# NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities

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NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities: In earlier classes, we have studied equations of one variable and two variables and solved many problems based on this. It is not always possible to translate a problem into equations, for example, the height of all the members in your family is less than 180 cm. An auditorium can occupy at most 120 tables or chairs or both. Here we write statements involving the sign ‘’ '>' (greater than), ‘≤’ (less than or equal) and ≥ (greater than or equal), '<' (less than) "which are known as inequalities.  In this NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities we will study about inequalities in one variable and two variables. Linear inequalities are used in various field of Mathematics and Science. For example, inequalities are used in problems of cost estimation subjected to many constraints.

An example which uses the concept mentioned in NCERT Solutions for Class 11 is given below.

A manufacturing unit makes two models p and q of a product. Each piece of p requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of q requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The manufacturing uni makes a profit of Rs 8000 on each piece of p and Rs 12000 on each piece of Model q. How many pieces of Model p and Model q should be manufactured per week to realise a maximum profit?

The above problem can be formulated using linear inequalities and can be solved using linear programming which we will study in NCERT Class 12 Maths.

The above problem is formulated as follows.

Let x is the number of pieces of Model p and y is the number of pieces of Model q

We have to maximize the profit Z= 8000x+12000y subjected to the following constraints

$\\9x+12y\leq 180 \(fabricating \ constraint)\\x+3y\leq 30\ (finishing\ constraint)$

Thus here the concept of inequality is used in formulating the constraints.

## The main topics of the NCERT Class 11 Maths Chapter 6 Linear Inequalities are given below:

6.1 Introduction

6.2 Inequalities

6.3 Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation

6.4 Graphical Solution of Linear Inequalities in Two Variables

6.5 Solution of System of Linear Inequalities in Two Variables

In the NCERT Solutions of this chapter contains many questions for practice.

## The NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities are given below:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities - Exercise 6.1

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities- Exercise 6.2

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-  Exercise 6.3

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities- Miscellaneous

## NCERT Solutions for Class 11 Mathematics

 Chapter-1 Sets Chapter-2 Relations and Functions Chapter-3 Trigonometric Functions Chapter-4 Principle of Mathematical Induction Chapter-5 Complex Numbers and Quadratic equations Chapter-7 Permutation and Combinations Chapter-8 Binomial Theorem Chapter-9 Sequences and Series Chapter-10 Straight Lines Chapter-11 Conic Section Chapter-12 Introduction to Three Dimensional Geometry Chapter-13 Limits and Derivatives Chapter-14 Mathematical Reasoning Chapter-15 Statistics Chapter-16 Probability

## NCERT Solutions for Class 11- Subject wise

 NCERT Solutions for Class 11 Biology NCERT Solutions for Class 11 Maths NCERT Solutions for Class 11 Chemistry NCERT Solutions for Class 11 Physics

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