Class 11 Maths Chapter 5 Linear Inequalities – Exercise 5.2 NCERT Solutions

Introduction

Exercise 5.2 focuses on linear inequalities in two variables. You will learn how to represent inequalities graphically, identify solution regions, and apply these concepts to real‑life problems. This exercise builds the foundation for linear programming and optimization.

Key Concepts

1. Linear Inequality in Two Variables: An inequality of the form

$$ax+by+c\le 0,ax+by+c\ge 0,ax+by+c<0,ax+by+c>0$$

where $a,b,c\in \mathbb{R},a^2+b^2\mathrm{\ne }0$.

2. Graphical Representation:

   • Draw the line $ax+by+c=0$.

   • Choose a test point (usually origin) to check inequality.

   • Shade the region satisfying inequality.

3. Boundary Condition:

   • If inequality is strict ($<,>$), boundary line is dotted.

   • If inequality is non‑strict ($\le ,\ge$), boundary line is solid.

NCERT Questions with Solutions (10)

Q1. Represent graphically $x+y\le 5$. Line: $x+y=5$. Region: below line including boundary.

Q2. Represent graphically $x+y\ge 5$. Line: $x+y=5$. Region: above line including boundary.

Q3. Represent graphically $2x+y<6$. Line: $2x+y=6$. Region: below line, boundary dotted.

Q4. Represent graphically $2x+y\ge 6$. Line: $2x+y=6$. Region: above line including boundary.

Q5. Represent graphically $x-y>2$. Line: $x-y=2$. Region: above line, boundary dotted.

Q6. Represent graphically $x-y\le 2$. Line: $x-y=2$. Region: below line including boundary.

Q7. Represent graphically $x\ge 0$. Region: right half‑plane including y‑axis.

Q8. Represent graphically $y\ge 0$. Region: upper half‑plane including x‑axis.

Q9. Represent graphically $x\le 0$. Region: left half‑plane including y‑axis.

Q10. Represent graphically $y\le 0$. Region: lower half‑plane including x‑axis.

FAQs (10)

1. What is linear inequality in two variables? Inequality involving $x$ and $y$.

2. How to represent solution? Graphically on coordinate plane.

3. What is boundary line? Line corresponding to equality.

4. When is boundary solid? For $\le ,\ge$.

5. When is boundary dotted? For $<,>$.

6. What is feasible region? Region satisfying inequality.

7. Can solution be infinite? Yes, region contains infinitely many points.

8. What is test point method? Substitute point to check region.

9. Why use graphical method? Easy visualization of solution set.

10. Why is this exercise important? It builds foundation for linear programming.

Conclusion

Exercise 5.2 has 10 solved questions and 10 FAQs that strengthen your understanding of linear inequalities in two variables. This builds the foundation for optimization problems in Class 11 Maths.

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New Syllabus- Class 11 Maths Chapter 5 Linear Inequalities – Exercise 5.2 NCERT Solutions