NCERT Solutions For Class 11 Maths Chapter 6: Linear Inequalities

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NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities are given in the article. Linear inequalities are the expressions where there is a comparison between two values by the inequality symbols like, ‘<’, ‘>’, ‘≤’ or ‘≥’. NCERT Solutions Class 11 Maths Chapter 6 cover the introduction of linear inequalities, graphing of linear inequalities, and its examples in more precise manner.

Also check: Addition of Two Real Functions

Download: NCERT Solutions for Class 11 Mathematics Chapter 6 pdf

Class 11 Maths NCERT Solutions Chapter 6 Linear Inequalities

Class 11 Maths NCERT Solutions Chapter Chapter 6 Linear Inequalities are as provided below:

NCERT Solutions

Also check: Linear Inequalities Important Questions

Important Topics for Class 11 Maths NCERT Solutions Chapter 6 Linear Inequalities

Important Topics for Class 11 Maths NCERT Solutions Chapter 6 Linear Inequalities are elaborated below:

Introduction to Linear Inequalities

Linear inequalities are inequalities that have at least one linear algebraic expression. This means, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1.

There are 5 symbols that are used to represent linear inequalities:

Symbol Name	Symbol	Example
Not equal	≠	x ≠ 3
Less than	(<)	x + 7 < √2
Greater than	(>)	1 + 10x > 2 + 16x
Less than or equal to	(≤)	y ≤ 4
Greater than or equal to	(≥)	-3 - √3x ≥ 10

Please note: If p < q, then p is a number that is less than q. If p ≤ q, then it means that p is a number that is either less than q or is exactly equal to q. Likewise, the pattern is applicable on remaining two inequalities > (greater than) and ≥ (greater than or equal to).

Graphing of linear inequalities

To graph a linear inequality in two variables (say, x and y ), first we put y alone on one side. Consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line.

Steps for Graphing Linear Inequalities:

Step 1: Rearrange the equation so "y" is on the left and everything else on the right.

Step 2: Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)

Step 3: Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).

NCERT Solutions For Class 11 Maths Chapter 6 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 6 Linear Inequalities under different exercises are as follows:

Also check:

Unit Related Important Topics
Solving Inequalities	Relation between Degree and Radian	Sequence and Series

Also check:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Arithmetic

CBSE CLASS XII Related Questions

1.
If $ xy = e^{x - y} $, then find $ \frac{dy}{dx} $.
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2.
Find:

If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of $p$ and $q$.
- $p = -\frac{2}{3}, \, q = \frac{5}{3}$
- $p = -\frac{8}{3}, \, q = \frac{20}{3}$
- $p = \frac{20}{3}, \, q = -\frac{8}{3}$
- $p = 0, \, q = 0$
View Solution
3.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]
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4.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:
- $-\frac{\pi}{2}$
- $-\frac{\pi}{4}$
- $\frac{\pi}{4}$
- $\frac{\pi}{2}$
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5.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.
6.
A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is
- Reflexive only
- Reflexive and Transitive
- Symmetric and Transitive
- Symmetric only
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