Class 10 Mathematics Real Numbers Expected Practice Questions
Expected Practice 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
Q555 Mark5 marksModerate
Write a long answer on Terminating decimal. Include definition, explanation and one application.
Answer
Terminating decimal — A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors. 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).
Q565 Mark5 marksModerate
Write a long answer on Non-terminating repeating. Include definition, explanation and one application.
Answer
Non-terminating repeating — If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal. 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).
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).
Q585 Mark5 marksModerate
Write a long answer on Euclid’s algorithm. Include definition, explanation and one application.
Answer
Euclid’s algorithm — Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b). 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).
Q595 Mark5 marksModerate
Write a long answer on Prime factorisation. Include definition, explanation and one application.
Answer
Prime factorisation — HCF is the product of smallest powers and LCM the product of greatest powers of common primes. 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).
Q605 Mark5 marksDifficult
Write a long answer on Real number. Include definition, explanation and one application.
Answer
Real number — Real numbers include all rationals and irrationals and fill the number line. 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).
Q70Case Based4 marksModerate
A student is revising Real Numbers and notes: “√2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0.” 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) Irrational numbers.
(ii) √2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0.
(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).
Q71Case Based4 marksModerate
A student is revising Real Numbers and notes: “Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b).” 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) Euclid’s algorithm.
(ii) Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b).
(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).
Q72Case Based4 marksDifficult
A student is revising Real Numbers and notes: “HCF is the product of smallest powers and LCM the product of greatest powers of common primes.” 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) Prime factorisation.
(ii) HCF is the product of smallest powers and LCM the product of greatest powers of common primes.
(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).
Q74Case Based4 marksModerate
A student is revising Real Numbers and notes: “Fundamental Theorem of Arithmetic (statement).” 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 Numbers.
(ii) Fundamental Theorem of Arithmetic (statement).
(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).
Q75Case Based4 marksModerate
A student is revising Real Numbers and notes: “HCF × LCM = product of two positive integers.” 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 Numbers.
(ii) HCF × LCM = product of two positive integers.
(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).
Q76Case Based4 marksDifficult
A student is revising Real Numbers and notes: “Terminating decimals: denominator 2^m 5^n after simplifying.” 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) Terminating decimals.
(ii) Terminating decimals: denominator 2^m 5^n after simplifying.
(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).
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).
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 “Expected Practice 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.
