Class 10 Mathematics Real Numbers Most Important Questions
Most Important Questions for Class 10 Mathematics Real Numbers. Try first, then reveal the answer. These are exam-oriented practice items, not copied board papers.
Practice questions aligned to NCERT topics used in CBSE classrooms. These are original exam-oriented questions for revision — not official CBSE board papers and not a guarantee of any exam question. Always match the textbook issued by your school and the latest PDFs on ncert.nic.in and cbseacademic.nic.in.
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Practice set
Q1MCQ1 markEasyRevision pick
Choose the correct statement related to Fundamental Theorem of Arithmetic in the chapter Real Numbers.
A. A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors
B. Fundamental Theorem of Arithmetic (statement)
C. Every composite number can be expressed as a product of primes, unique except for the order of factors
D. Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b)
Answer
C. Every composite number can be expressed as a product of primes, unique except for the order of factors
Explanation
Every composite number can be expressed as a product of primes, unique except for the order of factors. The other options mix ideas from nearby topics or reverse the textbook fact.
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Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q5MCQ1 markModerateRevision pick
Choose the correct statement related to Irrational numbers in the chapter Real Numbers.
A. Euclid’s algorithm finds HCF
B. HCF × LCM = product of two positive integers
C. √2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0
D. HCF is the product of smallest powers and LCM the product of greatest powers of common primes
Answer
C. √2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0
Explanation
√2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q9MCQ1 markEasyRevision pick
Choose the correct statement related to Real Numbers in the chapter Real Numbers.
A. This idea is not part of the NCERT chapter
B. Terminating decimals: denominator 2^m 5^n after simplifying
C. Fundamental Theorem of Arithmetic (statement)
D. Every composite number can be expressed as a product of primes, unique except for the order of factors
Answer
C. Fundamental Theorem of Arithmetic (statement)
Explanation
Fundamental Theorem of Arithmetic (statement). The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q13MCQ1 markEasyRevision pick
Choose the correct statement related to Real Numbers in the chapter Real Numbers.
A. √2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0
B. The textbook says the opposite of this statement
C. For two positive integers, HCF × LCM equals the product of the numbers
D. Euclid’s algorithm finds HCF
Answer
D. Euclid’s algorithm finds HCF
Explanation
Euclid’s algorithm finds HCF. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q17MCQ1 markEasyRevision pick
Choose the correct statement related to Non-terminating repeating in the chapter Real Numbers.
A. A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors
B. HCF × LCM = product of two positive integers
C. If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal
D. HCF is the product of smallest powers and LCM the product of greatest powers of common primes
Answer
C. If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal
Explanation
If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q413 Mark3 marksModerateRevision pick
Explain HCF and LCM in about three points, with one example.
Answer
For two positive integers, HCF × LCM equals the product of the numbers. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Explanation
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q453 Mark3 marksModerateRevision pick
Explain Euclid’s algorithm in about three points, with one example.
Answer
Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b). Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Explanation
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q575 Mark5 marksDifficultRevision pick
Write a long answer on Irrational numbers. Include definition, explanation and one application.
Answer
Irrational numbers — √2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
Explanation
Long answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q69Case Based4 marksModerateRevision pick
A student is revising Real Numbers and notes: “If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal.” Using this case, answer: (i) Name the idea. (ii) State it in your own words. (iii) Give one classroom or daily-life use.
Answer
(i) Non-terminating repeating.
(ii) If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Explanation
Case-based items recycle a short story. Pull the fact out first, then apply it. This is original practice in CBSE case style — not a copied board paper.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q73Case Based4 marksModerateRevision pick
A student is revising Real Numbers and notes: “Real numbers include all rationals and irrationals and fill the number line.” Using this case, answer: (i) Name the idea. (ii) State it in your own words. (iii) Give one classroom or daily-life use.
Answer
(i) Real number.
(ii) Real numbers include all rationals and irrationals and fill the number line.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Explanation
Case-based items recycle a short story. Pull the fact out first, then apply it. This is original practice in CBSE case style — not a copied board paper.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q77Competency Based3 marksModerateRevision pick
Competency practice: A classmate can recall the heading Real Numbers but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — √2, √3, √5 are irrational. Step 2: Show one example or diagram from the chapter and ask the classmate to repeat it in their own words.
Explanation
Competency-based items check whether you can use a concept, not only name it. Teach-back is a simple way to prove understanding.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q81Competency Based3 marksDifficultRevision pick
Competency practice: A classmate can recall the heading Terminating decimal but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors. Step 2: Show one example or diagram from the chapter and ask the classmate to repeat it in their own words.
Explanation
Competency-based items check whether you can use a concept, not only name it. Teach-back is a simple way to prove understanding.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q93HOTS3 marksDifficultRevision pick
HOTS: If someone ignored the idea “For two positive integers, HCF × LCM equals the product of the numbers”, what mistake could they make while solving a question from Real Numbers?
Answer
They would use the wrong term or the reverse relation. Remember: For two positive integers, HCF × LCM equals the product of the numbers. Always check the NCERT definition before jumping to a formula or a long explanation.
Explanation
HOTS items ask you to predict an error. That is still chapter revision — not a claim that this exact wording will appear in the board exam.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
FAQs
Are these official CBSE board questions?
No. They are original practice questions aligned to NCERT topics used in CBSE classrooms. Official sample papers are published on cbseacademic.nic.in.
Will these questions appear in the board exam?
Nobody can promise a question. Use them for revision of frequently tested concepts and exam-style practice.
Is the chapter list the latest NCERT list?
Yes, the catalog follows current NCERT textbooks used in CBSE schools (including new middle-stage books such as Ganita Prakash and Curiosity). Always match the book issued by your school.
How should I use the 100 questions?
Try the question first, then tap Show answer. Mix MCQs with long answers. Revise formulas and diagrams from the textbook alongside this set.
Where are NCERT solutions?
Open the NCERT-style practice link on this subject or chapter. For word-for-word textbook exercise answers, use the NCERT book itself; we do not copy solution keys from other websites.
What is the suggested URL pattern?
Hub /cbse/, then /cbse/class-10/, then subject and chapter slugs.
Why is this a separate URL?
So students searching for “Most Important Questions” land on a filtered set, while the chapter page remains the full 100-question bank. Same facts, different search intent.
Today's 3-step path
Follow this loop every day: mixed test, current affairs, then today's subject. A new set arrives tomorrow.
