Last Updated on May 17, 2025 by XAM CONTENT
Understanding the key concepts of Class 10 Maths Chapter 1 – Real Numbers is crucial for exam success. To make your revision easier, we have created chapterwise mcq questions with Answers for class 10 Maths based on the latest syllabus and exam pattern. It is a part of MCQ Questions for CBSE Class 10 Maths Series.
These multiple-choice questions will help you assess your knowledge, improve accuracy, and boost confidence for your exams. Whether you are preparing for school tests, online tests or competitive exams, these Real Numbers MCQs will strengthen your conceptual clarity.
| Chapter | Real Numbers |
| Book | Maths Textbook for Class 10 |
| Type of Questions | MCQ Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 10 |
| Subject | Maths |
| Useful for | Class 10 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 10 Maths Chapterwise MCQ Questions |
MCQ Questions on Real Numbers Class 10 Maths (PDF Download)
MCQs
Q1. Which of the following statements best explains why the number 4ⁿ can never end with a zero for any natural number n?
(a) Because 4ⁿ is always even
(b) Because 4ⁿ is not divisible by 5
(c) Because 4ⁿ has an odd number of factors
(d) Because 4ⁿ is irrational
Show Answer
Answer: (b)
Explanation: A number ending with 0 must be divisible by 10, which requires it to have both 2 and 5 as factors. But 4ⁿ = (2²)ⁿ = 2^(2n), so it only has 2 as a factor, not 5.
Q2. Which of the following is *not* a correct implication of the Fundamental Theorem of Arithmetic?
(a) Every composite number has a unique prime factorisation
(b) The prime factorisation of 60 is 2² × 3 × 5
(c) The number 1 has a unique prime factorisation
(d) Prime factorisation is used to find LCM and HCF
Show Answer
Answer: (c)
Explanation: The number 1 is not a composite number and does not have a prime factorisation. So (c) is incorrect.
Q3. If the product of two numbers is 540 and their HCF is 6, what is their LCM?
(a) 90
(b) 270
(c) 324
(d) 540
Show Answer
Answer: (c)
Explanation: By identity: HCF × LCM = Product of the numbers. So, LCM = 540 ÷ 6 = 90. But this conflicts with options; correct LCM is 90. Correct answer: (a)
Q4. Which of the following pairs of numbers will have 1 as their only common factor?
(a) 18 and 30
(b) 35 and 64
(c) 42 and 70
(d) 56 and 96
Show Answer
Answer: (b)
Explanation: 35 = 5 × 7; 64 = 2⁶. They have no common factors, so they are co-prime.
Q5. What can be inferred if the decimal expansion of a rational number terminates?
(a) Its denominator has no prime factors
(b) Its denominator has only 2 and/or 5 as prime factors
(c) It is not a rational number
(d) Its numerator is even
Show Answer
Answer: (b)
Explanation: A rational number has a terminating decimal if the denominator in lowest terms has only 2 and/or 5 as prime factors.
Q6. The number 32760 has the prime factorisation 2³ × 3² × 5 × 7 × 13. How many total factors does it have?
(a) 120
(b) 96
(c) 144
(d) 180
Show Answer
Answer: (c)
Explanation: Number of factors = (3+1)(2+1)(1+1)(1+1)(1+1) = 4×3×2×2×2 = 96
Q7. What is the least number which when divided by 6, 15 and 18 leaves remainder 5 in each case?
(a) 65
(b) 185
(c) 95
(d) 125
Show Answer
Answer: (c)
Explanation: LCM of 6, 15, and 18 = 90. Required number = 90 + 5 = 95.
Q8. Which of the following best explains the uniqueness of prime factorisation?
(a) Only one method of factorising exists
(b) Order of primes matters
(c) No two different sets of primes can produce the same composite
(d) Every prime has multiple factors
Show Answer
Answer: (c)
Explanation: The uniqueness means that any composite number can be expressed as product of primes in only one way, apart from order.
Q9. If 6n ends with 0, which of the following must be true?
(a) n is even
(b) n is odd
(c) 6n has 5 as a factor
(d) n is a multiple of 5
Show Answer
Answer: (c)
Explanation: For 6n to end in 0, it must be divisible by 10. So it must have both 2 and 5 as factors. 6 already has 2, so 5 must be a factor of n.
Q10. Which number cannot be expressed as a product of powers of primes?
(a) 12
(b) 17
(c) 49
(d) 1
Show Answer
Answer: (d)
Explanation: 1 is neither prime nor composite and does not have a prime factorisation.
Q11. What is the HCF of 2⁵ × 3² × 7 and 2³ × 3 × 5?
(a) 2³ × 3 = 24
(b) 2 × 3 × 5 = 30
(c) 2² × 3² = 36
(d) 2 × 3 = 6
Show Answer
Answer: (a)
Explanation: HCF = product of smallest powers of common primes = 2³ × 3 = 8 × 3 = 24
Q12. Which of the following best describes a composite number?
(a) A number divisible by 1 and itself only
(b) A number with exactly two factors
(c) A number that can be factorised into primes
(d) A number less than 1
Show Answer
Answer: (c)
Explanation: Composite numbers have more than two factors and can be written as a product of primes.
Q13. What is the LCM of 72 and 120 using their prime factorisations?
(a) 360
(b) 720
(c) 1440
(d) 120
Show Answer
Answer: (a)
Explanation: LCM = product of greatest powers: 2³ × 3² × 5 = 360
Q14. Why is 2.101101110111… an irrational number?
(a) It is a non-terminating decimal
(b) It repeats after a while
(c) It is a rational number
(d) It cannot be written as a fraction
Show Answer
Answer: (d)
Explanation: A non-terminating, non-repeating decimal cannot be expressed as p/q and is therefore irrational.
Q15. Which of the following numbers is irrational?
(a) 3/5
(b) √2
(c) 0.75
(d) 1.4142135
Show Answer
Answer: (b)
Explanation: √2 cannot be expressed as a ratio of two integers and is irrational.
Q16. What does the Fundamental Theorem of Arithmetic help prove?
(a) Euclid’s Division Lemma
(b) Decimal representation of fractions
(c) Irrationality of √2
(d) LCM of two numbers
Show Answer
Answer: (c)
Explanation: The proof of irrationality of √2 is based on the uniqueness of prime factorisation.
Q17. Which pair of numbers is not coprime?
(a) 7, 9
(b) 11, 13
(c) 8, 15
(d) 15, 25
Show Answer
Answer: (d)
Explanation: 15 = 3 × 5, 25 = 5 × 5. Common factor is 5, so not coprime.
Q18. If a number is divisible by 2 and 3 but not by 6, what can you infer?
(a) It is a prime number
(b) It ends in 6
(c) The number is irrational
(d) There is a mistake; it must be divisible by 6
Show Answer
Answer: (d)
Explanation: If a number is divisible by both 2 and 3, it must be divisible by their LCM, which is 6.
Q19. If two numbers are co-prime, what is their HCF?
(a) 1
(b) 0
(c) The smaller number
(d) The larger number
Show Answer
Answer: (a)
Explanation: Co-prime numbers have no common factor other than 1, so HCF is 1.
Q20. Which of the following is not a correct use of Euclid’s division lemma?
(a) Finding HCF of two numbers
(b) Proving irrationality of √2
(c) Establishing divisibility
(d) Expressing numbers in the form a = bq + r
Show Answer
Answer: (b)
Explanation: The proof of irrationality of √2 uses the Fundamental Theorem of Arithmetic, not Euclid’s lemma.
We hope the given mcq questions with Answers for Real Numbers Class 10 helps you in your learning.
Also check
- Arithmetic Progressions – Class 10 Maths Chapter 5 MCQ Questions with Answers (Updated)
- Quadratic Equations – Class 10 Maths Chapter 4 MCQ Questions with Answers (Updated)
- Pair of Linear Equations in Two Variables – Class 10 Maths Chapter 3 MCQ Questions with Answers (Updated)
- Polynomials – Class 10 Maths Chapter 2 MCQ Questions with Answers (Updated)
- Real Numbers – Class 10 Maths Chapter 1 MCQ Questions with Answers (Updated)
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Topics from which mcq questions may be asked
- Euclid’s division lemma
- HCF and LCM
- Irrational numbers
Understanding numbers helps us uncover the logic behind every mathematical structure.
Frequently Asked Questions (FAQs) on Real Numbers MCQ Questions
Q1: Why should I practice Class 10 Maths Chapter 1 MCQs?
A1: Practicing MCQs helps in quick revision, improves problem-solving speed, and enhances conceptual understanding of important topics in Class 10 Maths.
Q2: Are these Class 10 Maths MCQs based on the latest syllabus?
A2: Yes, all the MCQs are designed as per the latest CBSE syllabus and exam pattern to help students prepare effectively.
Q3: Where can I find more MCQs for Class 10 Maths?
A3: You can find more chapter-wise MCQs on our website. These are designed to cover important concepts and prepare you for exams.
Q4: Are the answers provided for all MCQs?
A4: Yes, each MCQ is accompanied by the correct answer and explanations to help students understand and learn better.
Q5: How can I improve my performance in Class 10 Maths MCQs?
A5: To improve your performance, practice regularly, revise key concepts, and take mock tests to assess your knowledge.
Q6: Do these MCQs help in school exams?
A6: Yes, these MCQs are aligned with school exam patterns and help in scoring well by strengthening conceptual clarity.
Q7: Can I download these MCQs for offline practice?
A7: Yes, you can download or print these MCQs for convenient offline practice.
Q8: Are there any resources available online for students to practice mcq questions on class 10 maths chapter 1 “Real Numbers“ for CBSE exams?
A6: Yes, several educational websites offer mcq questions for CBSE students preparing for maths examinations. We also offer a collection of mcq questions for all classes and subject on our website. Visit our website to access these questions and enhance your learning experience. for more mcq, you can also visit Physics Gurukul Website.
