Q

🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs

10Easy

18Medium

22Hard

0PYQs

75 secAvg Time/Q

4Topics

Easy 20% Medium 36% Hard 44%

Why Practise These MCQs?

JEE MainCBSEBITSAT

Linear Inequalities MCQs are among the fastest to solve — most take under 60 seconds. JEE Main asks 1–2 questions on solution sets and modulus inequalities. CBSE objective section tests graphical representation. BITSAT includes systems of inequalities. This chapter is a reliable marks-saver.

Topic-wise MCQ Breakdown

One-Variable Inequalities34 Q

Compound Inequalities10 Q

Fractional Inequalities6 Q

Word Problems0 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\mathrm{Multiply/divide\ by\ negative\ →\ flip\ inequality}$

$|x| < a ⟺ −a < x < a$

$|x| > a ⟺ x < −a or x > a$

$\mathrm{a < x < b\ on\ number\ line:\ open\ interval\ (a,b)}$

MCQ Solving Strategy

The golden rule: whenever you multiply or divide both sides by a negative number, flip the inequality sign — this single rule causes 60% of errors. For |x| < a type MCQs, always split into −a < x < a immediately. For graphical two-variable questions, shade the correct half-plane by testing the origin.

⚠ Common Traps & Errors

⚠Forgetting to flip inequality when dividing by negative
⚠|x−2| < 3 gives −1 < x < 5, not −3 < x < 3
⚠Open vs closed circles on number line (< vs ≤)
⚠Origin test fails if origin lies on the boundary line

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Solve basic linear inequality, shade on number line

② Medium

Modulus inequalities, intersection of two solution sets

③ Hard

System of three inequalities, word problems with constraints

★ PYQ

JEE Main — solution set as interval; CBSE — graphical shading

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Permutations & Combinations MCQs

🎯 Knowledge Check

Maths — LINEAR INEQUALITIES

50 Questions Class 11 MCQs

Which of the following represents a linear inequality in one variable?
(Class XI – Basics)

a a. $2x + 3 = 7$ b b. $x^2 - 1 < 0$ c c. $3x - 5 > 0$ d d. $x^2 = 4$

Solve the inequality $x - 4 \le 0$.
(Class XI – Basics)

a a. $x \le 4$ b b. $x < 4$ c c. $x \ge 4$ d d. $x > 4$

The solution set of $2x > 6$ is:
(Class XI – Basics)

a a. $x > 2$ b b. $x < 3$ c c. $x > 3$ d d. $x \ge 3$

Which symbol represents “less than or equal to”?
(Class XI – Basics)

a a. $<$ b b. $>$ c c. $\le$ d d. $\ge$

If $x < 5$, then which of the following is a solution?
(Class XI – Basics)

a a. $6$ b b. $5$ c c. $4$ d d. $7$

Solve $3x + 1 \ge 7$.
(Class XI – Easy)

a a. $x \ge 1$ b b. $x \le 2$ c c. $x \ge 2$ d d. $x > 1$

Solve $5x - 10 < 0$.
(Class XI – Easy)

a a. $x < 2$ b b. $x > 2$ c c. $x \le 2$ d d. $x \ge 2$

The solution of $-2x > 6$ is:
(Class XI – Easy)

a a. $x > -3$ b b. $x < -3$ c c. $x > 3$ d d. $x < 3$

Solve $4 - x \le 1$.
(Class XI – Easy)

a a. $x \le 3$ b b. $x \ge 3$ c c. $x < 3$ d d. $x > 3$

Which of the following is not a solution of $x \ge -1$?
(Class XI – Easy)

a a. $-1$ b b. $0$ c c. $2$ d d. $-2$

Solve the inequality $2( x - 3 ) > x + 1$.
(Class XI – Moderate)

a a. $x > 7$ b b. $x < 7$ c c. $x > 5$ d d. $x < 5$

The solution of $x + 5 < 2x - 1$ is:
(Class XI – Moderate)

a a. $x < 6$ b b. $x > 6$ c c. $x \le 6$ d d. $x \ge 6$

Solve $3x + 2 \le 2x + 5$.
(Class XI – Moderate)

a a. $x \le 3$ b b. $x \ge 3$ c c. $x < 3$ d d. $x > 3$

Solve $\dfrac{x}{2} > 3$.
(Class XI – Moderate)

a a. $x > 6$ b b. $x < 6$ c c. $x \ge 6$ d d. $x \le 6$

Which of the following satisfies $2x - 1 \ge 3$?
(Class XI – Moderate)

a a. $1$ b b. $2$ c c. $0$ d d. $-1$

Solve $\dfrac{3x - 1}{2} < 4$.
(Class XI – Moderate)

a a. $x < 3$ b b. $x < 5$ c c. $x > 3$ d d. $x > 5$

Solve $5 - 2x > 1$.
(Class XI – Moderate)

a a. $x < 2$ b b. $x > 2$ c c. $x \le 2$ d d. $x \ge 2$

Solve $7x - 3 \ge 4x + 6$.
(Class XI – Moderate)

a a. $x \ge 3$ b b. $x \le 3$ c c. $x > 3$ d d. $x < 3$

The solution of $-x + 4 \le 1$ is:
(Class XI – Moderate)

a a. $x \ge 3$ b b. $x \le 3$ c c. $x > 3$ d d. $x < 3$

Solve $2(3x + 1) \le 4x + 10$.
(Class XI – Moderate)

a a. $x \le 4$ b b. $x \ge 4$ c c. $x < 4$ d d. $x > 4$

Solve $1 < 2x + 3 \le 7$.
(Class XI – Higher)

a a. $-1 < x \le 2$ b b. $-1 \le x < 2$ c c. $-2 < x \le 2$ d d. $-1 < x < 2$

Solve $-3 \le x - 2 < 4$.
(Class XI – Higher)

a a. $-1 \le x < 6$ b b. $-5 \le x < 2$ c c. $-3 \le x < 4$ d d. $-1 < x \le 6$

Solve $2 \le 3x + 1 < 8$.
(Class XI – Higher)

a a. $\dfrac{1}{3} \le x < \dfrac{7}{3}$ b b. $1 \le x < 3$ c c. $\dfrac{2}{3} \le x < \dfrac{8}{3}$ d d. $\dfrac{1}{3} < x \le \dfrac{7}{3}$

Solve $-1 < \dfrac{x}{2} \le 3$.
(Class XI – Higher)

a a. $-2 < x \le 6$ b b. $-1 < x \le 3$ c c. $-2 \le x < 6$ d d. $-1 \le x < 3$

Solve $4x - 1 > 2x + 3$.
(Class XI – Higher)

a a. $x > 2$ b b. $x < 2$ c c. $x \ge 2$ d d. $x \le 2$

Solve $\dfrac{2x + 3}{5} \ge 1$.
(Class XI – Higher)

a a. $x \ge 1$ b b. $x > 1$ c c. $x \ge 2$ d d. $x > 2$

Solve $3 - 2x < 7 - x$.
(Class XI – Higher)

a a. $x < 4$ b b. $x > 4$ c c. $x \le 4$ d d. $x \ge 4$

Solve $-4x \le 8$.
(Class XI – Higher)

a a. $x \le -2$ b b. $x \ge -2$ c c. $x < -2$ d d. $x > -2$

If $x$ satisfies $2x - 5 \le 1$, then:
(Class XI – Higher)

a a. $x \le 3$ b b. $x \ge 3$ c c. $x < 3$ d d. $x > 3$

Solve $5x + 2 > 3x - 4$.
(Class XI – Higher)

a a. $x > -3$ b b. $x < -3$ c c. $x \ge -3$ d d. $x \le -3$

Solve $\dfrac{x - 1}{3} < 2$.
(Class XI – Advanced)

a a. $x < 7$ b b. $x > 7$ c c. $x \le 7$ d d. $x \ge 7$

Solve $2x + 1 \le 3(x - 1)$.
(Class XI – Advanced)

a a. $x \ge 4$ b b. $x \le 4$ c c. $x > 4$ d d. $x < 4$

Solve $-2 \le 5 - x < 4$.
(Class XI – Advanced)

a a. $1 < x \le 7$ b b. $1 \le x < 7$ c c. $-1 \le x < 5$ d d. $1 < x < 7$

Solve $3x - 7 > 2x + 5$.
(Class XI – Advanced)

a a. $x > 12$ b b. $x < 12$ c c. $x \ge 12$ d d. $x \le 12$

Solve $\dfrac{5 - x}{2} \ge 1$.
(Class XI – Advanced)

a a. $x \le 3$ b b. $x \ge 3$ c c. $x < 3$ d d. $x > 3$

Solve $x - 3 \le 2x + 1$.
(Class XI – Advanced)

a a. $x \ge -4$ b b. $x \le -4$ c c. $x > -4$ d d. $x < -4$

Solve $4( x - 2 ) < 2( x + 1 )$.
(Class XI – Advanced)

a a. $x < 5$ b b. $x > 5$ c c. $x \le 5$ d d. $x \ge 5$

Solve $-3x + 2 > -x - 4$.
(Class XI – Advanced)

a a. $x < 3$ b b. $x > 3$ c c. $x \le 3$ d d. $x \ge 3$

Solve $2 \le \dfrac{3x - 1}{2} < 5$.
(Class XI – Advanced)

a a. $\dfrac{5}{3} \le x < \dfrac{11}{3}$ b b. $1 \le x < 4$ c c. $\dfrac{3}{2} \le x < \dfrac{7}{2}$ d d. $\dfrac{5}{3} < x \le \dfrac{11}{3}$

Solve $-5 < 2 - x \le 1$.
(Class XI – Advanced)

a a. $1 \le x < 7$ b b. $1 < x \le 7$ c c. $-3 \le x < 4$ d d. $-3 < x \le 4$

Solve $\dfrac{2x - 3}{4} > \dfrac{x + 1}{2}$.
(Competitive – JEE Level)

a a. $x > 5$ b b. $x < 5$ c c. $x \ge 5$ d d. $x \le 5$

Solve $3 - \dfrac{x}{2} \le 1$.
(Competitive – JEE Level)

a a. $x \ge 4$ b b. $x \le 4$ c c. $x > 4$ d d. $x < 4$

Solve $5x + 1 > 2(2x + 3)$.
(Competitive – JEE Level)

a a. $x > 5$ b b. $x < 5$ c c. $x \ge 5$ d d. $x \le 5$

Solve $\dfrac{3x - 5}{2} \le \dfrac{x + 1}{4}$.
(Competitive – JEE Level)

a a. $x \le 3$ b b. $x \ge 3$ c c. $x < 3$ d d. $x > 3$

Solve $7 - 2x \ge 3x - 8$.
(Competitive – JEE Level)

a a. $x \le 3$ b b. $x \ge 3$ c c. $x < 3$ d d. $x > 3$

Solve $2(x + 1) > 3(x - 2)$.
(Competitive – JEE Level)

a a. $x < 8$ b b. $x > 8$ c c. $x \le 8$ d d. $x \ge 8$

Solve $-1 \le \dfrac{2x + 3}{3} < 3$.
(Competitive – JEE Level)

a a. $-3 \le x < 3$ b b. $-3 < x \le 3$ c c. $-6 \le x < 6$ d d. $-6 < x \le 6$

Solve $\dfrac{5 - 3x}{2} > \dfrac{1 - x}{4}$.
(Competitive – JEE Level)

a a. $x < 3$ b b. $x > 3$ c c. $x \le 3$ d d. $x \ge 3$

Solve $4x - 1 < 3( x + 2 )$.
(Competitive – JEE Level)

a a. $x < 7$ b b. $x > 7$ c c. $x \le 7$ d d. $x \ge 7$

Solve $-2 \le 3 - 2x < 4$.
(Competitive – JEE Level)

a a. $-\dfrac{1}{2} < x \le \dfrac{5}{2}$ b b. $-\dfrac{1}{2} \le x < \dfrac{5}{2}$ c c. $-\dfrac{5}{2} \le x < \dfrac{1}{2}$ d d. $-\dfrac{5}{2} < x \le \dfrac{1}{2}$

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Linear Inequalities Class 11 MCQs – 50 Questions with Answers | NCERT Chapter 5

Linear Inequalities Class 11 MCQs – 50 Questions with Answers | NCERT Chapter 5 — Complete Notes & Solutions · academia-aeternum.com

Linear Inequalities form a foundational pillar of NCERT Class XI Mathematics and act as a gateway to higher algebra, calculus, coordinate geometry, and optimization problems encountered in competitive examinations. Unlike equations, inequalities demand logical precision, careful handling of symbols, and a clear understanding of solution sets rather than single values. The following set of multiple-choice questions has been meticulously designed to strengthen conceptual clarity, procedural…

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Linear Inequalities

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — LINEAR INEQUALITIES

Frequently Asked Questions

Recent Posts

LINEAR INEQUALITIES — Learning Resources

Let's Connect

Linear Inequalities

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — LINEAR INEQUALITIES

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