NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 are the part of NCERT Solutions for Class 11 Maths. Here you can find the NCERT Solutions for Class 11 Maths chapter 6 Linear Inequalities Ex 6.2.


Solve the following inequalities graphically in two-dimensional plane.

Ex 6.2 Class 11 Maths Question 1.

x + y < 5

Solution.
We draw the graph of the equation x + y = 5.

This line passes through the points (0, 5) and (5, 0). The line x + y = 5 is represented by AB. Now, consider the inequality, x + y < 5

Put x = 0, y = 0
0 + 0 = 0 < 5, which is true.

So, the origin O lies in the plane x + y < 5.
The shaded region represents the inequality x + y < 5.

 

Ex 6.2 Class 11 Maths Question 2.

2x + y ≥ 6

Solution.
We draw the graph of the equation 2x + y = 6
The line passes through the points (0, 6) and (3, 0).
The line 2x + y = 6 is represented by AB.

Now, consider the inequality, 2x + y ≥ 6
Put x = 0, y = 0
0 + 0 ≥ 6, which does not satisfy this inequality.

Origin does not lie in the region of 2x + y ≥ 6.
The shaded region represents the inequality 2x + y ≥ 6.


Ex 6.2 Class 11 Maths Question 3.

3x + 4y ≤ 12

Solution.
We draw the graph of the equation 3x + 4y = 12.

The line passes through the points (4, 0) and (0, 3). This line is represented by AB.

Now, consider the inequality 3x + 4y ≤ 12.
Putting x = 0, y = 0, we get 0 + 0 = 0 ≤ 12, which is true.

Origin lies in the region of 3x + 4y ≤ 12.

The shaded region represents the inequality 3x + 4y ≤ 12.


Ex 6.2 Class 11 Maths Question 4.

y + 8 ≥ 2x

Solution.
Given inequality is y + 8 ≥ 2x.
We draw the graph of the equation y + 8 = 2x
The line passes through the points (4, 0) and (0, -8).
This line is represented by AB.

Now, consider the inequality y + 8 ≥ 2x.
Putting x = 0, y = 0, we get
0 + 8 ≥ 0, which is true.

Origin lies in the region of y + 8 ≥ 2x.
The shaded region represents the inequality y + 8 ≥ 2x.


Ex 6.2 Class 11 Maths Question 5.

x – y ≤ 2

Solution.
The given inequality is x – y ≤ 2.
Let us draw the graph of the line x – y = 2.
The line passes through the points (2, 0) and (0, -2).
This line is represented by AB.

Now, consider the inequality x – y ≤ 2.
Putting x = 0, y = 0, we get
0 – 0 ≤ 2, which is true.

Origin lies in the region of x – y ≤ 2.
The shaded region represents the inequality x – y ≤ 2.


Ex 6.2 Class 11 Maths Question 6.

2x – 3y > 6

Solution.
Let us draw the graph of line 2x – 3y = 6.
The line passes through the points (3, 0) and (0, -2)
AB represents the equation 2x – 3y = 6.
Now, consider the inequality 2x – 3y > 6.
Putting x = 0, y = 0, we get
0 – 0 > 6, which is not true.
Origin does not lie in the region of 2x – 3y > 6.

The shaded region represents the inequality 2x – 3y > 6.

 

Ex 6.2 Class 11 Maths Question 7.
-3x + 2y ≥ -6

Solution.
Let us draw the graph of the line -3x + 2y = -6
The line passes through the points (2, 0) and (0, -3).
The line AB represents the equation -3x + 2y = -6.
Now, consider the inequality -3x+ 2y ≥ -6.
Putting x = 0, y = 0, we get
0 + 0 ≥ -6, which is true.
Origin lies in the region of -3x + 2y ≥ -6.

The shaded region represents the inequality -3x + 2y ≥ –6.


Ex 6.2 Class 11 Maths Question 8.

3y – 5x < 30

Solution.
The given inequality is 3y – 5x < 30.
Let us draw the graph of the line 3y – 5x = 30.
The line passes through the points (-6, 0) and (0, 10).
The line AB represents the equation 3y – 5x = 30.
Now, consider the inequality 3y – 5x < 30.
Putting x = 0, y = 0, we get
0 – 0 < 30, which is true.
Origin lies in the region of 3y – 5x < 30.

The shaded region represents the inequality 3y – 5x < 30.


Ex 6.2 Class 11 Maths Question 9.

y < -2

Solution.
The given inequality is y < -2
Let us draw the graph of the line y = -2.
The line AB represents the equation y = -2.

Now, consider the inequality y < -2.
Putting y = 0, we get
0 < -2, which is not true.

Origin does not lie in the region of y < -2.

The solution region is the shaded region below the line.
Hence, every point below the line (excluding the line) is the solution region.


Ex 6.2 Class 11 Maths Question 10.

x > -3

Solution.
Let us draw the graph of x = -3.
AB represents the line x = -3.
Now, consider the inequality x > -3.

Putting x = 0, we get, 0 > -3, which is true.
Origin lies in the region of x > -3.

The graph of the inequality x > -3 is shown in the figure by the shaded region.


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