Class 11 Maths MCQ – Linear Inequalities

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Linear inequalities might seem intimidating at first, especially when encountered in the expansive realm of mathematics. However, with a strong foundation and consistent practice, mastering them becomes a fulfilling journey. This article presents a set of multiple-choice questions tailored for Class 11 students to reinforce their understanding of linear inequalities. Let’s dive in!

1. If x > 5, then which of the following is also true?

a) 2x > 10
b) x – 7 > -2
c) 3x < 15
d) x/2 < 3

Answer:

a) 2x > 10

Explanation:

Multiplying both sides by 2, we get 2x > 10.

2. The solution to the inequality 3x – 4 > 5 is:

a) x > 3
b) x < 3
c) x > -3
d) x < -3

Answer:

a) x > 3

Explanation:

Solving for x, 3x > 9 implies x > 3.

3. Which of the following inequalities is equivalent to x – 5 ≥ 7?

a) x ≥ 2
b) x ≤ 2
c) x ≥ 12
d) x ≤ 12

Answer:

c) x ≥ 12

Explanation:

Adding 5 to both sides, we get x ≥ 12.

4. The solution set for 2(x – 3) ≤ 4x – 6 is:

a) x ≥ 3
b) x ≤ 3
c) x ≥ 0
d) x ≤ 0

Answer:

b) x ≤ 3

Explanation:

Simplifying gives x ≤ 3.

5. If -2x < 8, then x is:

a) x > -4
b) x < -4
c) x > 4
d) x < 4

Answer:

a) x > -4

Explanation:

Dividing both sides by -2 and reversing the inequality, we get x > -4.

6. Which of the following represents a valid inequality?

a) 5x + 3 < 8x – 7
b) 4x – 7 ≥ 13 – 5x
c) 2x + 1 > 2x + 3
d) x/3 ≤ x/4

Answer:

a) 5x + 3 < 8x – 7

Explanation:

Solving the inequality proves it to be valid.

7. The graph of the inequality x + 2y ≤ 6 will be:

a) A straight line passing through (6,0) and (0,3)
b) A dashed line passing through (6,0) and (0,3)
c) A region below the line x + 2y = 6
d) A region above the line x + 2y = 6

Answer:

c) A region below the line x + 2y = 6

Explanation:

The inequality represents the region below the line x + 2y = 6.

8. For the inequality 2x + 3 > x + 7, x is:

a) Greater than 4
b) Less than 4
c) Greater than or equal to 4
d) Less than or equal to 4

Answer:

a) Greater than 4

Explanation:

Solving for x, we get x > 4.

9. Which of the following is the solution to 4x – 7 > 2x + 5?

a) x > 6
b) x < 6
c) x > 3
d) x < 3

Answer:

c) x > 3

Explanation:

Solving for x gives x > 3.

10. The solution for the inequality |x| < 3 is:

a) -3 < x < 3
b) x > 3 or x < -3
c) x ≥ 3
d) x ≤ -3

Answer:

a) -3 < x < 3

Explanation:

The absolute value of x is less than 3 only if x is between -3 and 3.

11. Which inequality is represented by the number line with a closed circle at -2 and shading to the left?

a) x > -2
b) x < -2
c) x ≥ -2
d) x ≤ -2

Answer:

d) x ≤ -2

Explanation:

A closed circle indicates that the number is included, and shading to the left means values less than the number.

12. If 5 ≤ 2x – 3 < 11, then x lies between:

a) 4 and 7
b) 3 and 6
c) 4 and 6
d) 3 and 7

Answer:

a) 4 and 7

Explanation:

Solving for x gives 4 ≤ x < 7.

13. The expression x^2 – 6x + 9 > 0 is true for:

a) x > 3
b) x < 3
c) All real values of x
d) No real values of x

Answer:

c) All real values of x

Explanation:

The expression is a perfect square, (x-3)^2, which is always non-negative.

14. For the inequality x/5 + 2 ≥ 3x/15 – 1, x is:

a) x ≤ 15
b) x ≥ 15
c) x < 15
d) x > 15

Answer:

a) x ≤ 15

Explanation:

Solving for x gives x ≤ 15.

15. Which inequality is equivalent to 2(x + 3) > x + 7?

a) x > 1
b) x < 1
c) x ≥ 1
d) x ≤ 1

Answer:

a) x > 1

Explanation:

Expanding and solving for x gives x > 1.

16. The solution to the inequality x^2 – 4 > 0 is:

a) x > 2 or x < -2
b) -2 < x < 2
c) x > 2 and x < -2
d) x > -2 and x < 2

Answer:

a) x > 2 or x < -2

Explanation:

Factoring gives (x-2)(x+2) > 0.

17. The inequality 5x – 3 < 2x + 6 is true when:

a) x > 3
b) x < 3
c) x ≥ 3
d) x ≤ 3

Answer:

a) x > 3

Explanation:

Solving for x gives x > 3.

18. Which of the following is the solution set for the inequality 3x – 4 < 2x + 1?

a) x < 5
b) x > 5
c) x ≤ 5
d) x ≥ 5

Answer:

a) x < 5

Explanation:

Solving for x gives x < 5.

19. The graph of the inequality 3x + 4y > 12 will shade:

a) Above the line
b) Below the line
c) To the left of the line
d) To the right of the line

Answer:

a) Above the line

Explanation:

For this inequality, points above the line will satisfy the condition.

20. If 7x + 2 ≥ 5x + 12, then x is:

a) Greater than 5
b) Less than 5
c) Greater than or equal to 5
d) Less than or equal to 5

Answer:

c) Greater than or equal to 5

Explanation:

Solving for x, we get x ≥ 5.

Related MCQ (Multiple Choice Questions) :

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