NCERT-style Solutions Practice · original practice
Class 10 Mathematics Real Numbers NCERT-style Solutions Practice
NCERT-style Solutions Practice 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
Q312 Mark2 marksModerate
Give two points to explain Irrational numbers as used in Real Numbers.
Answer
1. √2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Explanation
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q322 Mark2 marksDifficult
Give two points to explain Euclid’s algorithm as used in Real Numbers.
Answer
1. Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b).
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Explanation
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q332 Mark2 marksModerate
Give two points to explain Prime factorisation as used in Real Numbers.
Answer
1. HCF is the product of smallest powers and LCM the product of greatest powers of common primes.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Explanation
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q342 Mark2 marksModerate
Give two points to explain Real number as used in Real Numbers.
Answer
1. Real numbers include all rationals and irrationals and fill the number line.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Explanation
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q352 Mark2 marksModerate
Give two points to explain Real Numbers as used in Real Numbers.
Answer
1. Fundamental Theorem of Arithmetic (statement).
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Explanation
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q362 Mark2 marksDifficult
Give two points to explain Real Numbers as used in Real Numbers.
Answer
1. HCF × LCM = product of two positive integers.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Explanation
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q372 Mark2 marksModerate
Give two points to explain Terminating decimals as used in Real Numbers.
Answer
1. Terminating decimals: denominator 2^m 5^n after simplifying.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Explanation
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q382 Mark2 marksModerate
Give two points to explain Real Numbers as used in Real Numbers.
Answer
1. √2, √3, √5 are irrational.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Explanation
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q392 Mark2 marksModerate
Give two points to explain Real Numbers as used in Real Numbers.
Answer
1. Euclid’s algorithm finds HCF.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Explanation
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q402 Mark2 marksDifficult
Give two points to explain Fundamental Theorem of Arithmetic as used in Real Numbers.
Answer
1. Every composite number can be expressed as a product of primes, unique except for the order of factors.
2. 180 = 2² × 3² × 5
Explanation
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
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).
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).
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).
Q97NCERT-style2 marksModerate
NCERT-style exercise: In your own words, write what the chapter teaches about Euclid’s algorithm.
Answer
Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b). Keep the answer as short as the in-text questions in the textbook.
Explanation
This is original practice in the style of NCERT in-text/exercise questions. It is not copied from any solutions website.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q98NCERT-style2 marksModerate
NCERT-style exercise: In your own words, write what the chapter teaches about Prime factorisation.
Answer
HCF is the product of smallest powers and LCM the product of greatest powers of common primes. Keep the answer as short as the in-text questions in the textbook.
Explanation
This is original practice in the style of NCERT in-text/exercise questions. It is not copied from any solutions website.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q99NCERT-style2 marksModerate
NCERT-style exercise: In your own words, write what the chapter teaches about Real number.
Answer
Real numbers include all rationals and irrationals and fill the number line. Keep the answer as short as the in-text questions in the textbook.
Explanation
This is original practice in the style of NCERT in-text/exercise questions. It is not copied from any solutions website.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q100NCERT-style2 marksDifficult
NCERT-style exercise: In your own words, write what the chapter teaches about Real Numbers.
Answer
Fundamental Theorem of Arithmetic (statement). Keep the answer as short as the in-text questions in the textbook.
Explanation
This is original practice in the style of NCERT in-text/exercise questions. It is not copied from any solutions website.
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 “NCERT-style Solutions Practice” 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.
