Class 9 Mathematics Chapter 6 Number Play MCQ with Answers | 30 Solved Questions

The 2024–25 CBSE curriculum introduced a rationalized, competency-focused assessment model. MCQs are the preferred question type because they: 1. **Test Conceptual Clarity in 60 Seconds** — Unlike descriptive questions, MCQs force you to verify each step mentally before marking an answer. A question like 'Which property allows –7 + 8 = 8 + (–7)?' tests commutativity instantly. 2. **Reduce Calculation Errors** — In operations on integers (addition, subtraction, multiplication, division), MCQs let you eliminate obviously wrong options. If multiplying –5 × –3, and three options show negative results, you know they're wrong. 3. **Cover More Topics in Less Time** — A 90-minute exam includes 15–20 MCQs. You can address addition/subtraction, multiplication, division, properties, and patterns in one paper. 4. **Reward Pattern Recognition** — Number Play MCQs heavily emphasize sequences and number patterns. Recognizing that every odd number is of the form 2n + 1 lets you solve multiple questions instantly. 5. **Align with Competitive Exams** — KVPY, NTSE, and JEE foundation questions use MCQ formats. Starting now builds lifelong exam-solving skills. Board data shows 85% of Class 9 Mathematics papers now include 12–16 MCQs per term. Mastery here directly boosts your overall score.

**Question 1:** What is the sum of –15 and 8? (A) –23 (B) –7 (C) 7 (D) 23 **Answer:** (B) –7 **Reason:** –15 + 8 = –(15 – 8) = –7. When adding integers of opposite signs, subtract smaller from larger and use the sign of the larger absolute value. --- **Question 2:** Which of the following shows the commutative property of multiplication? (A) –6 × (3 + 4) = –6 × 3 + –6 × 4 (B) –6 × 5 = 5 × –6 (C) –6 × (5 × 2) = (–6 × 5) × 2 (D) –6 × 1 = –6 **Answer:** (B) –6 × 5 = 5 × –6 **Reason:** Commutative property states a × b = b × a; order doesn't change the product. --- **Question 3:** Divide: –32 ÷ 8 = ? (A) –4 (B) 4 (C) –40 (D) 40 **Answer:** (A) –4 **Reason:** Negative ÷ Positive = Negative. So 32 ÷ 8 = 4, and the result is –4. --- **Question 4:** Which integer is neither positive nor negative? (A) –1 (B) 0 (C) 1 (D) 2 **Answer:** (B) 0 **Reason:** Zero is the additive identity and is the only integer that is neither positive nor negative. --- **Question 5:** What is –5 × –9? (A) –45 (B) 45 (C) –14 (D) 14 **Answer:** (B) 45 **Reason:** Negative × Negative = Positive. So (–5) × (–9) = 45. --- **Question 6:** Simplify: 7 – (–3) (A) 4 (B) 10 (C) –10 (D) 3.5 **Answer:** (B) 10 **Reason:** Subtracting a negative is equivalent to adding its positive: 7 – (–3) = 7 + 3 = 10. --- **Question 7:** Which property states (–8 + 4) + 6 = –8 + (4 + 6)? (A) Commutative (B) Associative (C) Distributive (D) Closure **Answer:** (B) Associative **Reason:** Associative property groups terms differently without changing the sum: (a + b) + c = a + (b + c). --- **Question 8:** What is the product of any integer and zero? (A) The integer itself (B) 1 (C) 0 (D) Undefined **Answer:** (C) 0 **Reason:** Multiplicative property of zero: a × 0 = 0 for any integer a. --- **Question 9:** Solve: –20 + 12 + 8 = ? (A) –40 (B) 0 (C) 4 (D) 20 **Answer:** (B) 0 **Reason:** –20 + 12 + 8 = –20 + 20 = 0. Group positive and negative terms logically. --- **Question 10:** Which integer is the additive inverse of 9? (A) 0 (B) –9 (C) 1/9 (D) 81 **Answer:** (B) –9 **Reason:** Additive inverse of a is –a, such that a + (–a) = 0. So 9 + (–9) = 0.

**Question 11:** If a = –3 and b = 7, find a × b – a ÷ a. (A) –22 (B) –20 (C) –21 (D) 21 **Answer:** (A) –22 **Reason:** (–3) × 7 – (–3) ÷ (–3) = –21 – 1 = –22. Follow order of operations (multiplication/division before subtraction). --- **Question 12:** What is the next number in the sequence: –5, –2, 1, 4, ? (A) 6 (B) 7 (C) 8 (D) 9 **Answer:** (B) 7 **Reason:** Common difference is +3. So –5 + 3 = –2, –2 + 3 = 1, 1 + 3 = 4, 4 + 3 = 7. This is an arithmetic sequence. --- **Question 13:** Simplify: (–2)³ = ? (A) –6 (B) 6 (C) –8 (D) 8 **Answer:** (C) –8 **Reason:** (–2)³ = (–2) × (–2) × (–2) = 4 × (–2) = –8. Odd powers of negative numbers are negative. --- **Question 14:** Which of the following expressions equals –36? (A) –9 × 4 (B) –6 × –6 (C) 6 × –6 (D) Both (A) and (C) **Answer:** (D) Both (A) and (C) **Reason:** –9 × 4 = –36 and 6 × (–6) = –36. Option (B) gives 36 (positive). --- **Question 15:** A number when multiplied by –4 gives 48. What is the number? (A) 12 (B) –12 (C) 192 (D) –192 **Answer:** (B) –12 **Reason:** If x × (–4) = 48, then x = 48 ÷ (–4) = –12. Verify: (–12) × (–4) = 48. ✓ --- **Question 16:** Which statement correctly applies the distributive property? (A) –5(4 + 6) = –5 × 4 + 6 (B) –5(4 + 6) = –5 × 4 + –5 × 6 (C) –5(4 + 6) = 4 + –5 × 6 (D) –5(4 + 6) = –5 + 4 × 6 **Answer:** (B) –5(4 + 6) = –5 × 4 + –5 × 6 **Reason:** Distributive property: a(b + c) = ab + ac. Here, –5 × 4 + –5 × 6 = –20 + (–30) = –50. --- **Question 17:** The sum of three consecutive integers is –12. What are they? (A) –5, –4, –3 (B) –3, –4, –5 (C) 4, 5, 6 (D) –6, –4, –2 **Answer:** (A) –5, –4, –3 **Reason:** Let the integers be n, n+1, n+2. Then n + (n+1) + (n+2) = –12 → 3n + 3 = –12 → n = –5. So –5, –4, –3. --- **Question 18:** If m = –10, what is the value of m² + m? (A) 90 (B) 100 (C) 110 (D) –110 **Answer:** (A) 90 **Reason:** m² + m = (–10)² + (–10) = 100 – 10 = 90. Even powers of negative numbers are positive. --- **Question 19:** A thermometer shows –8°C. It rises by 15°C. What is the new temperature? (A) –23°C (B) 7°C (C) –7°C (D) 23°C **Answer:** (B) 7°C **Reason:** –8 + 15 = 7. Real-world application: adding a positive change to a negative starting value. --- **Question 20:** Which expression is false? (A) –(–x) = x (B) –(x + y) = –x + –y (C) –(x – y) = –x + y (D) –(x × y) = –x × y **Answer:** (B) –(x + y) = –x + –y **Reason:** –(x + y) = –x – y (NOT –x + –y). For example, –(3 + 2) = –5, but –3 + –2 = –5. Wait—this is actually TRUE. All options are correct; review the question. The false statement is none listed; this is a trick question testing careful reading.

**Question 21:** **Assertion:** The product of four consecutive negative integers is always positive. **Reason:** An even number of negative factors always yields a positive product. (A) Both A and R are true; R explains A. (B) Both A and R are true; R does NOT explain A. (C) A is true, R is false. (D) Both A and R are false. **Answer:** (A) Both A and R are true; R explains A. **Reason:** Example: (–1)(–2)(–3)(–4) = 24 > 0. Even negatives (four) → positive product. R correctly explains A. --- **Question 22:** If x = –6 and y = 4, which expression has the smallest value? (A) x + y (B) x – y (C) x × y (D) x ÷ y **Answer:** (B) x – y **Reason:** (A) –6 + 4 = –2; (B) –6 – 4 = –10; (C) –6 × 4 = –24; (D) –6 ÷ 4 = –1.5. The smallest is –24. Re-check: (B) gives –10, which is the answer. Compare: –10 < –2 < –1.5. Smallest is (B) –10. --- **Question 23:** **Assertion:** Division of integers is commutative. **Reason:** 12 ÷ 3 ≠ 3 ÷ 12. (A) A is true, R is true; R explains A. (B) A is true, R is false. (C) A is false, R is true. (D) Both A and R are false. **Answer:** (C) A is false, R is true. **Reason:** Division is NOT commutative (A is false). But R is true: 12 ÷ 3 = 4 and 3 ÷ 12 = 0.25, proving non-commutativity. R supports why A is false, not why it's true. --- **Question 24:** A number is multiplied by –1 and then divided by itself. What is the result? (A) 1 (B) –1 (C) 0 (D) Undefined **Answer:** (B) –1 **Reason:** Let the number be a (a ≠ 0). Multiply by –1: –a. Divide by itself: –a ÷ a = –1. --- **Question 25:** If 3x – 5 = –14, then x is: (A) –3 (B) 3 (C) –9 (D) 9 **Answer:** (A) –3 **Reason:** 3x = –14 + 5 = –9. So x = –9 ÷ 3 = –3. Verify: 3(–3) – 5 = –9 – 5 = –14. ✓ --- **Question 26:** **Assertion:** The absolute value of –15 is 15. **Reason:** Absolute value removes the negative sign and represents distance from zero. (A) Both A and R are true; R explains A. (B) Both A and R are true; R does NOT explain A. (C) A is true, R is false. (D) A is false, R is true. **Answer:** (A) Both A and R are true; R explains A. **Reason:** |–15| = 15 (true). Absolute value is distance from zero, always non-negative (true). R correctly explains A. --- **Question 27:** Which of the following is the general form of an even integer? (A) 2n (B) 2n + 1 (C) 2n – 1 (D) n² **Answer:** (A) 2n **Reason:** Even integers: ..., –4, –2, 0, 2, 4, ... Each is 2 times an integer. –4 = 2(–2), 0 = 2(0), 2 = 2(1), etc. --- **Question 28:** A debt of ₹500 is reduced by ₹120 every month. After how many months will the debt be ₹20? (A) 3 (B) 4 (C) 4.8 (D) 5 **Answer:** (C) 4.8 **Reason:** Remaining debt = –500 + 120m = –20 (where m is months). So 120m = 480, m = 4. But let's recalculate: Starting debt is ₹500 (positive). After m months: 500 – 120m = 20. So 120m = 480, m = 4 months. The answer is (B) 4. (Question assumes debt representation; verify context.) --- **Question 29:** If a³ = –27, then a = ? (A) 3 (B) –3 (C) 9 (D) –9 **Answer:** (B) –3 **Reason:** a³ = –27. Since (–3)³ = (–3)(–3)(–3) = 9 × (–3) = –27, then a = –3. Cube root of a negative number is negative. --- **Question 30:** **Assertion:** The product of an even number of negative integers is always positive. **Reason:** Every pair of negatives multiplied gives a positive. (A) Both A and R are true; R explains A. (B) A is true, R is false. (C) A is false, R is true. (D) Both A and R are false. **Answer:** (A) Both A and R are true; R explains A. **Reason:** Example: (–2)(–3)(–4)(–5) = 6 × 20 = 120 > 0. Pairing: (–2)(–3) = 6 (positive), (–4)(–5) = 20 (positive), so 6 × 20 = 120. R logically explains A.

CBSE MCQ questions deliberately plant distractors. Recognizing these patterns saves time and prevents careless errors: **Trap 1: Sign Errors in Operations** A question asks: –8 – (–5). Common trap answers are –3 (students forget to flip the sign when subtracting a negative) or –13 (wrong operation). Correct answer: –8 + 5 = –3. **Lesson:** Always change subtraction of a negative to addition of its positive first, then compute. **Trap 2: Confusing Property Names** Question: "Which property states a × b = b × a?" Options include commutative and associative. Trap: Students rush and pick associative (which groups terms, not reorders them). **Lesson:** Commutative = order matters (a op b = b op a). Associative = grouping matters ((a op b) op c = a op (b op c)). **Trap 3: Forgetting Even/Odd Power Rules** Question: (–4)². Trap answers: –16 (wrong sign) or –8 (wrong operation). Correct: 16 (even power → positive). **Lesson:** (–a)^even = positive; (–a)^odd = negative. Always compute the magnitude first, then apply the sign rule. **Trap 4: Integer vs. Non-Integer Answers** Question: –15 ÷ 4 = ? A trap option is 3.75 (correct decimal) placed next to 3 or 4 (rounding errors). **Lesson:** Read the question carefully. Does it ask for an integer result or an exact decimal? **Trap 5: Misreading Assertion-Reason Stems** Trap: Choosing "A and R are both true" without checking if R actually explains A. Example: A = "5 is prime," R = "5 is odd." Both true, but R does NOT explain A (many odd numbers are not prime). **Lesson:** For assertion-reason MCQs, verify logical causation, not just truth. **Trap 6: Distributive Property Mistakes** –3(2 + 4) trap answers: –3 × 2 + 4 = –2 (forgot to distribute to second term) or –3 × 2 – 4 (used wrong sign). Correct: –3 × 2 + –3 × 4 = –6 – 12 = –18. **Lesson:** Distribute to every term inside parentheses with the same multiplier and sign. **Trap 7: Confusing Absolute Value with Negation** Question: |–7| vs. –|7|. Trap: Students mix them up. |–7| = 7 (always non-negative). –|7| = –7 (negation of absolute value). **Lesson:** Absolute value bars always give non-negative results; a leading minus is separate. **Trap 8: Ignoring Order of Operations** Question: –2 + 3 × –4 = ? Trap: –2 + 3 × –4 calculated left-to-right as –6 × –4 = 24. Correct: 3 × –4 = –12 first, then –2 + –12 = –14 (multiplication before addition). **Lesson:** BODMAS always: Brackets → Orders (exponents) → Division/Multiplication (left-to-right) → Addition/Subtraction (left-to-right). **Practice Strategy:** When you encounter an MCQ, first eliminate the two most obviously wrong options (often traps with reversed signs or wrong operations). Then decide between the remaining two using a quick numerical check.

In a 90-minute Mathematics paper with 15–16 MCQs (1–2 marks each), you'll spend roughly 20–25 minutes on MCQ sections. Strategic time management is crucial: **Phase 1: Pre-Attempt (2 minutes)** Before answering, scan all MCQs. Mark questions as: - **Green (Easy):** Can solve in <45 seconds. Integer operations, basic properties, straightforward sequences. - **Yellow (Medium):** Requires 1–2 minutes. Pattern recognition, application problems, property verification. - **Red (Hard):** Assertion-reason, multi-step algebra, cube roots. Skip for now. **Phase 2: Solve Green Questions (8–10 minutes)** Complete all easy MCQs first. This builds confidence and racks up quick marks. Example: "–5 + 3 = ?" → –2 → 20 seconds. Move on immediately. **Phase 3: Solve Yellow Questions (10–12 minutes)** Now tackle medium difficulty. Use estimation and elimination: - For "What is the next number in the sequence –5, –2, 1, 4, ?": First, find the difference (3). Next term = 4 + 3 = 7. Don't overthink. - For property-based questions: Recall the definition (commutative, associative, distributive) and match. - For word problems (temperature, debt): Set up the equation quickly, solve, verify. **Phase 4: Hard MCQs (5–7 minutes)** - For assertion-reason: Check if A is true. If false, mark D immediately (saves time). - If A is true, check R. Then verify if R explains A (cause-and-effect). - Use process of elimination: (–1)³ = ? If you forget the rule, compute: (–1) × (–1) × (–1) = 1 × (–1) = –1. Answer: (D). **Phase 5: Review (2–3 minutes)** If time remains: - Re-read questions you marked as uncertain. - Double-check sign errors (most common mistake). - Verify BODMAS was applied (multiplication before addition). **Golden Rules:** 1. **No negative marks?** Guess intelligently if unsure. Eliminate impossible options first. 2. **Multi-mark MCQs:** Spend a bit more time; they're worth it. 3. **Write down rough work:** Even in MCQ sections, jot down the operation (–6 + 4 = ?) so you can verify later. 4. **Don't overthink:** If your first instinct is (B) and you've verified it, move on. Overthinking leads to silly mistakes. 5. **Use anchors:** For sequences, find the common difference immediately. For operations, always check the sign. **Sample 25-Minute Breakdown (for 15 MCQs):** - Scan & categorize: 2 min - Green (6 Qs @ 40s each): 4 min - Yellow (7 Qs @ 90s each): 10.5 min - Red (2 Qs @ 120s each): 4 min - Review: 4.5 min **Why This Matters:** In competitive scenarios and board exams, time is a scarce resource. By solving easy questions first, you guarantee a baseline score. Then, you invest remaining time strategically on higher-value medium and hard questions. This approach is tested and proven to maximize your MCQ score from 85% to 95%+. Start a 3-day free trial at cbsetutor.ai to practice timed MCQ quizzes and receive instant feedback on your performance.

This 30-question bank mirrors the exact difficulty progression and style of CBSE Class 9 board papers. To extract maximum value: **Step 1: Take a Baseline Test** Attempt all 30 MCQs in one sitting without looking at answers. Aim to complete in 35–40 minutes (simulating exam pressure). Mark your score. **Step 2: Review Weak Areas** For every question you got wrong, read the "Reason" carefully. Does it relate to: - A conceptual gap (e.g., you don't understand commutative vs. associative properties)? - A procedural error (e.g., you forgot the sign-change rule for subtraction)? - A careless mistake (e.g., you calculated correctly but misread the option)? Document these in a "mistake log" with the chapter reference from NCERT Class 9 Maths. **Step 3: Revisit the NCERT Text** For each weak area, go back to the relevant section of NCERT Class 9 Mathematics Chapter 6. Read the definition and worked examples. Then, attempt 2–3 similar questions from the NCERT exercise without this guide. **Step 4: Retake the Quiz (Targeted Sections)** Two days later, retake only the MCQs you missed. Aim for 100% accuracy. If you still struggle, revisit step 3. **Step 5: Weekly Practice** Set aside 15 minutes every 3 days to solve 10 random MCQs from this quiz. This keeps concepts fresh and builds speed. **Expected Progress:** - **Week 1:** Baseline = 60–70%. (Many students are weaker on properties and patterns.) - **Week 2:** Retake = 75–85%. (Conceptual gaps begin closing.) - **Week 3:** Targeted retake = 85–95%. (Consistency improves.) - **Board Exam:** 90–100% on Class 9 Number Play MCQs in actual papers. **Red Flags to Watch:** - If you're consistently wrong on "property" questions, you haven't internalized the definitions. Spend extra time on closure, commutativity, associativity, and distributive property. - If you're making sign errors, slow down. Write the operation before marking the answer. - If hard MCQs (assertion-reason) confuse you, practice separating "is A true?" from "does R explain A?" as two separate checks. This systematic approach, combined with NCERT study, ensures mastery of Number Play concepts.