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.
An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.
Based on the above information, answer the following questions :
2.
Find:
Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).
- \(\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}\)
- \(\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}\)
- \(\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}\)
- \(\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}\)
View Solution
3.
Find:

If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).
- \(0\)
- \(-2\)
- \(-1\)
- \(2\)
View Solution
4.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:
- \(-\frac{\pi}{2}\)
- \(-\frac{\pi}{4}\)
- \(\frac{\pi}{4}\)
- \(\frac{\pi}{2}\)
View Solution
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.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]
View Solution