Linear Inequality Practice Problems And Answers: Class 11 Mathematics

These Linear Inequality Practice Problems And Answers of Class 11 Mathematics are most important for your upcoming examinations including JEE Main & JEE Advanced. These Linear Inequality Practice Problems 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 Inequality Practice Problems And Answers

1. The solution of the inequality 3(x + 2) > 2 – x is

(A) x > 1

(B) x < 1

(C) x > -1

(D) x < -1

Answer: x > -1


2. Sum of two rational numbers is ______ number.

(A) rational

(B) irrational

(C) Integer

(D) Both 1, 2 and 3

Answer: rational


3. The interval in which f(x) = (x – 1)*(x – 2)*(x – 3) is negative is

(A) x > 2

(B) 2 < x and x < 1

(C) 2 < x < 1 and x < 3

(D) 2 < x < 3 and x < 1

Answer: 2 < x < 3 and x < 1


4. If x2 > 4 then the value of x is

(A) x < -2

(B) x > 2

(C) x < -2 or x > 2

(D) None of these

Answer: x < -2 or x > 2


5. If x2 < 4 then the value of x is

(A) (0, 2)

(B) (-2, 2)

(C) (-2, 0)

(D) None of these

Answer: (-2, 2)


6. If |x| > -5 then the value of x lies in the interval

(A) (-∞, -5)

(B) (∞, 5)

(C) (-5, 5)

(D) R

Answer: R


7. If (|x| – 1)/(|x| – 2) ≥ 0, x ∈ R, x ± 2 then the interval of x is

(A) (-∞, -2) U [-1, 1]

(B) [-1, 1] U (2, ∞)

(C) (-∞, -2) U (2, ∞)

(D) (-∞, -2) U [-1, 1] U (2, ∞)

Answer: (-∞, -2) U [-1, 1] U (2, ∞)


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

(A) (1, ∞)

(B) (-1, 3)

(C) (1, -3)

(D) (∞, 1)

Answer: (-1, 3)


9. If x2 < -4 then the value of x is

(A) (-2, 2)

(B) (2, ∞)

(C) (-2, ∞)

(D) No solution

Answer: No solution


10. Solve: |x – 3| < 5

(A) (2, 8)

(B) (-2, 8)

(C) (8, 2)

(D) (8, -2)

Answer: (-2, 8)


11. If x² = 4 then the value of x is

(A) -2

(B) 2

(C) -2, 2

(D) None of these

Answer: -2, 2


12. If (|x| – 1)/(|x| – 2) ≥ 0, x ∈ R, x ± 2 then the interval of x is

(A) (-∞, -2) ∪ [-1, 1]

(B) [-1, 1] ∪ (2, ∞)

(C) (-∞, -2) ∪ (2, ∞)

(D) (-∞, -2) ∪ [-1, 1] ∪ (2, ∞)

Answer: (-∞, -2) ∪ [-1, 1] ∪ (2, ∞)


13. If x² = -4 then the value of x is

(A) (-2, 2)

(B) (-2, ∞)

(C) (2, ∞)

(D) No solution

Answer: No solution


14. The interval in which f(x) = (x – 1) × (x – 2) × (x – 3) is negative is

(A) x > 2

(B) 2 < x and x < 1

(C) 2 < x < 1 and x < 3

(D) 2 < x < 3 and x < 1

Answer: 2 < x < 3 and x < 1


15. The solution of the -12 < (4 -3x)/(-5) < 2 is

(A) 56/3 < x < 14/3

(B) -56/3 < x < -14/3

(C) 56/3 < x < -14/3

(D) -56/3 < x < 14/3

Answer: -56/3 < x < 14/3


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