Chapter-5 Linear Inequalities — Online MCQ Test

Q: Which of the following is an example of a strict inequality?

Answer: B. x > 5 — A strict inequality uses symbols > or 5 is a strict inequality as it does not include the endpoint.

Q: What is a slack inequality also known as?

Answer: B. Non-strict inequality — Slack inequality (using ≥ or ≤) is also called non-strict inequality because it includes equality along with the inequality.

Q: Solve the compound inequality: -1 ≤ 2x + 3 ≤ 7

Answer: A. -2 ≤ x ≤ 2 — -1 ≤ 2x + 3 ≤ 7 → subtract 3 from all parts: -4 ≤ 2x ≤ 4 → divide by 2: -2 ≤ x ≤ 2.

Q: What is the solution set for the inequality: (x - 2)(x + 3) > 0 considering only linear analysis boundaries?

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.

MATHS · Grade 11 · CBSE(NCERT)

Practice Chapter-5 Linear Inequalities with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 11 MATHS. 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.

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Chapter-5 Linear Inequalities — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 11 MATHS — Chapter-5 Linear Inequalities, with answers and explanations. These are sample questions; the exam has its own separate question set.

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.

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.

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.

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.

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.