Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities

Kerala State Board New Syllabus Plus One Maths Chapter Wise Previous Questions and Answers Chapter 6 Linear Inequalities.

Kerala Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities

Plus One Maths Linear Inequalities 4 Marks Important Questions

Question 1.
i) Draw the graphs of 2x + 3y = 24 and x + y = 9 (IMP-2011)
ii) Solve the following system of inequalities graphically;
2x + 3y ≤ 24,
x + y ≤ 9, x, y ≥ 0
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 1
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 2

Question 2.
i) Solve 4x – 5 < 7, when x is a real number. (IMP-2012)
ii) Solve the following system of inequalities
graphically. 3x + 4y ≤ 12, x ≥ 0, y ≥ 0
Answer:
i) 4x – 5 < 7 => 4x < 12 => x < 3
ii) 3x + 4y ≤ 12, x ≥ 0, y ≥ 0
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 3

Question 3.
Solve: 4x + 3 < 3x + 7 represent the solution on the real line. (MARCH-2013)
ii) Solve the following system of inequalities graphically.
3x + 2y ≤ 12;
x,y ≥ 0
Answer:
i) 4x + 3 < 3x + 7 => 4x – 3x < 7 – 3 => x < 4
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 4

Question 4.
i) Represent the inequality x ≥ – 3 on a number line. (IMP-2014)
ii) Solve the following inequalities graphically:
x + y≥5;
x – y≤ 3
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 5

Question 5.
The interval representing the solution of the inequality 3x-1 ≥ 5, x∈R is (MARCH-2015)
a) [5,∞) b) [2, ∞)
c) [3,∞) d) (— ∞, ∞)
ii) Solve the system of inequality graphically
x + 2y ≤ 8,2x + y ≤ 8,
x ≥ 0,y ≥ 0
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 6

Question 6.
i) Which among the following is the interval corresponding to the inequality – 2 < x ≤ 3 . (MARCH-2016)
(a) [- 2,3]
(b) [- 2,3)
(c) (- 2,3]
(d) (- 2,3)
ii) Solve the following equation.
2x + y ≥ 4;
x + y ≤ 3;
2x – 3y ≤ 6.
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 7

Question 7.
i) Which among the following inequality represents the intervals [2,∞)
a) x – 3 ≥ 5, x∈R
b) 3x – 3 ≥5, x∈R
c) 3x – 1≥ 3, x∈R
d) 3x – 1 ≥ 5, x∈R
ii) Solve the following system of inequalities graphically. 3x + 2y ≤ 12; x ≥ 1; y ≥ 2
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 8

Plus One Maths Linear Inequalities 6 Marks Important Questions

Question 1.
i) Solve the inequality 3(x – 1) ≤ 2(x – 3)  (MARCH-2010)
ii) Solve the following system of inequalities graphically. 5x + 4y ≤ 20; x ≥ 1, y ≥ 2
Answer:
i) 3(x – 1) ≤ 2(x – 3) =>3x – 3 ≤2x – 6
=>3x – 2x ≤ 3 – 6
=> x ≤ – 3
ii) 5x + 4y = 20
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 9

Question 2.
i) 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 final examinations? (IMP-2010)
ii) Solve the following system of inequalities graphically 2x + y ≥6; 3x + 4y ≤12
Answer:
Let x denote the marks of arathi in first examination. then mark in second exam and third exam are x +5 and x + 10 respectively. Given average in three examinations is atleast 80.
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 10

Question 3.
i) Solve the inequality
2(2x + 3) – 10 < 6(x – 2) (MARCH-2011)
ii) Solve the following inequalities graphically. system of
x – 2y < 3;
3x + 4y ≥ 12; x,y ≥ 0
Answer:
i) 2(2x + 3) – 10 < 6(x – 2)
=> 4x + 6 – 10 ≤ 6x – 12
=> – 2x ≤ -12 + 4
=> – 2x ≤ – 8
=> x ≥ 4
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 11
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 12

Question 4.
i) Find all pairs of consecutive odd natural numbers, both of which are smaller than 10, such that their sum is more than 11. (IMP-2012)
ii) Solve 2x + y ≤ 6 graphically.
Answer:
i) Consecutive odd natural numbers be x and x+2. Then,
x + x + 2 > 11;
x + 2 < 10
=> 2x > 11 – 2;
x < 10 – 2
=> x > 9/5 = 4.5;
x < 8
5 ≤ x < 8 Therefore x can take values 5,7.
Hence the pairs are (5,7),(7,9)
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 13

Question 5.
i) Solve the inequality: 3(2 – x) ≥ 2(1 – x)  (MARCH-2013)
ii) Solve the following system of inequalities graphically.
2x + y ≥ 4;
x + y ≤ 3;
2x – 3 ≤ 6
Answer:
i) 3(2 – x) ≥ 2(1 – x)
=> 6 – 3x ≥ 2 — 2x
– 3x + 2x ≥ 2 – 6
=>- x ≥ – 4
=> x ≤ 4
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 14

Question 6.
i) Solve: 5x – 3 < 3x + l (MARCH-2014)
ii) Solve the following inequalities graphically.
x + 2y ≤ 8;
2x + y ≤ 8;
x,y ≥ 0
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 15

Question 7.
i) Raju obtained 70 and 60 marks in first two examinations. Find the minimum mark he should get in the third examination to have an average of atleast 50 marks. (IMP-2013)
ii) Solve the following system of inequalities graphically.
3x + 2y ≤ 12;
x ≥ 1;
y ≥ 2
Answer:
i) Let x be the mark obtained by Raju in third exam. Then,
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 16

Question 8.
i) Solve: 5x + 3 < 2x + 7 represent the solution on the real line. (MARCH-2014)
ii) Solve the following system of inequalities graphically.
x + 2y ≤ 8;
2x + y ≤ 8;
x, y ≥ 0
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 17

Question 9.
i) Solve: 7x + 3 < 5x + 9 represent the solution on the real line. (MARCH-2014)
ii) Solve the following system of inequalities graphically.
x + 2y ≤ 8;
2x + y ≤ 8;
x, y ≥ 0
Answer:
i)
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 18
ii)
15

Question 10.
i) Solve 10x – 23 < 3x + 5
ii) Solve the following system of inequalities graphically: 3x + 5y ≤ 15; 5x + 2y ≤ 10; x,y ≥ 0 (IMP-2014)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 19

Question 11.
i) Solve; 7x + 3 ≤ 5x + 9; x∈R . Express the solution on a number line.  (IMP-2015)
ii) Solve graphically; 3x + 4y ≤ 60;
x + 3y ≤ 30;
x,y ≥ 0.
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 20

Question 12.
Solve the inequality \(\frac{x}{3}>\frac{x}{2}+1\) (MARCH-2017)
Solve the system of inequality graphically
2x + y > 6,3x + 4y ≤ 12
Answer:
i) 2x > 3x + 6
=> – x > 6
=> x < – 6
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 6 Linear Inequalities 21

Leave a Comment