Class 10 Mathematics Chapter 1: Real Numbers — practice questions with answers
Free practice for Class 10 Mathematics, Chapter 1: Real Numbers. Try the solved questions below, then take a free test with instant marking and explanations.
57 questions20 easy, 23 medium, 14 hardNCERT · CBSE · State boards
Sample questions with solutions
Q1. What does the Fundamental Theorem of Arithmetic state?
- Every composite number can be expressed as a product of primes, and this factorisation is unique apart from the order of the factors
- Every number is prime
- Every number can be divided by 2
- Every prime number is odd
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Answer: A. Every composite number can be expressed as a product of primes, and this factorisation is unique apart from the order of the factors
Why: Theorem 1.1. [p.3]
Why: Theorem 1.1. [p.3]
Q2. Which is the prime factorisation of 140?
- 2^2 × 5 × 7
- 2 × 70
- 4 × 5 × 7
- 2 × 5 × 14
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Answer: A. 2^2 × 5 × 7
Why: 140 = 2² × 5 × 7. [p.5]
Why: 140 = 2² × 5 × 7. [p.5]
Q3. Using prime factorisation, HCF of two numbers is the product of ______.
- the smallest power of each common prime factor
- the greatest power of every prime factor
- all prime factors
- the two numbers
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Answer: A. the smallest power of each common prime factor
Why: LCM uses the greatest powers. [p.4]
Why: LCM uses the greatest powers. [p.4]
Q4. Find the HCF of 96 and 404.
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Answer: 4 (± 0)
Why: 96 = 2⁵ × 3, 404 = 2² × 101 → HCF = 2² = 4. [p.4]
Why: 96 = 2⁵ × 3, 404 = 2² × 101 → HCF = 2² = 4. [p.4]
Q5. Sonia takes 18 minutes and Ravi 12 minutes to drive one round of a circular path. Starting together at the same point and direction, after how many minutes will they next meet at the starting point?
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Answer: 36 (± 0)
Why: LCM(18, 12) = 36 minutes. [p.5]
Why: LCM(18, 12) = 36 minutes. [p.5]
Q6. Theorem 1.2 says: if a prime p divides a², then ______.
- p divides a
- p divides a only if a is even
- a is prime
- p = a
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Answer: A. p divides a
Why: Proved using the FTA. [p.3]
Why: Proved using the FTA. [p.3]
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Frequently asked questions
How many practice questions are there for Class 10 Mathematics Chapter 1: Real Numbers?
57 questions (20 easy, 23 medium, 14 hard). A few are solved on this page; the free test shows the answer and explanation for every question after you submit.
Is this chapter from the NCERT book?
Yes — it follows the NCERT Class 10 Mathematics syllabus, used by CBSE and many state boards.