Mathematics
MCQ | Class 11 | Chapter 06
Linear Inequalities
Multiple Choice Questions (MCQ)
- MCQ Based on the Linear inequalities.
- MCQ Based on the Graph of Linear Inequalities.
- MCQ Based on the average of numbers.
Features
- In this post given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations.
- Solution Hints are also given to some difficult problems.
- Each MCQ contains four options from which one option is correct.
Action Plan
- First of all students should Learn and write all basic points and Formulas related to the Linear Inequalities.
- Start solving the NCERT Problems with examples.
- Solve the important assignments on the Linear Inequalities Chapter 6 Class XI.
- Then start solving the following MCQ.
MCQ | CHAPTER 6 | CLASS 11
LINEAR INEQUALITIES
Question 1)
The length of a rectangle is three times the breadth. If the
minimum perimeter of the rectangle is 160 cm, then
(a) breadth >20 cm
(b) length <20 cm
(c) breadth x ≥20 cm
(d) length ≤ 20cm
Answer: (c)
Solution: Let x be the breadth of a rectangle.
So, length = 3x
Given that the
minimum perimeter of a rectangle is 160 cm. Thus,
⇒ 2 (3x + x)
≥ 160
⇒ 4x ≥ 80 ⇒ x ≥ 20
a) linear inequality
b) quadratic inequality
c) numerical inequality
d) literal inequality
Answer: c
Explanation: Since
here numbers are compared with inequality sign so, it is called numerical
inequality.
x is a whole number and 10x ≤ 50 then find solution set of x.
a) {0, 1, 2, 3, 4, 5}
b) {1, 2, 3, 4, 5}
c) {1, 2, 3, 4}
d) {0, 1, 2, 3, 4}
Answer: a
Explanation: 10x ≤ 50
Dividing by 10 on both sides, x ≤ (50/10) ⇒ x ≤ 5
Since x is a whole number so x = 0, 1, 2, 3, 4, 5.
(a) x ∈ (10, ∞)
(b) x ∈ [10, ∞)
(c) x ∈ (– ∞, 10]
(d) x ∈ [– 10, 10)
Answer: (a)
Solution:
Given, -3x + 17< -13
Subtracting 17 from both sides,
-3x + 17 – 17 < -13 – 17
⇒ -3x < -30
⇒ x > 10 {since the division by negative number inverts the inequality sign}
⇒ x ∈ (10, ∞)
2x + 1 > 5 then which is true?
a) x > 4
b) x < 4
c) x > 2
d) x < 2
Answer c
a) double inequality
b) quadratic inequality
c) numerical inequality
d) literal inequality
Answer: d
Explanation: Since a variable ‘x’ is compared
with number ‘5’ with inequality sign so it is called literal inequality.
x – 1 > – x + 7 then which is true?
a) x > 4
b) x < 4
c) x > 2
d) x < 2
Answer a
a) double inequality
b) quadratic inequality
c) numerical inequality
d) linear inequality
Answer b
obtained 20 and 25 marks in first two tests. Find the minimum marks he should
get in the third test to have an average of at least 30 marks.
a) 60
b) 35
c) 180
d) 45
Answer: d
|x −1| > 5, then
(a) x ∈
(– 4, 6)
(b) x ∈
[– 4, 6]
(c) x ∈
(– ∞, – 4) U (6, ∞)
(d) x ∈
[– ∞, – 4) U [6, ∞)
Answer: (c)
Solution: |x – 1| > 5
x – 1 < – 5
and x – 1 > 5
x < -4 and x
> 6
Therefore, x ∈
(-∞, -4) U (6, ∞)
all pairs of consecutive odd positive integers both of which are smaller than 8
such that their sum is more than 10.
a) (5, 7)
b) (3, 5), (5, 7)
c) (3, 5), (5, 7), (7, 9)
d) (5, 7), (7, 9)
Answer: a
(a) x ∈
[7, ∞)
(b) x ∈
(7, ∞)
(c) x ∈
(– ∞, 7)
(d) x ∈
(– ∞, 7]
Answer: (b)
Solution:
Given, |x –
7|/(x – 7) ≥ 0
This is possible
when x − 7 ≥ 0, and x – 7 ≠ 0.
Here, x ≥ 7 but
x ≠ 7
Therefore, x
> 7, i.e. x ∈ (7, ∞).
longest side of a triangle is 2 times the shortest side and the third side is 4
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.
a) 7
b) 9
c) 11
d) 13
Answer: d
Question 14): If
Ram has x rupees and he pay 40 rupees to shopkeeper then find range of x if
amount of money left with Ram is at least 10 rupees is given by inequation is
a) x ≥ 10
b) x ≤ 10
c) x ≤ 50
d) x ≥ 50
Answer
d
Explanation: Amount
left is at least 10 rupees i.e. amount left ≥ 10.
x – 40 ≥ 10
⇒ x ≥ 50.
3| ≥ 10, then
(a) x ∈
(– 13, 7]
(b) x ∈
(– 13, 7]
(c) x ∈
(– ∞, – 13] ∪ [7, ∞)
(d) x ∈
[– ∞, – 13] ∪ [7, ∞)
Answer: (d)
Solution:
Given, |x + 3| ≥
10
⇒ x + 3 ≤ – 10 or x + 3 ≥ 10
⇒ x ≤ – 13 or x ≥ 7
⇒ x ∈ (– ∞, –
13] ∪ [7, ∞)
+ y > 5. Which of the following will satisfy the given equation?
a) (1, 1)
b) (1, 2)
c) (2, 1)
d) (2, 2)
Answer d
3 < 6x +7, then x belongs to the interval
(a) (2, ∞)
(b) (-2, ∞)
(c) (-∞, 2)
(d) (-4, ∞)
Answer: (b)
Solution: Given, 4x + 3 < 6x + 7
Subtracting 3
from both sides,
4x + 3 – 3 <
6x + 7 – 3
⇒ 4x < 6x + 4
Subtracting 6x
from both sides,
4x – 6x < 6x
+ 4 – 6x
⇒ – 2x < 4 or
⇒ x > – 2 i.e., all the real numbers
greater than –2, are the solutions of the given inequality.
Hence, the
solution set is (–2, ∞), i.e. x ∈ (-2, ∞)
solution is to be kept between 77° F and 86° F. What is the range in temperature
in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is
given by F = 9/5 C + 32° ?
a) [15°, 20°]
b) [20°, 25°]
c) [25°, 30°]
d) [30°, 35°]
Answer c
Rohit has x rupees and he pay 40 rupees to shopkeeper then find range of x if
amount of money left with Rohit is at most 10 rupees is given by inequation
a) x ≥ 10
b) x ≤ 10
c) x ≤ 50
d) x ≥ 50
Answer: c
Explanation: Amount
left is at most 10 rupees i.e. amount left ≤ 10.
x – 40 ≤ 10 ⇒ x ≤ 50.
– 8 ≤ 5x – 3 < 7, we get
(a) –1/2 ≤ x ≤ 2
(b) 1 ≤ x < 2
(c) –1 ≤ x <
2
(d) –1 < x ≤
2
Answer: (c
Solution: Given,
– 8 ≤ 5x – 3 and 5x – 3 < 7
Let us solve
these two inequalities simultaneously.
– 8 ≤ 5x – 3 and
5x – 3 < 7 can be written as:
– 8 ≤ 5x –3 <
7
Adding 3, we get
– 8 + 3 ≤ 5x – 3
+ 3 < 7 + 3
⇒ –5 ≤ 5x < 10
Dividing by 5,
we get
–1 ≤ x < 2
x is a positive integer and 20x<100 then find solution set of x.
a) {0, 1, 2, 3, 4, 5}
b) {1, 2, 3, 4, 5}
c) {1, 2, 3, 4}
d) {0, 1, 2, 3, 4}
Answer: c
Explanation:
20x < 100
Dividing by 20 on both sides, x < (100/20) ⇒ x < 5
Since x is a positive integer so x = 1, 2, 3, 4.
x is a natural number and 20x ≤ 100 then find solution set of x.
a) {0, 1, 2, 3, 4, 5}
b) {1, 2, 3, 4, 5}
c) {1, 2, 3, 4}
d) {0, 1, 2, 3, 4}
Answer: b
Explanation: 20x ≤ 100
Dividing by 20 on both sides, x ≤ (100/20) ⇒ x ≤ 5
Since x is a natural number so x = 1, 2, 3, 4, 5.
the figure given below.
The interval at
which the value of x lies is
(a) x ∈
(– ∞, – 2)
(b) x ∈
(– ∞, – 2]
(c) x ∈
(– 2, ∞]
(d) x ∈
[– 2, ∞)
Answer (b)
Solution: In the given figure, the circle is
filled with dark color at -2 which means -2 is included and the highlighted is
towards the left of -2.
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