# 6. Linear Inequalities

##### 4 LECTURES

• This page has links to complete syllabus of NCERT Chapter 6 Linear Inequalities based on syllabus recommended by CBSE based on class 11 maths.
• There are 4 video lectures having explanations from basic to advance concepts, each and every NCERT solutions, questions and all important examples. You can access them directly from the lecture menu or just scroll down the page.
• All lecture were uploaded on YouTube so for better learning experience here you will find link to YouTube Playlist of Chapter 6 Linear Inequalities.
• Also, there are detailed highlights of each video lecture with exact timestamp links so that you can easily access all topics and questions directly.
• Just click on the timestamp link and you will be redirected to video watch page at exactly that time.

##### 6(A) || NCERT Exercise 6.1 (Q1 to Q20)

00:05:55 Working with inequalities: Adding positive or negative numbers Subtracting positive or negative numbers Multiplying by positive or negative numbers Dividing by positive or negative numbers

00:18:10 Representing Real numbers in form of open intervals and closed intervals

00:23:15 NCERT Exercise 6.1 Question 1

00:25:45 NCERT Exercise 6.1 Question 2

00:28:45 NCERT Exercise 6.1 Question 3

00:33:55 NCERT Exercise 6.1 Question 4

00:36:55 NCERT Exercise 6.1 Question 5

00:39:45 NCERT Exercise 6.1 Question 6

00:41:05 NCERT Exercise 6.1 Question 7

00:42:35 NCERT Exercise 6.1 Question 9

00:43:55 NCERT Exercise 6.1 Question 11

00:46:25 NCERT Exercise 6.1 Question 13

00:47:45 NCERT Exercise 6.1 Question 15

00:49:45 NCERT Exercise 6.1 Question 8

00:50:55 NCERT Exercise 6.1 Question 10

00:52:05 NCERT Exercise 6.1 Question 12

00:53:55 NCERT Exercise 6.1 Question 14

00:55:25 NCERT Exercise 6.1 Question 16

00:58:35 NCERT Exercise 6.1 Question 17

00:59:55 NCERT Exercise 6.1 Question 18

01:01:05 NCERT Exercise 6.1 Question 19

01:02:15 NCERT Exercise 6.1 Question 20

##### 6(B) || Exercise 6.1 (Q21 to Q26) Exercise 6.2

00:00:54 NCERT Exercise 6.1 Question 21 Ravi obtained 70 and 75 marks in first two unit test. Find the minimum marks he should get in the third test to have an average of at least 60 marks.

00:06:14 NCERT Exercise 6.1 Question 22 To receive Grade ‘A’ in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita’s marks in first four examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain in fifth examination to get grade ‘A’ in the course.

00:09:14 NCERT Exercise 6.1 Question 23 Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

00:18:34 NCERT Exercise 6.1 Question 24 Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.

00:23:54 NCERT Exercise 6.1 Question 25 The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

00:26:54 NCERT Exercise 6.1 Question 26 A man wants to cut three lengths from a single piece of board of length 91cm. The second length is to be 3cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5cm longer than the second?

00:37:04 Graphical Representation of Inequalities

00:53:04 NCERT Exercise 6.2 Question 1

00:59:44 NCERT Exercise 6.2 Question 2

01:03:54 NCERT Exercise 6.2 Question 3

01:07:44 NCERT Exercise 6.2 Question 4

01:11:34 NCERT Exercise 6.2 Question 7

01:13:54 NCERT Exercise 6.2 Question 9

01:15:14 NCERT Exercise 6.2 Question 10

##### 6(C) || Exercise 6.3 (Q10 to Q15)

00:01:39 Working with system of inequalities

00:04:20 NCERT Exercise 6.3 Question 10

00:15:59 NCERT Exercise 6.3 Question 11

00:23:39 NCERT Exercise 6.3 Question 12

00:30:39 NCERT Exercise 6.3 Question 13

00:40:29 NCERT Exercise 6.3 Question 14

00:47:09 NCERT Exercise 6.3 Question 15

##### 6(D) || Miscellaneous Exercise

00:00:05 Working with double inequalities

00:01:17 NCERT Miscellaneous Exercise Question 1

00:04:07 NCERT Miscellaneous Exercise Question 2

00:05:37 NCERT Miscellaneous Exercise Question 3

00:08:37 NCERT Miscellaneous Exercise Question 4

00:09:57 NCERT Miscellaneous Exercise Question 5

00:11:47 NCERT Miscellaneous Exercise Question 6

00:18:47 NCERT Miscellaneous Exercise Question 7

00:22:27 NCERT Miscellaneous Exercise Question 8

00:24:57 NCERT Miscellaneous Exercise Question 9

00:27:27 NCERT Miscellaneous Exercise Question 10

00:30:57 NCERT Miscellaneous Exercise Question 11

00:33:57 NCERT Miscellaneous Exercise Question 12 A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

00:45:57 NCERT Miscellaneous Exercise Question 13 How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

00:54:17 NCERT Miscellaneous Exercise Question 14