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Updated on 11 Jun 2026, 13:09 IST
Practise the best Linear Inequalities MCQ Questions Class 11 with Answers PDF for CBSE, NCERT, school exams, online tests, and quick revision. This page includes chapter-wise objective questions, answer key, detailed solutions, important rules, common mistakes, and PDF download options for Class 11 Maths Linear Inequalities.
Linear Inequalities is an important topic in Class 11 Mathematics. In this chapter, students learn how to solve inequalities in one variable, represent solution sets on the number line, write answers in interval notation, and understand linear inequalities in two variables through graphical representation.
Download the complete Linear Inequalities MCQ Questions with Answers PDF for offline practice.
Before solving the MCQs, revise these important rules of linear inequalities.
If the same number is added to or subtracted from both sides of an inequality, the inequality sign does not change.
Example:
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x + 3 > 7
⇒ x > 4
If both sides of an inequality are multiplied or divided by a positive number, the inequality sign does not change.
Example:
2x > 10
⇒ x > 5
If both sides of an inequality are multiplied or divided by a negative number, the inequality sign reverses.
Example:
JEE
NEET
Foundation JEE
Foundation NEET
CBSE
−2x > 6
⇒ x < −3
This is one of the most important rules in Linear Inequalities.
| Symbol | Meaning |
| > | Greater than |
| < | Less than |
| ≥ | Greater than or equal to |
| ≤ | Less than or equal to |
| Inequality | Number Line Rule |
| x > a | Open circle at a, shade right |
| x < a | Open circle at a, shade left |
| x ≥ a | Closed circle at a, shade right |
| x ≤ a | Closed circle at a, shade left |
Basic Linear Inequalities MCQs
Q1. What is the solution of x + 3 > 7?
A. x > 3
B. x > 4
C. x < 4
D. x ≥ 4
Answer: B. x > 4
Q2. What is the solution of 2x − 5 ≤ 9?
A. x ≤ 7
B. x ≥ 7
C. x < 7
D. x > 7
Answer: A. x ≤ 7
Q3. What is the solution of −3x < 12?
A. x < −4
B. x > −4
C. x < 4
D. x > 4
Answer: B. x > −4
Q4. What is the solution of 5 − 2x ≥ 1?
A. x ≥ 2
B. x ≤ 2
C. x > 2
D. x < 2
Answer: B. x ≤ 2
Q5. What is the solution of x/4 + 2 ≤ 5?
A. x ≤ 10
B. x ≥ 12
C. x ≤ 12
D. x > 12
Answer: C. x ≤ 12
Linear Inequalities in One Variable MCQs
Q6. What is the solution of 3(x − 2) > 2x + 1?
A. x > 7
B. x < 7
C. x ≥ 7
D. x ≤ 7
Answer: A. x > 7
Q7. What is the solution of 4x + 1 ≤ 2x + 9?
A. x ≤ 4
B. x ≥ 4
C. x < 4
D. x > 4
Answer: A. x ≤ 4
Q8. What is the solution of 5x − 7 < 3x + 5?
A. x < 5
B. x > 6
C. x < 6
D. x ≤ 6
Answer: C. x < 6
Q9. What is the solution of −2(x + 3) ≤ 10?
A. x ≤ −8
B. x ≥ −8
C. x > −8
D. x < −8
Answer: B. x ≥ −8
Q10. What is the solution of 7 − 3x > 1?
A. x < 2
B. x > 2
C. x ≤ 2
D. x ≥ 2
Answer: A. x < 2
Interval Notation and Number Line MCQs
Q11. What is the interval notation for x ≥ −1?
A. (−1, ∞)
B. [−1, ∞)
C. (−∞, −1]
D. (−∞, −1)
Answer: B. [−1, ∞)
Q12. What is the interval notation for −2 < x ≤ 5?
A. [−2, 5]
B. (−2, 5)
C. (−2, 5]
D. [−2, 5)
Answer: C. (−2, 5]
Q13. How many integer solutions satisfy 1 ≤ x < 5?
A. 3
B. 4
C. 5
D. 6
Answer: B. 4
Q14. How is x < 3 represented on the number line?
A. Open circle at 3 and shading to the left
B. Closed circle at 3 and shading to the left
C. Open circle at 3 and shading to the right
D. Closed circle at 3 and shading to the right
Answer: A. Open circle at 3 and shading to the left
Q15. How is x ≥ 2 represented on the number line?
A. Open circle at 2 and shading to the left
B. Closed circle at 2 and shading to the right
C. Open circle at 2 and shading to the right
D. Closed circle at 2 and shading to the left
Answer: B. Closed circle at 2 and shading to the right
Compound Linear Inequalities MCQs
Q16. What is the solution of 2 < x + 1 ≤ 5?
A. 1 < x ≤ 4
B. 1 ≤ x < 4
C. 2 < x ≤ 5
D. x > 1
Answer: A. 1 < x ≤ 4
Q17. What is the solution of −1 ≤ 2x + 3 < 7?
A. −2 < x < 2
B. −2 ≤ x < 2
C. −1 ≤ x < 7
D. −4 ≤ x < 4
Answer: B. −2 ≤ x < 2
Q18. What is the solution of 3x − 4 ≥ 2 and x < 5?
A. [2, 5)
B. (2, 5]
C. (−∞, 5)
D. [5, ∞)
Answer: A. [2, 5)
Q19. What is the solution of 2x + 1 < 5 or x − 3 ≥ 4?
A. x < 2 or x ≥ 7
B. x > 2 or x ≥ 7
C. x ≤ 2 or x > 7
D. x < 7
Answer: A. x < 2 or x ≥ 7
Q20. What is the solution of x/2 − x/3 > 1?
A. x > 3
B. x > 6
C. x < 6
D. x ≥ 6
Answer: B. x > 6
Rules of Linear Inequalities MCQs
Q21. When both sides of an inequality are multiplied by a negative number, the inequality sign:
A. Remains the same
B. Reverses
C. Becomes equal to
D. Disappears
Answer: B. Reverses
Q22. Which operation does not change the direction of an inequality sign?
A. Multiplying by −2
B. Dividing by −5
C. Adding the same number to both sides
D. Multiplying by a negative variable
Answer: C. Adding the same number to both sides
Q23. What is the smallest integer greater than −2?
A. −3
B. −2
C. −1
D. 0
Answer: C. −1
Q24. What is the largest integer less than 4?
A. 2
B. 3
C. 4
D. 5
Answer: B. 3
Q25. If x is a natural number and x ≤ 4, what are the possible values of x?
A. 0, 1, 2, 3, 4
B. 1, 2, 3, 4
C. −1, 0, 1, 2, 3, 4
D. 1, 2, 3
Answer: B. 1, 2, 3, 4
Q26. If x is an integer and −3 ≤ x < 2, how many possible values of x are there?
A. 4
B. 5
C. 6
D. 7
Answer: B. 5
Word Problems on Linear Inequalities MCQs
Q27. How is “at least 18” written as an inequality?
A. x > 18
B. x < 18
C. x ≥ 18
D. x ≤ 18
Answer: C. x ≥ 18
Q28. How is “more than 50” written as an inequality?
A. x > 50
B. x ≥ 50
C. x < 50
D. x ≤ 50
Answer: A. x > 50
Q29. How is “no more than 12” written as an inequality?
A. x < 12
B. x > 12
C. x ≤ 12
D. x ≥ 12
Answer: C. x ≤ 12
Q30. How is “less than or equal to 7” written as an inequality?
A. x < 7
B. x ≤ 7
C. x > 7
D. x ≥ 7
Answer: B. x ≤ 7
Q31. The sum of a number and 5 is less than 12. Which inequality represents this statement?
A. x + 5 < 12
B. x + 5 > 12
C. x − 5 < 12
D. 5x < 12
Answer: A. x + 5 < 12
Q32. Twice a number is at least 16. What is the solution?
A. x > 8
B. x ≥ 8
C. x < 8
D. x ≤ 8
Answer: B. x ≥ 8
Q33. A notebook costs ₹20 and each pen costs ₹p. If 5 pens and 1 notebook cost at most ₹100, what is the maximum value of p?
A. ₹12
B. ₹14
C. ₹16
D. ₹18
Answer: C. ₹16
Q34. A student has scored 28 marks and needs at least 40 marks. If x is the additional marks needed, which inequality is correct?
A. x ≤ 12
B. x ≥ 12
C. x > 40
D. x < 12
Answer: B. x ≥ 12
Q35. If 3x + 2 ≥ 11 and x is a natural number, what is the least possible value of x?
A. 2
B. 3
C. 4
D. 5
Answer: B. 3
Linear Inequalities Practice MCQs
Q36. What is the solution of 10 − 2x < 4?
A. x > 3
B. x < 3
C. x ≥ 3
D. x ≤ 3
Answer: A. x > 3
Q37. What is the solution of (x − 1)/3 ≤ 2?
A. x ≤ 5
B. x ≤ 7
C. x ≥ 7
D. x > 7
Answer: B. x ≤ 7
Q38. What is the solution of (2x + 5)/3 > 1?
A. x > −1
B. x < −1
C. x > 1
D. x < 1
Answer: A. x > −1
Q39. What is the solution of 0.5x + 2 ≤ 6?
A. x ≤ 4
B. x ≤ 6
C. x ≤ 8
D. x ≥ 8
Answer: C. x ≤ 8
Q40. What is the solution of 4 ≤ x + 2 < 9?
A. 2 ≤ x < 7
B. 2 < x ≤ 7
C. 4 ≤ x < 9
D. x ≥ 2
Answer: A. 2 ≤ x < 7
Linear Inequalities in Two Variables MCQs
Q41. Which point satisfies x + y ≤ 4?
A. (3, 2)
B. (2, 1)
C. (5, 0)
D. (4, 2)
Answer: B. (2, 1)
Q42. Does the point (3, 2) satisfy 2x + y < 8?
A. Yes
B. No
C. Cannot be determined
D. Only if x = y
Answer: B. No
Q43. What is the boundary line of the inequality x + y ≤ 5?
A. x + y < 5
B. x + y = 5
C. x + y > 5
D. x − y = 5
Answer: B. x + y = 5
Q44. For the inequality y > 2x + 1, the boundary line is:
A. Solid line
B. Dashed line
C. Vertical line
D. Horizontal line only
Answer: B. Dashed line
Q45. For the inequality y ≤ −x + 3, the boundary line is:
A. Dashed and shaded above
B. Solid and shaded below
C. Dashed and shaded below
D. Solid and shaded above only
Answer: B. Solid and shaded below
Q46. What does the inequality x ≥ 0 represent?
A. Region to the left of the y-axis
B. Region to the right of the y-axis including the y-axis
C. Region above the x-axis
D. Region below the x-axis
Answer: B. Region to the right of the y-axis including the y-axis
Q47. What does the inequality y < 4 represent?
A. Region above the line y = 4
B. Region below the line y = 4 with dashed boundary
C. Region below the line y = 4 with solid boundary
D. Only the line y = 4
Answer: B. Region below the line y = 4 with dashed boundary
Q48. Does the point (0, 0) satisfy x + y ≥ 1?
A. Yes
B. No
C. Sometimes
D. Cannot be determined
Answer: B. No
Q49. What is the solution of x ≥ 1 and x ≤ 4?
A. (1, 4)
B. [1, 4]
C. (−∞, 1]
D. [4, ∞)
Answer: B. [1, 4]
Q50. What is the solution of x < 0 or x > 0?
A. (−∞, ∞)
B. (−∞, 0) ∪ (0, ∞)
C. [0, ∞)
D. (−∞, 0]
Answer: B. (−∞, 0) ∪ (0, ∞)
| Q. No. | Answer | Q. No. | Answer | Q. No. | Answer | Q. No. | Answer | Q. No. | Answer |
| 1 | B | 2 | A | 3 | B | 4 | B | 5 | C |
| 6 | A | 7 | A | 8 | C | 9 | B | 10 | A |
| 11 | B | 12 | C | 13 | B | 14 | A | 15 | B |
| 16 | A | 17 | B | 18 | A | 19 | A | 20 | B |
| 21 | B | 22 | C | 23 | C | 24 | B | 25 | B |
| 26 | B | 27 | C | 28 | A | 29 | C | 30 | B |
| 31 | A | 32 | B | 33 | C | 34 | B | 35 | B |
| 36 | A | 37 | B | 38 | A | 39 | C | 40 | A |
| 41 | B | 42 | B | 43 | B | 44 | B | 45 | B |
| 46 | B | 47 | B | 48 | B | 49 | B | 50 | B |
Solution 1
x + 3 > 7
⇒ x > 7 − 3
⇒ x > 4
Correct answer: B
Solution 2
2x − 5 ≤ 9
⇒ 2x ≤ 14
⇒ x ≤ 7
Correct answer: A
Solution 3
−3x < 12
Divide both sides by −3. The inequality sign reverses.
⇒ x > −4
Correct answer: B
Solution 4
5 − 2x ≥ 1
⇒ −2x ≥ −4
Divide both sides by −2. The inequality sign reverses.
⇒ x ≤ 2
Correct answer: B
Solution 5
x/4 + 2 ≤ 5
⇒ x/4 ≤ 3
⇒ x ≤ 12
Correct answer: C
Solution 6
3(x − 2) > 2x + 1
⇒ 3x − 6 > 2x + 1
⇒ x − 6 > 1
⇒ x > 7
Correct answer: A
Solution 7
4x + 1 ≤ 2x + 9
⇒ 2x + 1 ≤ 9
⇒ 2x ≤ 8
⇒ x ≤ 4
Correct answer: A
Solution 8
5x − 7 < 3x + 5
⇒ 2x − 7 < 5
⇒ 2x < 12
⇒ x < 6
Correct answer: C
Solution 9
−2(x + 3) ≤ 10
⇒ −2x − 6 ≤ 10
⇒ −2x ≤ 16
Divide both sides by −2. The inequality sign reverses.
⇒ x ≥ −8
Correct answer: B
Solution 10
7 − 3x > 1
⇒ −3x > −6
Divide both sides by −3. The inequality sign reverses.
⇒ x < 2
Correct answer: A
Solution 11
x ≥ −1 means −1 is included.
So the interval is:
[−1, ∞)
Correct answer: B
Solution 12
−2 < x ≤ 5 means −2 is not included and 5 is included.
So the interval is:
(−2, 5]
Correct answer: C
Solution 13
1 ≤ x < 5
Integer values are:
1, 2, 3, 4
Total integer solutions = 4
Correct answer: B
Solution 14
x < 3 means 3 is not included, so use an open circle at 3. Since the values are less than 3, shade to the left.
Correct answer: A
Solution 15
x ≥ 2 means 2 is included, so use a closed circle at 2. Since the values are greater than 2, shade to the right.
Correct answer: B
Solution 16
2 < x + 1 ≤ 5
⇒ 1 < x ≤ 4
Correct answer: A
Solution 17
−1 ≤ 2x + 3 < 7
⇒ −4 ≤ 2x < 4
⇒ −2 ≤ x < 2
Correct answer: B
Solution 18
3x − 4 ≥ 2
⇒ 3x ≥ 6
⇒ x ≥ 2
Also, x < 5.
So the combined solution is:
[2, 5)
Correct answer: A
Solution 19
2x + 1 < 5
⇒ 2x < 4
⇒ x < 2
x − 3 ≥ 4
⇒ x ≥ 7
So the solution is:
x < 2 or x ≥ 7
Correct answer: A
Solution 20
x/2 − x/3 > 1
⇒ (3x − 2x)/6 > 1
⇒ x/6 > 1
⇒ x > 6
Correct answer: B
Solution 21
When both sides of an inequality are multiplied by a negative number, the inequality sign reverses.
Correct answer: B
Solution 22
Adding the same number to both sides of an inequality does not change the inequality sign.
Correct answer: C
Solution 23
Integers greater than −2 are:
−1, 0, 1, 2, ...
The smallest integer greater than −2 is −1.
Correct answer: C
Solution 24
Integers less than 4 include:
..., 1, 2, 3
The largest integer less than 4 is 3.
Correct answer: B
Solution 25
Natural numbers generally start from 1.
If x ≤ 4, then possible natural values are:
1, 2, 3, 4
Correct answer: B
Solution 26
−3 ≤ x < 2
Integer values are:
−3, −2, −1, 0, 1
Total values = 5
Correct answer: B
Solution 27
“At least 18” means 18 or more.
So:
x ≥ 18
Correct answer: C
Solution 28
“More than 50” means strictly greater than 50.
So:
x > 50
Correct answer: A
Solution 29
“No more than 12” means 12 or less.
So:
x ≤ 12
Correct answer: C
Solution 30
“Less than or equal to 7” is written as:
x ≤ 7
Correct answer: B
Solution 31
“The sum of a number and 5 is less than 12” means:
x + 5 < 12
Correct answer: A
Solution 32
Twice a number is at least 16.
2x ≥ 16
⇒ x ≥ 8
Correct answer: B
Solution 33
Cost of 5 pens = 5p
Cost of notebook = ₹20
Total cost is at most ₹100.
5p + 20 ≤ 100
⇒ 5p ≤ 80
⇒ p ≤ 16
Maximum value of p = ₹16
Correct answer: C
Solution 34
The student has 28 marks and needs at least 40 marks.
28 + x ≥ 40
⇒ x ≥ 12
Correct answer: B
Solution 35
3x + 2 ≥ 11
⇒ 3x ≥ 9
⇒ x ≥ 3
The least natural value of x is 3.
Correct answer: B
Solution 36
10 − 2x < 4
⇒ −2x < −6
Divide both sides by −2. The inequality sign reverses.
⇒ x > 3
Correct answer: A
Solution 37
(x − 1)/3 ≤ 2
⇒ x − 1 ≤ 6
⇒ x ≤ 7
Correct answer: B
Solution 38
(2x + 5)/3 > 1
⇒ 2x + 5 > 3
⇒ 2x > −2
⇒ x > −1
Correct answer: A
Solution 39
0.5x + 2 ≤ 6
⇒ 0.5x ≤ 4
⇒ x ≤ 8
Correct answer: C
Solution 40
4 ≤ x + 2 < 9
⇒ 2 ≤ x < 7
Correct answer: A
Solution 41
Check point (2, 1):
x + y ≤ 4
⇒ 2 + 1 ≤ 4
⇒ 3 ≤ 4
The point satisfies the inequality.
Correct answer: B
Solution 42
Check point (3, 2):
2x + y < 8
⇒ 2(3) + 2 < 8
⇒ 8 < 8
This is false.
Correct answer: B
Solution 43
The boundary line of an inequality is found by replacing the inequality sign with an equal sign.
x + y ≤ 5
Boundary line: x + y = 5
Correct answer: B
Solution 44
For y > 2x + 1, the inequality is strict. Therefore, the boundary line is dashed.
Correct answer: B
Solution 45
For y ≤ −x + 3, the boundary line is included because the sign is ≤. The region is below the line.
Correct answer: B
Solution 46
x ≥ 0 represents all points whose x-coordinate is positive or zero. This is the region to the right of the y-axis including the y-axis.
Correct answer: B
Solution 47
y < 4 represents all points below the line y = 4. Since the inequality is strict, the boundary line is dashed.
Correct answer: B
Solution 48
Check point (0, 0):
x + y ≥ 1
⇒ 0 + 0 ≥ 1
⇒ 0 ≥ 1
This is false.
Correct answer: B
Solution 49
x ≥ 1 and x ≤ 4 means x lies between 1 and 4, including both endpoints.
So the interval is:
[1, 4]
Correct answer: B
Solution 50
x < 0 or x > 0 includes all real numbers except 0.
So the solution is:
(−∞, 0) ∪ (0, ∞)
Correct answer: B
Students often lose marks in Linear Inequalities because of small sign and interval mistakes. Avoid these common errors.
Mistake 1: Not Reversing the Inequality Sign
Incorrect:
−2x > 6
⇒ x > −3
Correct:
−2x > 6
⇒ x < −3
The sign reverses because both sides are divided by −2.
Mistake 2: Confusing < and ≤
x < 5 means 5 is not included.
x ≤ 5 means 5 is included.
Mistake 3: Using the Wrong Circle on the Number Line
Use an open circle for < and >.
Use a closed circle for ≤ and ≥.
Mistake 4: Writing Wrong Interval Notation
x > 2 should be written as:
(2, ∞)
It should not be written as:
[2, ∞)
Mistake 5: Wrong Shading in Graphical Linear Inequalities
For y > mx + c, shade above the line.
For y < mx + c, shade below the line.
For strict inequalities, use a dashed boundary line.
For ≤ or ≥, use a solid boundary line.
Linear Inequalities is an important Class 11 Maths chapter that helps students understand inequality symbols, solution sets, number line representation, interval notation, and graphical solutions. Practising Linear Inequalities MCQ Questions with Answers is one of the best ways to revise the chapter quickly.
Add these internal links to help students and improve topical coverage:
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Linear Inequalities are mathematical statements that compare two expressions using symbols such as <, >, ≤, and ≥. In Class 11 Maths, students learn to solve inequalities in one variable, represent them on the number line, and understand inequalities in two variables.
Yes, these Linear Inequalities MCQs are designed for CBSE Class 11 Maths students and follow the NCERT-based pattern of objective questions, number line representation, interval notation, and graphical inequalities.
Students can download the Linear Inequalities MCQ Questions with Answers PDF from the download section given on this page. The PDF should include MCQs, answers, and detailed explanations.
In the current NCERT sequence, Linear Inequalities is commonly listed as Chapter 5. Some older resources may mention it as Chapter 6. Students should follow the latest textbook and syllabus prescribed by their school.
The most important rule is that the inequality sign reverses when both sides are multiplied or divided by a negative number.
Example:
−2x > 6
⇒ x < −3
To solve Linear Inequalities MCQs quickly, first simplify both sides, collect like terms, apply the sign reversal rule carefully, and then check whether the answer needs interval notation or number line representation.
Yes, number line questions are very important. Students should know the difference between open and closed circles and should understand shading direction for less than and greater than inequalities.
Yes, graphical questions can be included, especially for linear inequalities in two variables. These questions usually involve boundary lines, shaded regions, and checking whether a point satisfies an inequality.
Yes, these MCQs are useful for school tests, unit tests, periodic assessments, objective-type practice, and quick revision before exams.
Students should practise at least 40 to 50 Linear Inequalities MCQs before exams. They should include basic inequalities, word problems, interval notation, number line questions, and two-variable inequality questions.