## Kerala Plus One Maths Chapter Wise Previous Questions and Answers Chapter 6 Linear Inequalities

Question 1.

a. Solve the inequality

b. Represent the solution on a number line. [March-2018]

Answer:

Question 2.

The graphical solution of a system of linear inequalities is shown in the figure.

a. Find the equation of the lines L_{1}, L_{2}, L_{3 }b. Find the inequalities representing the solution region .[March – 2018]

Answer:

Question 3.

a. Solve the inequality

b. Solve the system of inequalities I graphically:

2x+y>6

3x + 4y≤12 [March-2017]

Answer:

.

Question 4.

a. Which among the following is the interval corresponding to the inequality -2<x≤3?

i. [-2,3]

ii. [-2,3)

iii. (-2,3]

iv. (-2,3)

b. Solve the following inequalities graphically

2x + y≥ 4

x + y <3

2x-3y <6

Answer:

a. iii) (-2, 3]

b. 2x + y = 4

Solution region:

2x + y>4

⇒ 0 >4, which is false. || by putting x = 0, y = 0 Hence shade the half plane, which does not contain the origin.

x+y<3

⇒ 0 ≥ 3, which is true.

Hence shade the half plane, which contains the origin.

2x-3y≤6

⇒ 0≤6, which is true.

Hence shade the half plane, which contains the origin. The common region shown in the figure is the solution region.

Question 5.

a. The interval representing the solution of the inequality 3x -1 ≥ 5, x ∈ R is ………..

i. [5, ∞)

ii. [2, ∞)

iii. [3, ∞)

iv. (- ∞, ∞)

b. Solve the system of inequalities graphically.

x + 2y ≤ 8,2x + y ≤ 8, x ≥c [March-2015]

Answer:

a. 3x -1 > 5 3

x ≥6

x ≥2

ie.,x ∈[2, ∞)

b. Shaded region is the solution of the inequalities.

(0, 0) is on the plane. So the shaded region is the solution.

Question 6.

Solve 7x + 3<5x + 9 and represent the solution on the number line. [March-2014]

Answer:

7x + 3<5x + 9 x<3

ie.,x ∈(-∞,3)

Question 7.

a. Solve 4x + 3 < 3x +7. Represent the solution on the real line.

b. Solve the following system of inequalities graphically.

3x + 2y ≤ 12

x ≥ 0, y ≥ 0 [March-2013]

Answer:

a. 4x + 3 < 3x + 7

4x -3x <7-3

x <4

x ∈ (- ∞, 4)

Question 8.

i. Solve the inequality(2x + 3) -10 <6(x – 2)

ii. Solve the following system of inequalities graphically,

x – 2y ≤ 8, 2x + y ≤ 8, x ≥ 0, y ≥ 0 [February-2013]

Answer:

Question 9.

a. Solve the inequality 3(2 – x) ≥ 2 (1 – x)

b. Solve the following system of inequalities graphically.

2x + y≥4; x + y ≤ 3,

2x – 3y ≤ 6 [March-2012]

Answer:

Question 10.

i. Solve the inequality (2x + 3) -10<6(x- 2)

ii. Solve the following system of inequalities graphically,

x – 2y ≤ 3, 3x + 4y≥12, x ≥ 0,y≥0. [March-2011]

Answer:

i. 2 (2x + 3) -10 < 6 (x – 2)

4x + 6- 10<6x-12 4x-4<6x-12

2x > 8; x > 4; x∈ (4,∞)

(0,0) is not on 3x + 4y > 12. so the shaded are is the solution.

Question 11.

i. Solve the inequality 3 (x -1) ≤ 2 (x – 3)

ii. Solve the following system of inequalities graphically.

5x + 4y≤ 20, x ≥1, y≥ 2. [March-2010]

Answer:

i. 3 (x -1) ≤ 2 (x – 3)

3x – 3≤ 2x – 6

3x-2x ≤ – 6 + 3; x ≤- 3

(0, 0) is not on 5x + 4y = 0. So the shaded region is the solution.

Question 12.

a. Arathi took 3 examinations in an year. The marks obtained by her in the second and third examinations are more than 5 and 10 respectively than in the first examination. If her average mark is at least 80 find the minimum mark that she should get in the first examination.

b. Solve the following system of inequalities graphically.

2x +y ≥6, 3x + 4y≤ 12. [September-2010]

Answer:

So the shaded region is the solution.

Question 13.

i. Solve the inequality

ii. Solve the following system of linear inequalities graphically:

x + 2y ≤8,2x + y≤8,x≥0,y≥0 [September-2009]

Answer:

ii.

Question 14.

a Solve the inequality 2 (2x+3)-10 <6(x- 2) when x is a real number.

b. Solve the following inequalities graphically

2x + y ≤ 24, x + y ≤ 11,2x + 5y ≤ 40, x≥0,y≥0 [March-2009]

Answer:

a.

2 (2x + 3) -10 < 6 (x – 2)

4x + 6- 10<6x-12 4x-4<6x-12

2x > 8; x > 4; x∈ (4,∞)

b. Drawing the graph of the lines

Question 15.

Solve the system of inequalities graphically.

i. 2x + y ≥8, x + 2y ≥10

ii. 4x+3 ≤ 6x+y [September-2008]

Answer:

(0, 0) is not on 2x + y≥ 3. So the shaded region is the solution of the system.

Question 16.

Draw the graph of the following system of in-equation and mark the solution.

2x + y- 3≥0, x-2y+1 ≤ 0, y ≤3 [June-2008]

Answer:

Shaded region is the solution of the system

Question 17.

i. Solve | x | < 5

ii. Represent the solution graphically. [February-2008]

Answer:

Question 18.

i. Draw the graph of x +y = 2 and 2x +3y= 6

ii. Shade the region satisfying the inequalities x + y ≤ 2,2x + 3y ≤ 6, x ≥ 0, y ≥ 0 [September – 2008]

Answer:

Question 19.

i. Solve the inequations. 2-3x≥ 2 (x+6), x∈R

ii. Represent the solution set graphically. [June-2007]

Answer:

2-3x≥2x+ 12,

-3x-2x≥12-2 -5x≥ 10,

5x≤ -10,x≤ -2 i.e., (-∞, -2]