These Linear Inequalities Question and Answers of Class 11 Mathematics are most important for your upcoming examinations including JEE Main & JEE Advanced. These Linear Inequalities Question and Answers of Class 11 Mathematics will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## Linear Inequalities Question and Answers

1. If x² = -4 then the value of x is

(A) (-2, 2)

(B) (-2, ∞)

(C) (2, ∞)

(D) No solution

**Answer:** No solution

2. f(x) = {(x – 1)×(2 – x)}/(x – 3) ≥ 0

(A) (-∞, 1] ∪ (2, ∞)

(B) (-∞, 1] ∪ (2, 3)

(C) (-∞, 1] ∪ (3, ∞)

(D) None of these

**Answer:** (-∞, 1] ∪ (2, 3)

3. The solution of |2/(x – 4)| > 1 where x ≠ 4 is

(A) (2, 6)

(B) (2, 4) ∪ (4, 6)

(C) (2, 4) ∪ (4, ∞)

(D) (-∞, 4) ∪ (4, 6)

**Answer:** (2, 4) ∪ (4, 6)

4. The graph of the inequations x ≥ 0, y ≥ 0, 3x + 4y ≤ 12 is

(A) none of these

(B) interior of a triangle including the points on the sides

(C) in the 2nd quadrant

(D) exterior of a triangle

**Answer:** interior of a triangle including the points on the sides

5. If |x| < 5 then the value of x lies in the interval

(A) (-∞, -5)

(B) (∞, 5)

(C) (-5, ∞)

(D) (-5, 5)

**Answer:** (-5, 5)

6. Sum of two rational numbers is ______ number.

(A) rational

(B) irrational

(C) Integer

(D) Both 1, 2 and 3

**Answer:** rational

7. The region of the XOY-plane represented by the inequalities x ≥ 6, y ≥ 2, 2x + y ≤ 10 is

(A) unbounded

(B) a polygon

(C) none of these

(D) exterior of a triangle

**Answer:** none of these

8. The solution of the 15 < 3(x – 2)/5 < 0 is

(A) 27 < x < 2

(B) 27 < x < -2

(C) -27 < x < 2

(D) -27 < x < -2

**Answer:** 27 < x < 2

9. If | x − 1| > 5, then

(A) x∈(−∞, −4)∪(6, ∞]

(B) x∈[6, ∞)

(C) x∈(6, ∞)

(D) x∈(−∞, −4)∪(6, ∞)

**Answer:** x∈(−∞, −4)∪(6, ∞)

10. 1 ≤ |x – 1| ≤ 3

(A) [-2, 0]

(B) [2, 4]

(C) [-2, 0] ∪ [2, 4]

(D) None of these

**Answer:** [-2, 0] ∪ [2, 4]

11. Solve: (x + 1)² + (x² + 3x + 2)² = 0

(A) x = -1, -2

(B) x = -1

(C) x = -2

(D) None of these

**Answer:** x = -1

12. If (x + 3)/(x – 2) > 1/2 then x lies in the interval

(A) (-8, ∞)

(B) (8, ∞)

(C) (∞, -8)

(D) (∞, 8)

**Answer:** (-8, ∞)

13. If -2 < 2x – 1 < 2 then the value of x lies in the interval

(A) (1/2, 3/2)

(B) (-1/2, 3/2)

(C) (3/2, 1/2)

(D) (3/2, -1/2)

**Answer:** (-1/2, 3/2)

14. The solution of the inequality |x – 1| < 2 is

(A) (1, ∞)

(B) (-1, 3)

(C) (1, -3)

(D) (∞, 1)

**Answer:** (-1, 3)

15. The solution of the inequality 3(2-x)≥2(1-x) for real x is :

(A) x < 4

(B) x > 4

(C) x ≤4

(D) x ≥ 4

**Answer:** x ≤4

16. What is the region represented by x > 0 and y < 0?

(A) 2nd quadrant

(B) 3rd quadrant

(C) 4th quadrant

(D) 1st quadrant

**Answer:** 4th quadrant

17. Find the solution for the pair of solution x > 1 and x > -1

(A) No solution

(B) -1 < x < 1

(C) x < -1

(D) x > 1

**Answer:** x > 1

18. Find the solution for the pair of inequations x > 1 and x < -1

(A) no solution

(B) x < -1

(C) -1 < x < 1

(D) x > 1

**Answer:** no solution

19. In a game a person wins a TV if in four throws of a dice he get sum greater than 20 .In three throws he got numbers as 5,3,6. What should be his fourth throw so that he wins a TV?

(A) 5 or 6

(B) never wins.

(C) 5

(D) 6

**Answer:** never wins.

20. The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then

(A) breadth ≥ 20

(B) breadth > 20

(C) length ≤ 20

(D) length < 20

**Answer:** breadth ≥ 20