Chapter-5 Linear Inequalities — Online MCQ Test
MATHS · Grade 11 · CBSE(NCERT)
Practice Chapter-5 Linear Inequalities with a free chapter-wise online MCQ test.
This chapter covers: Algebraic inequality - Strict inequality - Slack inequality - Number line representation - Solution interval - One-variable inequalities.
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter-5 Linear Inequalities — Important Questions & Answers
Which of the following is an example of a strict inequality?
- A. x ≥ 5
- B. x > 5
- C. x ≤ 5
- D. x = 5
Answer: B. x > 5
A strict inequality uses symbols > or < without equality. x > 5 is a strict inequality as it does not include the endpoint.
A strict inequality uses symbols > or < without equality. x > 5 is a strict inequality as it does not include the endpoint.
What is a slack inequality also known as?
- A. Strict inequality
- B. Non-strict inequality
- C. Equation
- D. Linear equation
Answer: B. Non-strict inequality
Slack inequality (using ≥ or ≤) is also called non-strict inequality because it includes equality along with the inequality.
Slack inequality (using ≥ or ≤) is also called non-strict inequality because it includes equality along with the inequality.
Solve: 5 - 3x > -1
- A. x < 2
- B. x > 2
- C. x ≤ 2
- D. x ≥ 2
Answer: A. x < 2
5 - 3x > -1 → -3x > -6. Dividing by -3 reverses the inequality: x < 2.
5 - 3x > -1 → -3x > -6. Dividing by -3 reverses the inequality: x < 2.
Solve the compound inequality: -1 ≤ 2x + 3 ≤ 7
- A. -2 ≤ x ≤ 2
- B. -1 ≤ x ≤ 2
- C. -2 ≤ x ≤ 1
- D. -3 ≤ x ≤ 1
Answer: A. -2 ≤ x ≤ 2
-1 ≤ 2x + 3 ≤ 7 → subtract 3 from all parts: -4 ≤ 2x ≤ 4 → divide by 2: -2 ≤ x ≤ 2.
-1 ≤ 2x + 3 ≤ 7 → subtract 3 from all parts: -4 ≤ 2x ≤ 4 → divide by 2: -2 ≤ x ≤ 2.
What is the solution set for the inequality: (x - 2)(x + 3) > 0 considering only linear analysis boundaries?
- A. Only between -3 and 2
- B. x < -3 or x > 2 (considering quadratic nature)
- C. Cannot determine from linear methods alone
- D. x > -3
Answer: C. Cannot determine from linear methods alone
While this appears to be a product, solving (x - 2)(x + 3) > 0 requires quadratic analysis (sign analysis), not linear methods covered in Grade 11 linear inequalities chapter.
While this appears to be a product, solving (x - 2)(x + 3) > 0 requires quadratic analysis (sign analysis), not linear methods covered in Grade 11 linear inequalities chapter.