Linear Inequalities — Class 11 MCQs with Answers

Linear Inequalities — important questions & MCQs with answers (Class 11 Mathematics)

14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.

1. Q1Easy

   Solve 2x > 6:

   A.x > 3✓ Correct

   B.x < 3

   C.x = 3

   D.x ≥ 3

   Answer: A. x > 3

   Explanation: Dividing both sides by the positive number 2 keeps the direction: 2x > 6 → x > 3. The sign only flips when you divide by a negative number, not here.

2. Q2Easy

   Solve x + 3 > 5:

   A.x ≥ 2

   B.x > 2✓ Correct

   C.x < 2

   D.x = 2

   Answer: B. x > 2

   Explanation: Subtract 3 from both sides of x + 3 > 5 to get x > 2 — a strict inequality, since no equality was introduced, so x = 2 itself is not included.

3. Q3Easy

   Number line representation of x > 0 is:

   A.Both ends shaded

   B.Closed circle at 0

   C.Open circle at 0, arrow right✓ Correct

   D.No shading

   Answer: C. Open circle at 0, arrow right

   Explanation: A strict inequality like x > 0 is drawn with an open (hollow) circle at 0, since 0 itself is excluded, with the arrow shading rightward toward larger x.

4. Q4Easy

   Multiplying inequality by negative number:

   A.Adds 1

   B.Keeps sign

   C.Removes sign

   D.Reverses sign✓ Correct

   Answer: D. Reverses sign

   Explanation: Multiplying or dividing an inequality by a negative number flips it: 2 < 3 becomes −2 > −3 after ×(−1). Forgetting this reversal is the chapter's classic trap.

5. Q5Easy

   Solve 2x < 10:

   A.x = 5

   B.x > 5

   C.x < 5✓ Correct

   D.x ≤ 5

   Answer: C. x < 5

   Explanation: Dividing 2x < 10 by the positive number 2 keeps the sign unchanged: x < 5. Only a negative divisor would flip the arrow.

6. Q6Easy

   x ≥ 2 on number line uses:

   A.Closed circle at 2✓ Correct

   B.Open circle at 2

   C.Two circles

   D.No circle

   Answer: A. Closed circle at 2

   Explanation: x ≥ 2 includes the value 2, so the number line uses a closed (filled) circle at 2 — a hollow circle would signal the strict x > 2 instead.

7. Q7Medium

   Solve 1 ≤ x+2 < 5:

   A.−1 ≤ x < 3✓ Correct

   B.1 ≤ x ≤ 5

   C.x > 0

   D.x ≥ 1

   Answer: A. −1 ≤ x < 3

   Explanation: Subtract 2 from every part of 1 ≤ x+2 < 5 to isolate x: −1 ≤ x < 3. The left end stays closed (≤) and the right stays open (<) — don't merge them into one type.

8. Q8Medium

   Solve −5 < 2x − 3 ≤ 5:

   A.−1 < x ≤ 4✓ Correct

   B.x > −1

   C.x ≤ 4

   D.x ≥ −1

   Answer: A. −1 < x ≤ 4

   Explanation: Add 3 to every part of −5 < 2x − 3 ≤ 5 to get −2 < 2x ≤ 8, then divide by the positive 2: −1 < x ≤ 4, keeping the left strict and right closed.

9. Q9Medium

   Boundary of x − y ≤ 0 passes through origin and has slope:

   A.1✓ Correct

   B.−1

   C.0

   D.∞

   Answer: A. 1

   Explanation: The boundary of x − y ≤ 0 is the line x − y = 0, i.e. y = x — it passes through the origin with slope 1, the ratio of rise to run being 1:1.

10. Q10Medium

    Region representing x+y≤1 in xy-plane is:

    A.All R²

    B.Above line

    C.Line only

    D.Half-plane below line x+y=1 (incl. line)✓ Correct

    Answer: D. Half-plane below line x+y=1 (incl. line)

    Explanation: Test a point off the line, like the origin: 0+0=0 ≤ 1 is true, so (0,0) lies in the region — meaning x+y≤1 is the closed half-plane containing the origin, not the far side.

11. Q11Medium

    Solution of system x + y ≤ 6 and x ≥ 0, y ≥ 0 is:

    A.Infinite strip

    B.Rectangle

    C.Whole plane

    D.Triangle with vertices (0,0), (6,0), (0,6)✓ Correct

    Answer: D. Triangle with vertices (0,0), (6,0), (0,6)

    Explanation: x ≥ 0 and y ≥ 0 confine the region to the first quadrant, and x + y ≤ 6 cuts it off along a line through (6,0) and (0,6), leaving a triangle with those two points and the origin as vertices.

12. Q12Hard

    Solve |x|<3:

    A.x < −3

    B.x > 3

    C.−3 < x < 3✓ Correct

    D.x = 0

    Answer: C. −3 < x < 3

    Explanation: |x|<3 means x is within 3 units of 0 on both sides, giving the intersection −3 < x < 3. Don't confuse this with |x|>3, which splits into two separate rays instead.

13. Q13Hard

    Cost of producing x units of an item is 3x + 100. Cost should be at most 250. Maximum x:

    A.60

    B.50✓ Correct

    C.100

    D.150

    Answer: B. 50

    Explanation: Cost 3x + 100 must satisfy 3x + 100 ≤ 250, so 3x ≤ 150 and x ≤ 50 — the maximum whole number of units is 50, not any value above it.

14. Q14Hard

    Area of region x + y ≤ 6, 2x + y ≤ 8, x ≥ 0, y ≥ 0:

    A.20

    B.16

    C.14 sq units✓ Correct

    D.12

    Answer: C. 14 sq units

    Explanation: The feasible region's vertices are (0,0), (4,0), (2,4) and (0,6), found by intersecting the boundary lines pairwise; the shoelace formula on these four points gives an area of 14 square units.

Linear Inequalities — FAQs

More Class 11 Mathematics chapters

• 01Sets
• 02Relations and Functions
• 03Trigonometric Functions
• 04Principle of Mathematical Induction
• 05Complex Numbers and Quadratic Equations
• 07Permutations and Combinations

Class 11 — other subjects

• Class 11 Biology chapters
• Class 11 Chemistry chapters
• Class 11 Computer Science chapters
• Class 11 English chapters
• Class 11 Physics chapters