The NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities Miscellaneous Exercise cover every question of the mixed exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
The Miscellaneous Exercise mixes every idea from the chapter, from double inequalities to word problems on temperature and mixtures. The exercise has 14 questions built around these skills:
- Solving a double inequality such as 3 ≤ 2x − 1 < 7 in one step.
- Finding the solution set of a linear inequality and writing it as an interval.
- Turning real situations about temperature, acid mixtures and IQ into inequalities.
Topics Covered in the Miscellaneous Exercise
This exercise brings together the full chapter. Students meet single inequalities, double inequalities and word problems in one place. The algebra rules are the same as Exercise 5.1, but the questions are longer and often need two conditions handled together.
- Double inequalities: solving a chain like −5 ≤ (5 − 3x)/2 ≤ 8 across all three parts.
- Solution as an interval: writing answers such as −1 < x ≤ 4 clearly.
- Word problems: the Fahrenheit to Celsius range, adding water or acid to a solution, and the IQ formula.
- Checking the sign rule: every division by a negative number still flips the sign.
- Combining conditions: some problems need two inequalities to both hold at once.
Important: in a double inequality, whatever you do to the middle part must be done to both outer parts at the same time.
Question-wise Breakdown of the Miscellaneous Exercise
The NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities Miscellaneous Exercise solve all 14 questions in order. The table below groups the questions by type so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Questions | What they ask | Skill tested |
|---|---|---|
| Q1 to Q6 | Solve single and double inequalities | Solving over the real numbers |
| Q7 to Q10 | Solve chained double inequalities and write the interval | Handling both bounds together |
| Q11 to Q14 | Word problems on temperature, acid mixtures and IQ | Forming an inequality |
The last four questions are the ones examiners like most, because they test whether students can turn a real situation into an inequality and solve it.
Key Formulas and Definitions for the Miscellaneous Exercise
This exercise uses the same rules as Exercise 5.1, plus two standard formulas that appear in its word problems. Students should keep these ready before solving.
| Rule / Formula | Meaning |
|---|---|
| Double inequality | A chain like a ≤ expression ≤ b, solved on all parts at once |
| Sign rule | Dividing or multiplying by a negative number reverses every sign in the chain |
| Interval answer | Writing the solution as a range, such as [2, 6) or −3 < x ≤ 5 |
| Temperature link | F = (9/5)C + 32, used to convert a Celsius range to Fahrenheit |
| IQ formula | IQ = (MA / CA) × 100, used in the last word problem |
Tip: in the mixture problems, let the unknown be the litres of water or acid added, then form the inequality for the required strength.
Common Mistakes in the Miscellaneous Exercise
Students lose marks in this exercise on longer, two-step slips. The list below covers the errors that show up most often in tests on the NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities Miscellaneous Exercise.
- Changing only one part of a double inequality. Every operation must hit all three parts.
- Forgetting to flip both signs when the middle part is divided by a negative number.
- Setting up the mixture word problem with the wrong quantity as the unknown.
- Writing the interval with the wrong bracket. Use ( ) for a strict sign and [ ] when the end is included.
Practice Questions for the Miscellaneous Exercise
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for the Miscellaneous Exercise.
Practice Card: Solved Practice Questions for Class 11 Maths Linear Inequalities Miscellaneous Exercise — attempt each question, then check the worked solution.
Other Exercises of Chapter 5 Linear Inequalities
Chapter 5 Linear Inequalities has one main exercise plus this Miscellaneous Exercise. Use the table to revise the one-variable basics in Exercise 5.1 first.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 5.1 | Class 11 Maths Linear Inequalities Exercise 5.1 Solutions |
More Class 11 Maths Linear Inequalities Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 5 Linear Inequalities are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Linear Inequalities Notes |
| Handwritten Notes | Class 11 Maths Linear Inequalities Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Linear Inequalities NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | You are here |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 11,930 Class 11 students conducted before the 2026 exams, 66% of students said the acid-mixture word problem was the hardest question in the Miscellaneous Exercise, while the straight double inequalities were rated the most reliable place to score full marks.
FAQs on NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities Miscellaneous Exercise
Linear Inequalities NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in the Class 11 Maths Chapter 5 Linear Inequalities Miscellaneous Exercise?
Ans. The Miscellaneous Exercise has 14 questions. It mixes single inequalities, double inequalities and word problems. The last few questions cover the Fahrenheit to Celsius temperature range, adding water or acid to a solution, and the IQ formula, which makes this the most exam-like exercise in the chapter.
Ques. How do you solve a double inequality in this exercise?
Ans. For a chain like 3 ≤ 2x − 1 < 7, add or subtract on all three parts together, then divide all three by the coefficient. If you divide by a negative number, reverse both signs. The final answer is an interval such as 2 ≤ x < 4.
Ques. What formula is used in the temperature word problem?
Ans. The temperature question gives a range in Fahrenheit and asks for the matching Celsius range. Use the relation F = (9/5)C + 32, substitute the two Fahrenheit bounds, and solve the double inequality for C. The answer comes out as a Celsius interval.
Ques. How do you approach the acid-mixture problem?
Ans. In the mixture problems, take the litres of water or acid added as the unknown. Write the amount of pure acid before and after, then form an inequality for the percentage the solution must stay within. Solving it gives the allowed range of litres.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities Miscellaneous Exercise free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities Miscellaneous Exercise are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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