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Subject specialists have created NCERT Exemplar Solutions for Class 11 Maths Chapter 6 Linear Inequalities, which includes thorough solutions for reference. All of the unsolved questions from the textbook’s exercises are answered here. The NCERT Exemplar Solutions for Class 11 provide useful solutions for improving conceptual knowledge and help in entrance examinations like JEE mains and advanced.
The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Exemplar Solutions for Class 11. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 11 pupils perform well in upcoming competitive exams.
The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.
The chapter Linear Inequalities is part of the unit Algebra in the second term Class 11 Maths CBSE Syllabus for 2021-22, and it includes three exercises and a random exercise to assist students fully comprehend the topics covered in the chapter. NCERT Exemplar Solutions for Class 11 Chapter 6 Linear Inequalities covers the following topics:
6.1 Introduction
An inequality is formed by two algebraic expressions or real numbers linked by any of the symbols ≤, ≥, <, and > For instance, if px + qy > 0, then 3a –19b<0. Students will learn how to solve word problems by translating them to inequalities in this lesson.
6.2 Inequalities
Real-life events that can be turned into linear inequalities are used to demonstrate this topic. There are also plenty of practice problems as well as solved examples.
6.3 Algebraic Solutions of Linear Inequalities in 1 Variable and their Graphical Representation
Students can learn the meaning of a solution of linear inequalities as well as the graphical depiction of these solutions in this assignment. In addition, the methods for solving linear inequalities have been demonstrated using examples.
6.4 Graphical Solution of Linear Inequalities in Two Variables
Students will be able to comprehend how to describe the solution of linear inequalities in two variables on the Cartesian plane after completing this course. They can also determine the solution zone for inequalities.
6.5 Solution of System of Linear Inequalities in Two Variables
The use of graphical methods to solve a system of linear inequalities in two variables is presented with numerous examples to assist students to grasp the topic better.
Exercise 6.1 Solutions 26 Questions
Exercise 6.2 Solutions 10 Questions
Exercise 6.3 Solutions 15 Questions
Miscellaneous Exercise On Chapter 6 Solutions 14 Questions
The following is a summary of the concepts covered in NCERT Exemplar Solutions for Class 11 Maths Chapter 6 of Infinity Learn:
- An inequality is formed by two real numbers or two algebraic expressions linked by the symbols, <, >, ≤ or ≥.
- Both sides of an inequality can have equal numbers added to (or taken from).
- Inequality can be multiplied (or divided) by the same positive value on both sides. The inequality is reversed when both sides are multiplied (or divided) by a negative value.
- The values of x that make an inequality a true statement are referred to as inequality solutions.
- Put a circle on the number a and a dark line to the left (or right) of the number a to indicate x <a (or x > a) on a number ‘a’.
- Put a dark circle on the number a and a dark line to the left (or right) of the number x to symbolize x ≤ a (or x ≥ a) on a number line.
- If the inequality has ≤ or ≥ sign, then the points on the line are also included in the inequality’s solutions, and the graph of the inequality lies to the left (below) or right (above) of the graph of the equality, which is represented by a black line that fulfils an arbitrary point in that area.
- If inequality has the symbol < or >, the points on the line are not included in the solutions, and the graph of the inequality is to the left (below) or right (above) of the graph of the corresponding equality, which is represented by a dotted line that fulfils an arbitrary point in that part.
- The solution area of a system of inequalities is the region that concurrently fulfils all of the system’s provided inequalities.
Key Features of NCERT Exemplar Solutions for Class 11 Maths Chapter 6- Linear Inequalities
The following ideas were discussed in BYJU’S answers for NCERT problems for Class 11 Maths Chapter 6: These solutions are precisely crafted to eliminate errors, ensuring that students receive full scores after practicing them.
- Linear inequalities have a specific meaning.
- The number line representation of algebraic solutions of linear inequalities in one variable.
- Linear inequalities in two variables are graphically solved.
- Finding a solution to systems of linear inequalities in two variables using a graphical technique.
Frequently Asked Questions
Does Infinity Learn give the most reliable answers in Chapter 6 of NCERT Exemplar Solutions for Class 11 Maths?
Infinity learn has the most exact and dependable NCERT Exemplar Solutions for Class 11 Maths Chapter 6. Students can quickly download the solutions, which are available in PDF format, and use them to prepare for the term - I test. The solutions are framed and prepared by a group of experienced academics with years of experience in the various areas. The most in-depth solutions to the exercise-by-exercise challenges have been compiled with the goal of assisting students in acing the first-term exam without anxiety.
Explain the steps to plot a graph of linear inequality covered in NCERT Exemplar Solutions for Class 11 Maths Chapter 6.
The equation should be set up so that 'y' is on the left side and the other terms are on the right. Plot the 'y' line (constant line when y <= or y >=) and the dotted line (when y< or y >). When y > or y >=, shade the region above the 'y' line, and when y< or y<=, shade the area below the 'y' line. Students can use the answers PDF to obtain a better understanding of the stages involved in producing the graph of a linear inequality.
Why Opt for Infinity Learn?
In this chapter Infinity Learn provides videos, notes, NCERT textbook solutions, other practice book solutions and assignments that help you learn the concepts and to memorise the concepts for entrance exams and board exams. Most important, Infinity learn provide instant doubt support by subject experts.
Question: List out the number of exercises present in NCERT Exemplar Solutions for Class 11 Maths Chapter 6 Linear Inequalities.
Answer: There are three exercises in this chapter and one random exercise that cover all of the themes. Each exercise’s total number of questions is listed below.
- 26 Questions in Exercise 6.1
- 10 Questions (Exercise 6.2)
- 15 Questions for Exercise 6.3
- 14 Questions for a Miscellaneous Exercise
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