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.
On a number line, how is the solution to x > 3 represented?
- A. Filled circle at 3 with arrow to the right
- B. Empty circle at 3 with arrow to the right
- C. Filled circle at 3 with arrow to the left
- D. Empty circle at 3 with arrow to the left
Answer: B. Empty circle at 3 with arrow to the right
For strict inequality x > 3, an empty (unfilled) circle is used at 3 to show 3 is NOT included, with an arrow extending to the right.
For strict inequality x > 3, an empty (unfilled) circle is used at 3 to show 3 is NOT included, with an arrow extending to the right.
Solve: 2x + 3 < 9
- A. x < 3
- B. x > 3
- C. x ≤ 3
- D. x ≥ 3
Answer: A. x < 3
2x + 3 < 9 → 2x < 6 → x < 3. Subtracting 3 and dividing by 2 gives x < 3.
2x + 3 < 9 → 2x < 6 → x < 3. Subtracting 3 and dividing by 2 gives x < 3.
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.
What happens to an inequality symbol when both sides are multiplied by a negative number?
- A. It remains the same
- B. It reverses direction
- C. It becomes an equation
- D. It becomes undefined
Answer: B. It reverses direction
When multiplying or dividing an inequality by a negative number, the inequality symbol must be reversed to maintain the truth of the statement.
When multiplying or dividing an inequality by a negative number, the inequality symbol must be reversed to maintain the truth of the statement.
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.
Solve: |x - 3| < 2 and express in interval notation.
- A. (1, 5)
- B. [1, 5]
- C. (1, 3)
- D. (3, 5)
Answer: A. (1, 5)
|x - 3| < 2 means -2 < x - 3 < 2, which gives 1 < x < 5 or (1, 5) in interval notation.
|x - 3| < 2 means -2 < x - 3 < 2, which gives 1 < x < 5 or (1, 5) in interval notation.
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.
A student claims that if x < 5 then x² < 25. Which evaluation is correct?
- A. The claim is always true
- B. The claim is always false
- C. The claim is sometimes true and sometimes false (e.g., x = -6 gives x² = 36 > 25)
- D. Cannot be determined without additional information
Answer: C. The claim is sometimes true and sometimes false (e.g., x = -6 gives x² = 36 > 25)
For x < 5: if 0 < x < 5, then x² < 25 is true; but if x < 0 (say x = -6), then x² = 36 > 25, making the claim false. Squaring non-linear operations don't preserve inequality direction for all real numbers.
For x < 5: if 0 < x < 5, then x² < 25 is true; but if x < 0 (say x = -6), then x² = 36 > 25, making the claim false. Squaring non-linear operations don't preserve inequality direction for all real numbers.