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Practice Class 10 Maths Chapter 1 Real Numbers MCQ Questions with Answers based on NCERT syllabus. Learn Euclid’s Division Lemma, HCF, LCM, prime factorization, irrational numbers, and decimal expansions with detailed solutions and board exam oriented questions.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Real Numbers
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Moderate
Based On: NCERT Latest Syllabus
Introduction:
Real Numbers is one of the most scoring chapters in Class 10 Mathematics. The concepts of prime factorization, Euclid’s Division Lemma, irrational numbers, and decimal expansions are frequently used in board examinations. Understanding these topics helps students build a strong mathematical foundation and improves problem-solving abilities. This practice set focuses on concept-based and application-based questions that are useful for revision and exam preparation.
What You Will Learn?
✔ Prime Factorization
✔ Euclid’s Division Lemma
✔ HCF and LCM Applications
✔ Irrational Numbers
✔ Rational Numbers
✔ Decimal Expansions
✔ Board Exam Level Concepts
Why This Topic Is Important?
Questions from Real Numbers are regularly asked in board examinations. A strong understanding of this chapter also helps students in algebra, coordinate geometry, and higher mathematics.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. Which of the following numbers is neither prime nor composite?
A) $$0$$
B) $$1$$
C) $$2$$
D) $$3$$
Answer:
$$1$$
Useful Formula for this Question:
A prime number has exactly two factors.
A composite number has more than two factors.
Solution:
The number $$1$$ has only one factor:
$$1$$
Therefore, it is neither prime nor composite.
Hence, the correct answer is:
$$1$$
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Q2. The product of the HCF and LCM of two numbers is $$540$$. If the HCF is $$18$$, then the LCM is:
A) $$20$$
B) $$25$$
C) $$30$$
D) $$35$$
Answer:
$$30$$
Useful Formula for this Question:
$$HCF \times LCM = Product\ of\ two\ numbers$$
Solution:
Given:
$$HCF = 18$$
$$HCF \times LCM = 540$$
Therefore:
$$18 \times LCM = 540$$
$$LCM = \frac{540}{18}$$
$$LCM = 30$$
Hence, the correct answer is:
$$30$$
————————————————–
Q3. Which of the following numbers has a non-terminating recurring decimal expansion?
A) $$\frac{7}{8}$$
B) $$\frac{9}{20}$$
C) $$\frac{5}{12}$$
D) $$\frac{13}{25}$$
Answer:
$$\frac{5}{12}$$
Useful Formula for this Question:
A denominator containing prime factors other than $$2$$ and $$5$$ produces a recurring decimal.
Solution:
For:
$$\frac{5}{12}$$
Denominator:
$$12 = 2^2 \times 3$$
Since factor $$3$$ is present, the decimal expansion is non-terminating recurring.
Therefore, the correct answer is:
$$\frac{5}{12}$$
————————————————–
Q4. The prime factorization of $$150$$ is:
A) $$2 \times 3 \times 5^2$$
B) $$2 \times 3^2 \times 5$$
C) $$2^2 \times 3 \times 5^2$$
D) $$2 \times 5^3$$
Answer:
$$2 \times 3 \times 5^2$$
Useful Formula for this Question:
Prime factorization expresses a number as a product of prime numbers only.
Solution:
$$150 = 2 \times 75$$
$$75 = 3 \times 25$$
$$25 = 5 \times 5$$
Therefore:
$$150 = 2 \times 3 \times 5^2$$
Hence, the correct answer is:
$$2 \times 3 \times 5^2$$
————————————————–
Q5. Using Euclid’s Division Lemma, if:
$$38 = 7 \times 5 + r$$
then the value of $$r$$ is:
A) $$1$$
B) $$2$$
C) $$3$$
D) $$4$$
Answer:
$$3$$
Useful Formula for this Question:
$$a = bq + r$$
Solution:
Given:
$$38 = 7 \times 5 + r$$
$$38 = 35 + r$$
$$r = 38 – 35$$
$$r = 3$$
Therefore, the correct answer is:
$$3$$
————————————————–
Important Formulas and Concepts
Euclid’s Division Lemma:
$$a = bq + r$$
where
$$0 \le r < b$$
Fundamental Theorem of Arithmetic:
Every composite number can be expressed as a unique product of prime numbers.
Relationship between HCF and LCM:
$$HCF \times LCM = Product\ of\ two\ numbers$$
————————————————–
FAQs
Q. Is 1 a prime number?
Answer:
No. The number $$1$$ is neither prime nor composite.
Q. What is the Fundamental Theorem of Arithmetic?
Answer:
Every composite number can be expressed as a unique product of prime numbers.
Q. What type of decimal expansion does $$\frac{1}{3}$$ have?
Answer:
A non-terminating recurring decimal expansion.
————————————————–
Common Mistakes Students Make
❌ Treating 1 as a prime number.
❌ Forgetting the factor 3 while checking decimal expansion.
❌ Mixing up HCF and LCM formulas.
❌ Writing a remainder greater than the divisor.
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Quick Revision Notes
✔ 1 is neither prime nor composite.
✔ 2 is the smallest prime number.
✔ HCF × LCM = Product of two numbers.
✔ Euclid’s Division Lemma is:
$$a = bq + r$$
✔ Recurring decimals occur when the denominator contains factors other than $$2$$ and $$5$$.
————————————————–
Conclusion:
These Class 10 Maths Chapter 1 Real Numbers MCQs with detailed solutions help students strengthen important concepts related to prime factorization, HCF, LCM, irrational numbers, and Euclid’s Division Lemma. Regular practice improves accuracy and exam confidence.
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