Class 9 Mathematics Chapter 10: The Other Side of Zero – 30 MCQ with Answers & Explanations

The 2024-25 rationalized CBSE syllabus heavily emphasizes conceptual clarity over rote learning. Multiple-choice questions dominate modern Class 9 assessments because they test: (1) speed of recall — can you identify the correct integer rule in 30 seconds? (2) Conceptual depth — do you understand *why* −3 < −1 on the number line? (3) Application ability — can you solve a real-world temperature or debt problem using integer operations? Unlike long-form answers, MCQs force you to distinguish between four plausible options, which sharpens your critical thinking. Research shows that students who solve 25+ quality MCQs before the final exam improve their scores by 15–20%. The new CBSE pattern includes more assertion-reason pairs (Type D MCQs) where both a statement and its reasoning must be true — a format that rewards deeper conceptual work. This quiz trains you on all three MCQ types: standalone single-correct (Type A), multiple-correct (Type B), and assertion-reason (Type D). Practicing now builds the neural pathways for fast, accurate exam performance.

**Q1.** Which of the following is NOT an integer? (A) −5 (B) 0 (C) 3.5 (D) 12 **Answer:** (C) 3.5 **Reason:** Integers are whole numbers (positive, negative, or zero); 3.5 is a decimal, not an integer. **Q2.** On a number line, which number is to the right of −2? (A) −5 (B) −3 (C) −1 (D) −6 **Answer:** (C) −1 **Reason:** Numbers increase from left to right on a number line; −1 > −2. **Q3.** What is the additive inverse of 7? (A) 7 (B) −7 (C) 1/7 (D) 0 **Answer:** (B) −7 **Reason:** Additive inverse of a number is what you add to it to get 0; 7 + (−7) = 0. **Q4.** Compare: −4 ____ −8 (A) < (B) > (C) = (D) ≤ **Answer:** (B) > **Reason:** −4 is closer to 0 on the number line, so it is greater than −8. **Q5.** The temperature drops from 5°C to −3°C. What is the change? (A) 2°C (B) 8°C (C) −8°C (D) 3°C **Answer:** (B) 8°C **Reason:** Change = Final − Initial = −3 − 5 = −8; absolute change is 8°C drop. **Q6.** What is −6 + 4? (A) −10 (B) −2 (C) 2 (D) 10 **Answer:** (B) −2 **Reason:** Start at −6, move 4 units right: −6 + 4 = −2. **Q7.** Which integer is between −2 and 2? (A) −3 (B) 2 (C) −2 (D) 0 **Answer:** (D) 0 **Reason:** 0 lies strictly between −2 and 2 on the number line. **Q8.** A bank account shows a balance of −₹500 (overdraft). What does this mean? (A) ₹500 profit (B) ₹500 debt (C) ₹500 saved (D) No balance **Answer:** (B) ₹500 debt **Reason:** Negative balance indicates money owed to the bank. **Q9.** What is 3 − (−5)? (A) −2 (B) 2 (C) 8 (D) −8 **Answer:** (C) 8 **Reason:** Subtracting a negative is the same as adding a positive: 3 − (−5) = 3 + 5 = 8. **Q10.** A submarine is at 200 metres depth. Express this as an integer. (A) 200 (B) −200 (C) 0 (D) 100 **Answer:** (B) −200 **Reason:** Depth below sea level is represented as a negative integer.

**Q11.** Solve: −12 + (−8) − (−5) = ? (A) −15 (B) −5 (C) 25 (D) −25 **Answer:** (A) −15 **Reason:** −12 − 8 + 5 = −20 + 5 = −15. **Q12.** A company's profit/loss over 4 months: +₹10,000, −₹5,000, −₹3,000, +₹8,000. Net result? (A) Loss of ₹10,000 (B) Profit of ₹10,000 (C) Loss of ₹5,000 (D) Profit of ₹5,000 **Answer:** (B) Profit of ₹10,000 **Reason:** 10,000 − 5,000 − 3,000 + 8,000 = 10,000. **Q13.** If x = −6, what is the value of −2x + 3? (A) 15 (B) 9 (C) −9 (D) −15 **Answer:** (A) 15 **Reason:** −2(−6) + 3 = 12 + 3 = 15. **Q14.** Arrange in ascending order: −1, 3, −5, 0, 2 (A) −5, −1, 0, 2, 3 (B) 3, 2, 0, −1, −5 (C) −1, −5, 0, 2, 3 (D) 0, −1, −5, 2, 3 **Answer:** (A) −5, −1, 0, 2, 3 **Reason:** Ascending means left to right on the number line from smallest to largest. **Q15.** A diver descends 15 metres, then ascends 6 metres. Net position relative to start? (A) −9 metres (B) 9 metres (C) −21 metres (D) 21 metres **Answer:** (A) −9 metres **Reason:** −15 + 6 = −9 (still 9 metres below starting point). **Q16.** The sum of two integers is −8. If one integer is 3, the other is: (A) −5 (B) 5 (C) −11 (D) 11 **Answer:** (C) −11 **Reason:** If 3 + x = −8, then x = −8 − 3 = −11. **Q17.** Which statement is true? (A) −20 > −10 (B) −20 < −10 (C) −20 = −10 (D) −20 ≥ −10 **Answer:** (B) −20 < −10 **Reason:** −20 is further left on the number line, hence smaller than −10. **Q18.** Temperature at midnight: −2°C. After 3 hours, it drops by 4°C. Temperature now: (A) 2°C (B) 6°C (C) −6°C (D) −1°C **Answer:** (C) −6°C **Reason:** −2 − 4 = −6°C. **Q19.** Simplify: (−7) × (−3) + (−5) = ? (A) 16 (B) 26 (C) −26 (D) −16 **Answer:** (A) 16 **Reason:** (−7) × (−3) = 21 (negative × negative = positive); 21 + (−5) = 16. **Q20.** Which pair of integers has a sum of −3? (A) −5 and 2 (B) 4 and −7 (C) −6 and 3 (D) 1 and −4 **Answer:** (A) −5 and 2 **Reason:** −5 + 2 = −3.

**Q21. (Assertion-Reason)** **Assertion (A):** The product of three negative integers is always negative. **Reason (R):** When multiplied, an even number of negatives gives positive, an odd number gives negative. (A) Both A and R are true; R is the correct explanation of A (B) Both A and R are true; R is NOT the correct explanation (C) A is true; R is false (D) A is false; R is true **Answer:** (A) **Reason:** Three negatives (odd count) → negative product; R correctly explains why. **Q22.** If |x| = 7, then x could be: (A) Only 7 (B) Only −7 (C) Either 7 or −7 (D) Neither **Answer:** (C) Either 7 or −7 **Reason:** Absolute value |x| = 7 means x is 7 units from 0, so x = ±7. **Q23.** A number on the number line is 5 units to the left of −3. Which integer is it? (A) 2 (B) −2 (C) −8 (D) 8 **Answer:** (C) −8 **Reason:** 5 units left of −3 means −3 − 5 = −8. **Q24. (Assertion-Reason)** **Assertion (A):** −5 + (−3) = −8 **Reason (R):** When adding two negative integers, add their absolute values and place a negative sign. (A) Both A and R are true; R is the correct explanation (B) Both A and R are true; R is NOT the correct explanation (C) A is true; R is false (D) A is false; R is true **Answer:** (A) **Reason:** |−5| + |−3| = 5 + 3 = 8; result is −8. R correctly justifies A. **Q25.** For integers a, b, c, if a < b and b < c, then: (A) a = c (B) a > c (C) a < c (D) a ≤ b < c **Answer:** (C) a < c **Reason:** Transitivity of inequality: if a < b and b < c, then a < c. **Q26.** A lift starts at floor 5, goes down 8 floors, then up 3 floors. Which floor now? (A) 16 (B) 0 (C) 6 (D) −2 (basement) **Answer:** (B) 0 (ground floor) **Reason:** 5 − 8 + 3 = 0 (no basement; floor 0 is ground). **Q27. (Assertion-Reason)** **Assertion (A):** For any integer n, n − (−n) = 2n **Reason (R):** Subtracting a negative equals adding a positive. (A) Both A and R are true; R is the correct explanation (B) Both A and R are true; R is NOT the correct explanation (C) A is true; R is false (D) A is false; R is true **Answer:** (A) **Reason:** n − (−n) = n + n = 2n. R correctly explains why the subtraction becomes addition. **Q28.** Which expression does NOT equal 10? (A) 15 + (−5) (B) −8 − (−18) (C) 20 − 10 (D) −5 + 14 **Answer:** (C) 20 − 10 = 10 (Wait, this DOES equal 10.) *Correction:* Let me redo this. **Q28.** Which expression DOES equal −10? (A) 15 + (−5) (B) −8 − 2 (C) 20 − 10 (D) −5 − 5 **Answer:** (D) −5 − 5 = −10 **Reason:** (A) = 10, (B) = −10, (C) = 10, (D) = −10. Both B and D work; if single-answer format, (D) is clearer. **Q29.** A bank ledger shows: Deposit +₹2,000, Withdrawal −₹500, Fine −₹100, Interest +₹50. Final balance relative to opening: (A) +₹1,550 (B) +₹1,450 (C) −₹1,450 (D) +₹2,500 **Answer:** (B) +₹1,450 **Reason:** 2,000 − 500 − 100 + 50 = 1,450. **Q30. (Assertion-Reason)** **Assertion (A):** The integer −1 is greater than −10. **Reason (R):** On the number line, numbers to the right are always greater. (A) Both A and R are true; R is the correct explanation (B) Both A and R are true; R is NOT the correct explanation (C) A is true; R is false (D) A is false; R is true **Answer:** (A) **Reason:** −1 is to the right of −10, so −1 > −10. R correctly justifies A.

**Trap 1: Confusing Absolute Value with the Integer Itself** Many students pick |−5| = 5 and then forget that the original integer is −5, not 5. In comparison questions like '−5 ___ −3', the trap option is often 5 > 3, so −5 > −3, which is FALSE. The correct answer is −5 < −3. *Always remember:* On the number line, further left = smaller. **Trap 2: Sign Errors in Subtraction of Negatives** Subtracting a negative is adding a positive: 3 − (−5) = 3 + 5 = 8. A common wrong answer is 3 − 5 = −2 (students forget to flip the sign). Test yourself: what is −10 − (−4)? Correct: −10 + 4 = −6. Wrong: −10 − 4 = −14. **Trap 3: Misinterpreting Real-World Contexts** In debt/depth/temperature questions, negatives represent opposite directions. If a submarine descends 200 m, that's −200, not +200. If a bank balance is −₹500, it's a debt, not an asset. The trap is picking the positive number thinking 'deeper' or 'more in debt' means bigger magnitude. *Always assign signs based on context first.* **Trap 4: Order of Operations Mistakes** In expressions like −2 × (−3) + (−5), students often compute left-to-right: −2 × −3 = 6, then 6 + (−5) = 1 (CORRECT). But some students do −2 × (−3 + (−5)) = −2 × (−8) = 16 (WRONG — they didn't follow BODMAS). *Always multiply/divide before adding/subtracting.* **Trap 5: Confusing Comparison Symbols** The symbol '<' looks like it points to the smaller number, and it does: −7 < −2 (−7 is on the left, so it's smaller). But visually, since −7 appears 'bigger' in magnitude, students flip it. *Read carefully: the open end of '<' always faces the larger number.* **Trap 6: Adding vs. Subtracting in Word Problems** If temperature 'drops by 4°C', you subtract: current − 4. If a diver 'descends 15 m', you use −15. The trap is confusing 'increase' with 'positive' and 'decrease' with 'negative' — they're not synonyms; the sign depends on direction. *Reread the verb: 'drops', 'descends', 'loses' all mean subtract or go negative.* Start a 3-day free trial at cbsetutor.ai to access video explanations for each trap and interactive drills that catch these errors before your exam.

In a typical CBSE Class 9 Mathematics exam, you'll face 5–10 MCQs from Chapters 10–12 combined, worth 1–2 marks each. To maximize your score, allocate time wisely. **Phase 1: Quick Scan (1 minute)** Before answering, skim all MCQs and mentally sort them: 'easy' (number line comparisons, basic arithmetic), 'medium' (multi-step operations, simple word problems), 'hard' (assertion-reason, abstract integer rules). Solve easy ones first — they're your confidence builders. **Phase 2: Solve Easy MCQs (6–7 minutes)** Questions like 'Compare −4 and −8' or 'What is 3 + (−5)?' should take 15–20 seconds each. These are non-negotiable points; never skip or rush them. Use rough working on paper to avoid arithmetic errors. **Phase 3: Solve Medium MCQs (8–10 minutes)** Multi-step calculations or single-context word problems require 1–1.5 minutes each. Read the scenario once, underline key numbers, set up the calculation, and verify. For example: 'A company profit/loss over 4 months is +10, −5, −3, +8. Net result?' Write: 10 − 5 − 3 + 8 = 10 on paper before selecting the answer. **Phase 4: Tackle Hard / Assertion-Reason MCQs (10–12 minutes)** These are worth the same points as easy MCQs, so don't overinvest. Read the Assertion carefully. Read the Reason carefully. Decide: (1) Is A true? (2) Is R true? (3) Does R explain A? If unsure, mark for review and move on — don't waste 3 minutes on one hard MCQ. **Phase 5: Review & Verify (3–4 minutes)** With remaining time, re-check your marked questions. In assertion-reason MCQs, cross-verify by substituting an example (e.g., if A says 'product of three negatives is negative', test −1 × −2 × −3 = −6. Yes, true). For word problems, reverse-check: if you got net profit ₹10,000, does 10 − 5 − 3 + 8 = 10? Yes. **Timing Benchmark:** - Easy MCQs: 1 min for 6–7 questions - Medium MCQs: 10 min for 8–10 questions - Hard MCQs: 8 min for 3–5 questions - Review: 2–3 min **Pro Tip:** If a word problem is confusing, re-read it once. If still unclear, note the answer choices and work backward: 'If the net result is −15, then the total must be... did the calculation prove it?' This saves time versus building the answer from scratch. Practice this strategy with the 30 MCQs above, timing yourself with a stopwatch.

Completing all 30 MCQs is an excellent checkpoint. If you scored 25+ (83%), you're ready for Chapter 11 (Linear Equations) and beyond. If you scored 18–24 (60–80%), review the 'Common Trap Options' section and retry the medium MCQs — they often reveal weak spots in sign rules. If you scored below 18, focus on the Easy and Medium MCQs and understand the *why* behind each answer, not just the correct option. **Next learning steps:** 1. **Revise NCERT Chapter 10 key rules:** Integers on number line, absolute value, additive/multiplicative identity, properties of operations (closure, commutativity, associativity). 2. **Practice word problems** beyond the 30 MCQs. Create your own: 'A lift scenario', 'A temperature scenario', 'A bank balance scenario' and solve them in 2 minutes each. 3. **Learn assertion-reason structure:** These MCQs are CBSE's way of testing conceptual depth. Allocate 10 minutes weekly to assertion-reason pairs from NCERT examples. 4. **Connect Chapter 10 to Algebra:** Integer rules directly apply to solving equations (Chapter 14). If you're weak here, you'll struggle later. 5. **Take full-length mock tests:** After mastering MCQs, attempt mixed-chapter tests (Chapters 1–12) to see how integers fit into the broader exam landscape. For personalized guidance, diagnostic reports, and video walkthroughs of difficult concepts, try cbsetutor.ai's structured Class 9 Mathematics path — it systematically builds from Chapter 10 through to final-year topics.