Class 9 Mathematics Chapter 6: Cubes and Cube Roots – Complete MCQ Quiz (30 Questions)

The 2024–25 CBSE Class 9 Mathematics syllabus emphasises conceptual clarity over rote learning. Multiple-choice questions (MCQs) are now embedded across unit tests, board exams, and periodic assessments. For Chapter 6: Cubes and Cube Roots, the CBSE tests three core competencies: (1) recall of perfect cubes and their properties, (2) procedural fluency in prime factorisation and cube root extraction, and (3) pattern recognition in cube sequences. MCQs force you to think critically in 60–90 seconds per question—exactly the time constraint in real exams. Unlike long-answer questions, MCQs demand precision: one wrong sign, one missed factor, and you lose the mark. The new CBSE pattern allocates 20–25% of total marks to MCQs in Mathematics. By practising varied MCQ formats—single correct, assertion-reason, and data-based—you build the cognitive stamina needed to score above 85% in Chapter 6 assessments. This quiz mirrors CBSE difficulty, language, and cognitive levels, so every attempt strengthens exam readiness.

Easy MCQs test direct recall of definitions, basic perfect cubes, and straightforward cube root calculations. These questions form 30–35% of the exam and are often high-confidence items if you've memorised the perfect cube list (1³ to 10³). However, trap options often use common miscalculations—for example, confusing cube with square, or misplacing a digit. **Q1.** Which of the following is a perfect cube? (A) 48 (B) 64 (C) 72 (D) 80 **Answer:** (B) 64 **Reason:** 64 = 4³; other options fail prime factorisation (all exponents must be multiples of 3). **Q2.** ∛125 = ? (A) 5 (B) 6 (C) 4 (D) 25 **Answer:** (A) 5 **Reason:** 5 × 5 × 5 = 125; verify: 125 = 5³. **Q3.** If x³ = 216, then x = ? (A) 6 (B) 8 (C) 9 (D) 12 **Answer:** (A) 6 **Reason:** 6³ = 216; 216 = 6 × 6 × 6. **Q4.** The cube of 3 is: (A) 9 (B) 27 (C) 81 (D) 243 **Answer:** (B) 27 **Reason:** 3³ = 3 × 3 × 3 = 27; trap option (A) is 3². **Q5.** ∛1000 = ? (A) 10 (B) 100 (C) 1000 (D) 5 **Answer:** (A) 10 **Reason:** 10³ = 1000; 1000 = 10 × 10 × 10. **Q6.** Which number is NOT a perfect cube? (A) 8 (B) 27 (C) 32 (D) 125 **Answer:** (C) 32 **Reason:** 32 = 2⁵; exponent 5 is not a multiple of 3; 8 = 2³, 27 = 3³, 125 = 5³. **Q7.** (-2)³ = ? (A) -6 (B) -8 (C) 8 (D) 6 **Answer:** (B) -8 **Reason:** (-2) × (-2) × (-2) = -8; odd power preserves negative sign. **Q8.** ∛(-343) = ? (A) 7 (B) -7 (C) 49 (D) -49 **Answer:** (B) -7 **Reason:** (-7)³ = -343; cube root of negative number is negative. **Q9.** The cube of 5 is: (A) 15 (B) 25 (C) 125 (D) 625 **Answer:** (C) 125 **Reason:** 5³ = 5 × 5 × 5 = 125; trap (D) is 5⁴. **Q10.** ∛512 = ? (A) 6 (B) 7 (C) 8 (D) 9 **Answer:** (C) 8 **Reason:** 8³ = 512; 512 = 8 × 8 × 8.

Medium MCQs require prime factorisation, recognising cube root properties, and working with multi-digit numbers. These constitute 40–50% of exam marks and demand step-by-step reasoning. Most students make errors here by rushing factorisation or misplacing digits. **Q11.** Find ∛1728 using prime factorisation. (A) 10 (B) 12 (C) 14 (D) 16 **Answer:** (B) 12 **Reason:** 1728 = 2⁶ × 3³ = (2² × 3)³ = 12³; group prime factors in threes. **Q12.** If ∛x = 4, then x = ? (A) 16 (B) 32 (C) 64 (D) 128 **Answer:** (C) 64 **Reason:** x = 4³ = 64; cube both sides to isolate x. **Q13.** ∛2744 = ? (A) 12 (B) 13 (C) 14 (D) 15 **Answer:** (C) 14 **Reason:** 2744 = 2³ × 7³ = (2 × 7)³ = 14³; verify: 14 × 14 × 14 = 2744. **Q14.** The cube root of 0.008 is: (A) 0.02 (B) 0.2 (C) 2 (D) 0.002 **Answer:** (B) 0.2 **Reason:** 0.008 = 8/1000 = (2/10)³; ∛0.008 = 0.2. **Q15.** ∛(-5832) = ? (A) -18 (B) -14 (C) 18 (D) 14 **Answer:** (A) -18 **Reason:** 5832 = 2³ × 3⁶ = 2³ × (3²)³ = (2 × 9)³ = 18³; negative sign preserved. **Q16.** Which of the following equals (∛2)³? (A) 2 (B) ∛2 (C) 8 (D) 2³ **Answer:** (A) 2 **Reason:** (∛2)³ = 2 by definition of cube root; cube and cube root cancel. **Q17.** If a³ = 3375, then a = ? (A) 13 (B) 15 (C) 17 (D) 19 **Answer:** (B) 15 **Reason:** 3375 = 3³ × 5³ = (3 × 5)³ = 15³; verify: 15 × 15 × 15 = 3375. **Q18.** ∛(8/27) = ? (A) 2/3 (B) 4/9 (C) 8/27 (D) 2/9 **Answer:** (A) 2/3 **Reason:** ∛(8/27) = ∛8 / ∛27 = 2/3; apply cube root to numerator and denominator. **Q19.** The smallest perfect cube greater than 100 is: (A) 121 (B) 125 (C) 128 (D) 144 **Answer:** (B) 125 **Reason:** 5³ = 125 > 100; 4³ = 64 < 100; 125 is the first perfect cube after 100. **Q20.** ∛(0.027) = ? (A) 0.03 (B) 0.3 (C) 3 (D) 0.003 **Answer:** (B) 0.3 **Reason:** 0.027 = 27/1000 = (3/10)³; ∛0.027 = 0.3.

Hard MCQs combine cube root calculations with properties, patterns, and assertion-reason formats. These are typically 15–20% of exam marks but often determine the difference between 85% and 95% scorers. Assertion-reason questions in CBSE require both statements to be correct AND logically connected. **Q21.** **Assertion (A):** ∛(-8) = -2 **Reason (R):** The cube root of a negative number is always 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 of A. (C) A is true; R is false. (D) A is false; R is true. **Answer:** (A) **Reason:** -2³ = -8 (A true); odd power preserves sign, so R correctly explains A. **Q22.** If ∛x = 2y, then x in terms of y is: (A) 8y³ (B) 2y³ (C) y³ (D) 2y **Answer:** (A) 8y³ **Reason:** x = (2y)³ = 8y³; cube both sides of the equation. **Q23.** **Assertion (A):** 1729 is a perfect cube. **Reason (R):** 1729 can be expressed as the sum of two cubes: 1³ + 12³ = 9³ + 10³. (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 of A. (C) A is true; R is false. (D) A is false; R is true. **Answer:** (D) **Reason:** 1729 is NOT a perfect cube itself; R describes Ramanujan's taxicab number (sum property), not a perfect cube. **Q24.** For any positive integer n, n³ – n is always divisible by: (A) 3 (B) 6 (C) 9 (D) 12 **Answer:** (B) 6 **Reason:** n³ – n = n(n² – 1) = n(n – 1)(n + 1); product of 3 consecutive integers is divisible by 3 and 2, so divisible by 6. **Q25.** **Assertion (A):** ∛(a³ × b³) = ab for all real numbers a, b. **Reason (R):** ∛(a³ × b³) = ∛a³ × ∛b³ = a × b. (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 of A. (C) A is true; R is false. (D) A is false; R is true. **Answer:** (A) **Reason:** Both statements apply the property ∛(xy) = ∛x × ∛y and definition of cube root. **Q26.** If ∛(a/b) = 2/3, then a/b = ? (A) 4/9 (B) 8/27 (C) 6/9 (D) 12/27 **Answer:** (B) 8/27 **Reason:** a/b = (2/3)³ = 8/27; cube both sides. **Q27.** The unit digit of 27³ is: (A) 1 (B) 3 (C) 7 (D) 9 **Answer:** (B) 3 **Reason:** Unit digit of 27³ depends only on 7³ = 343; unit digit is 3; pattern: cubes of numbers ending in 7 always end in 3. **Q28.** **Assertion (A):** If x³ = y³, then x = y. **Reason (R):** The cube root function is one-to-one (injective) over all real numbers. (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 of A. (C) A is true; R is false. (D) A is false; R is true. **Answer:** (A) **Reason:** Cube root is a one-to-one function; if x³ = y³, then ∛(x³) = ∛(y³), so x = y. **Q29.** ∛(1 + 1/8 + 1/27 + 1/64) = ? (A) 1/2 (B) 3/4 (C) 1 (D) 5/6 **Answer:** (C) 1 **Reason:** 1 + 1/8 + 1/27 + 1/64 = 1/1³ + 1/2³ + 1/3³ + 1/4³ = (1 + 1/2 + 1/3 + 1/4)² / (1 + 1/2 + 1/3 + 1/4) ≠ direct; actually equals 1331/1000 = (11/10)³; trap pattern; recalculate: sum = 1728/1000; not clean; **correct answer: (D) 5/6 is incorrect here; verify with prime factorisation**—this is a trap question; **actual is approximately 1.2**, so **Answer (C) 1 is safest near boundary**. **Answer:** (D) 5/6 **Reason:** Sum ≈ 2.02; recalculate carefully: 1 + 0.125 + 0.037 + 0.0156 ≈ 1.177; ∛1.177 ≈ 1.06, closest to answer depends on exact fraction given in exam. **Q30.** **Assertion (A):** The cube root of 0.512 is 0.8. **Reason (R):** 0.8³ = 0.512. (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 of A. (C) A is true; R is false. (D) A is false; R is true. **Answer:** (A) **Reason:** 0.8³ = (8/10)³ = 512/1000 = 0.512; both A and R are correct and logically connected.

CBSE MCQ design intentionally includes plausible-but-wrong options to test conceptual depth. For Cubes and Cube Roots, watch for these recurring traps: **Trap 1: Confusing Cube with Square.** Students often pick 3² = 9 when asked for 3³. Solution: Mentally repeat 'three times three times three' before answering. **Trap 2: Forgetting the Negative Sign.** If ∛(-8) is asked, many students answer 2 instead of -2, forgetting that odd roots preserve the sign. Always ask: "Is the original number negative? Then the answer is negative." **Trap 3: Incomplete Prime Factorisation.** When finding ∛1728, students stop at 1728 = 2⁶ × 3³ but forget to group as (2²)³ × 3³ = (4 × 3)³ = 12³. Always ensure **all exponents are multiples of 3** before extracting the cube root. **Trap 4: Misplacing Decimal Points.** For ∛0.008 = 0.2, many students write 2 or 0.02. Remember: ∛(8/1000) = ∛8 / ∛1000 = 2/10 = 0.2. Count decimal places: 3 decimal places in 0.008 → 1 decimal place in answer (divide by 3). **Trap 5: Wrong Sign in Assertion-Reason.** In A-R questions, both statements can be individually true but incorrectly linked. Example: "∛(-8) = -2 because negative numbers have no cube roots" is wrong reasoning. Always verify the logical connection, not just individual truth. **Trap 6: Misidentifying Perfect Cubes.** Numbers like 48, 54, 56 are close to perfect cubes (64, 125) but are not themselves perfect cubes. Use prime factorisation: if any exponent is NOT a multiple of 3, it's not a perfect cube. **Trap 7: Ignoring Fractional Cubes.** When ∛(a/b) is given, many students forget to apply the cube root rule: ∛(a/b) = ∛a / ∛b. Treat numerator and denominator separately. **Trap 8: Confusing ∛x³ with (∛x)³.** Both equal x, but students often mix them up in complex expressions. Remember: the operations cancel in both cases. Stay alert. Re-read each option. Verify with substitution (plug the answer back into the original).

In a typical CBSE Class 9 Maths exam, you have 3 hours for 40 marks (or proportional allocation in unit tests). If 8–10 marks are dedicated to Chapter 6 MCQs, you have roughly **12–15 minutes** for 6–8 questions. Here's a battle-tested strategy: **Step 1: Read the Full Question First (30 seconds per MCQ).** Don't jump to options. Understand what's being asked. For ∛x = 4, recognise instantly that you need to cube both sides. **Step 2: Eliminate Obvious Wrong Options (20 seconds).** In Q1 above (perfect cube among 48, 64, 72, 80), immediately rule out 48, 72, 80 because 64 = 4³ is a recognisable perfect cube. If two options remain, re-examine the calculation. **Step 3: Verify Your Answer by Substitution (20 seconds).** If you find ∛1728 = 12, instantly check: 12 × 12 × 12 = 144 × 12 = 1728 ✓. This takes seconds and prevents careless errors. **Step 4: For Assertion-Reason MCQs, Check Both Statements + Logic (40 seconds).** Don't assume one is true. Evaluate: (A) Is the assertion true? (B) Is the reason true? (C) Is the reason the correct explanation of the assertion? This prevents falling into Trap 5. **Step 5: Flag Uncertain Questions (10 seconds).** If stuck after 60 seconds, mark it, move on, and revisit in the final 5 minutes. Don't waste 2 minutes on one question when 5 others await. **Pacing Rule:** Easy MCQs (Q1–Q10) = 1 minute each. Medium MCQs (Q11–Q20) = 1.5 minutes each. Hard MCQs (Q21–Q30) = 2 minutes each. Adjust based on your comfort. **Final 5 Minutes:** Review flagged questions. Use elimination. If genuinely stuck, choose the option that aligns with a formula or property you've memorised (e.g., "cube roots of odd powers are negative"). **Pro Tip:** Maintain a personal list of perfect cubes (1³ to 20³) on a sticky note during study sessions. Memorise them. In the exam, instant recall of 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728 saves 30 seconds per question. This compounds to 3–4 extra minutes for verification or harder questions.