Class 10 Mathematics Real Numbers 3 Mark Questions
3 Mark 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.
Answers opened: 0
Practice set
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).
Q423 Mark3 marksModerate
Explain Terminating decimal in about three points, with one example.
Answer
A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors. Example: 7/8 = 0.875
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).
Q433 Mark3 marksModerate
Explain Non-terminating repeating in about three points, with one example.
Answer
If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal. Example: 1/3 = 0.333…
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).
Q443 Mark3 marksDifficult
Explain Irrational numbers in about three points, with one example.
Answer
√2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0. 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).
Q463 Mark3 marksModerate
Explain Prime factorisation in about three points, with one example.
Answer
HCF is the product of smallest powers and LCM the product of greatest powers of common primes. 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).
Q473 Mark3 marksModerate
Explain Real number in about three points, with one example.
Answer
Real numbers include all rationals and irrationals and fill the number line. 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).
Q483 Mark3 marksDifficult
Explain Real Numbers in about three points, with one example.
Answer
Fundamental Theorem of Arithmetic (statement). 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).
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).
Q78Competency Based3 marksDifficult
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 — Euclid’s algorithm finds HCF. 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).
Q79Competency Based3 marksModerate
Competency practice: A classmate can recall the heading Fundamental Theorem of Arithmetic but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — Every composite number can be expressed as a product of primes, unique except for the order of 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).
Q80Competency Based3 marksModerate
Competency practice: A classmate can recall the heading HCF and LCM but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — For two positive integers, HCF × LCM equals the product of the numbers. 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).
Q82Competency Based3 marksModerate
Competency practice: A classmate can recall the heading Non-terminating repeating but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal. 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).
Q83Competency Based3 marksModerate
Competency practice: A classmate can recall the heading Irrational 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 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0. 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).
Q84Competency Based3 marksDifficult
Competency practice: A classmate can recall the heading Euclid’s algorithm but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b). 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).
Q85Application Based3 marksModerate
Apply the idea of Prime factorisation to a real situation you might meet in school or daily life.
Answer
HCF is the product of smallest powers and LCM the product of greatest powers of common primes. Use this fact to explain a real object, habit, experiment or measurement from the chapter.
Explanation
Application questions reward a specific situation. Name the place (kitchen, playground, lab) and connect it to the fact.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q86Application Based3 marksModerate
Apply the idea of Real number to a real situation you might meet in school or daily life.
Answer
Real numbers include all rationals and irrationals and fill the number line. Use this fact to explain a real object, habit, experiment or measurement from the chapter.
Explanation
Application questions reward a specific situation. Name the place (kitchen, playground, lab) and connect it to the fact.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q87Application Based3 marksModerate
Apply the idea of Real Numbers to a real situation you might meet in school or daily life.
Answer
Fundamental Theorem of Arithmetic (statement). Use this fact to explain a real object, habit, experiment or measurement from the chapter.
Explanation
Application questions reward a specific situation. Name the place (kitchen, playground, lab) and connect it to the fact.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q88Application Based3 marksDifficult
Apply the idea of Real Numbers to a real situation you might meet in school or daily life.
Answer
HCF × LCM = product of two positive integers. Use this fact to explain a real object, habit, experiment or measurement from the chapter.
Explanation
Application questions reward a specific situation. Name the place (kitchen, playground, lab) and connect it to the fact.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q89Application Based3 marksModerate
Apply the idea of Terminating decimals to a real situation you might meet in school or daily life.
Answer
Terminating decimals: denominator 2^m 5^n after simplifying. Use this fact to explain a real object, habit, experiment or measurement from the chapter.
Explanation
Application questions reward a specific situation. Name the place (kitchen, playground, lab) and connect it to the fact.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q90Application Based3 marksModerate
Apply the idea of Real Numbers to a real situation you might meet in school or daily life.
Answer
√2, √3, √5 are irrational. Use this fact to explain a real object, habit, experiment or measurement from the chapter.
Explanation
Application questions reward a specific situation. Name the place (kitchen, playground, lab) and connect it to the fact.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q91HOTS3 marksModerate
HOTS: If someone ignored the idea “Euclid’s algorithm finds HCF”, what mistake could they make while solving a question from Real Numbers?
Answer
They would use the wrong term or the reverse relation. Remember: Euclid’s algorithm finds HCF. 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).
Q92HOTS3 marksModerate
HOTS: If someone ignored the idea “Every composite number can be expressed as a product of primes, unique except for the order of factors”, what mistake could they make while solving a question from Real Numbers?
Answer
They would use the wrong term or the reverse relation. Remember: Every composite number can be expressed as a product of primes, unique except for the order of factors. 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).
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).
Q94HOTS3 marksModerate
HOTS: If someone ignored the idea “A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors”, what mistake could they make while solving a question from Real Numbers?
Answer
They would use the wrong term or the reverse relation. Remember: A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors. 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).
Q95HOTS3 marksModerate
HOTS: If someone ignored the idea “If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal”, what mistake could they make while solving a question from Real Numbers?
Answer
They would use the wrong term or the reverse relation. Remember: If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal. 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).
Q96HOTS3 marksDifficult
HOTS: If someone ignored the idea “√2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0”, what mistake could they make while solving a question from Real Numbers?
Answer
They would use the wrong term or the reverse relation. Remember: √2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0. 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 “3 Mark 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.
