Linear Inequalities Question and Answers: Class 11 Mathematics

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


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