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Linear Inequalities — NEET Maths MCQs

30 questions written by hand against the NCERT chapter. Every wrong option is explained, not just the right one.

30questions
10/14/6easy / medium / hard
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Sample questions from this chapter

Solve 3x < 12.
  1. x < 4 ✓
  2. x > 4
  3. x ≤ 4
  4. x < 9
Answer: A. Divide both sides by the positive number 3: x < 4. Dividing by a positive number leaves the direction unchanged.
Why not B: Reverses the inequality. The sign flips only when you multiply or divide by a NEGATIVE number, and 3 is positive.
Why not C: Includes 4, but the original inequality is strict: 3 × 4 = 12, which is not less than 12.
Why not D: Subtracts 3 from both sides instead of dividing by it.
Solve 3(x − 1) ≤ 2(x + 4).
  1. x ≤ 11 ✓
  2. x ≤ 7
  3. x ≥ 11
  4. x ≤ 9
Answer: A. 3x − 3 ≤ 2x + 8 → x ≤ 11. Both brackets must be expanded in full.
Why not B: Multiplies only the x inside the second bracket, using 2x + 4 instead of 2x + 8.
Why not C: Reverses the inequality, though nothing was multiplied by a negative number.
Why not D: Multiplies only the x inside the first bracket, using 3x − 1 instead of 3x − 3.
Solve |2x − 1| ≤ 5.
  1. −2 ≤ x ≤ 3 ✓
  2. x ≤ 3
  3. −3 ≤ x ≤ 2
  4. x ≤ −2 or x ≥ 3
Answer: A. |2x − 1| ≤ 5 means −5 ≤ 2x − 1 ≤ 5. Add 1: −4 ≤ 2x ≤ 6. Divide by 2: −2 ≤ x ≤ 3.
Why not B: Keeps only the upper branch. x = −10 satisfies x ≤ 3 but |2(−10) − 1| = 21, far above 5.
Why not C: Swaps the two bounds, as though the expression inside were 1 − 2x rather than 2x − 1.
Why not D: This is the solution of |2x − 1| ≥ 5 — the values FAR from the centre, not the ones near it.

These are 3 of the 30 questions in the test. Take the full chapter test →

Read the chapter first

Every NCERT question in this chapter is solved, free: NCERT solutions — Linear Inequalities →

Other NEET Maths chapters

SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsPermutations and CombinationsBinomial Theorem

All 27 chapters →

Questions

How many NEET questions are there on Linear Inequalities?

This chapter test has 30 questions — 10 easy, 14 medium and 6 hard — all written against the NCERT Class 11 chapter.

Is this NEET Maths chapter test free?

Yes. Every chapter test is free with no login, and you get your all-India rank on every one. Nothing on the site is on sale right now.

Do the questions explain the wrong options?

Yes — every distractor carries its own explanation naming the specific misconception that makes a student pick it. That is the part most question banks skip, and it is the part that changes your next attempt.