Revision Notes 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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Revision notes
Fundamental Theorem of Arithmetic. Every composite number can be expressed as a product of primes, unique except for the order of factors.
HCF and LCM. For two positive integers, HCF × LCM equals the product of the numbers.
Terminating decimal. A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors.
Non-terminating repeating. If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal.
Irrational numbers. √2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0.
Euclid’s algorithm. Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b).
Prime factorisation. HCF is the product of smallest powers and LCM the product of greatest powers of common primes.
Real number. Real numbers include all rationals and irrationals and fill the number line.
Real Numbers. Fundamental Theorem of Arithmetic (statement).
Real Numbers. HCF × LCM = product of two positive integers.
Terminating decimals. Terminating decimals: denominator 2^m 5^n after simplifying.
Real Numbers. √2, √3, √5 are irrational.
Real Numbers. Euclid’s algorithm finds HCF.
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.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q2MCQ1 markEasy
Choose the correct statement related to HCF and LCM in the chapter Real Numbers.
A. HCF × LCM = product of two positive integers
B. HCF is the product of smallest powers and LCM the product of greatest powers of common primes
C. For two positive integers, HCF × LCM equals the product of the numbers
D. If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal
Answer
C. For two positive integers, HCF × LCM equals the product of the numbers
Explanation
For two positive integers, HCF × LCM equals the product of the numbers. 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).
Q3MCQ1 markEasy
Choose the correct statement related to Terminating decimal in the chapter Real Numbers.
A. Terminating decimals: denominator 2^m 5^n after simplifying
B. Real numbers include all rationals and irrationals and fill the number line
C. √2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0
D. A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors
Answer
D. A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors
Explanation
A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors. 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).
Q4MCQ1 markEasy
Choose the correct statement related to Non-terminating repeating in the chapter Real Numbers.
A. Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b)
B. Fundamental Theorem of Arithmetic (statement)
C. √2, √3, √5 are irrational
D. If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal
Answer
D. 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).
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).
Q6MCQ1 markEasy
Choose the correct statement related to Euclid’s algorithm in the chapter Real Numbers.
A. Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b)
B. Terminating decimals: denominator 2^m 5^n after simplifying
C. Real numbers include all rationals and irrationals and fill the number line
D. This idea is not part of the NCERT chapter
Answer
A. Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b)
Explanation
Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b). 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).
Q7MCQ1 markEasy
Choose the correct statement related to Prime factorisation in the chapter Real Numbers.
A. √2, √3, √5 are irrational
B. Fundamental Theorem of Arithmetic (statement)
C. HCF is the product of smallest powers and LCM the product of greatest powers of common primes
D. The textbook says the opposite of this statement
Answer
C. HCF is the product of smallest powers and LCM the product of greatest powers of common primes
Explanation
HCF is the product of smallest powers and LCM the product of greatest powers of common primes. 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).
Q8MCQ1 markEasy
Choose the correct statement related to Real number in the chapter Real Numbers.
A. Real numbers include all rationals and irrationals and fill the number line
B. This happens only in a laboratory and never in daily life
C. Euclid’s algorithm finds HCF
D. HCF × LCM = product of two positive integers
Answer
A. Real numbers include all rationals and irrationals and fill the number line
Explanation
Real numbers include all rationals and irrationals and fill the number line. 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).
Q10MCQ1 markModerate
Choose the correct statement related to Real Numbers in the chapter Real Numbers.
A. The textbook says the opposite of this statement
B. √2, √3, √5 are irrational
C. HCF × LCM = product of two positive integers
D. For two positive integers, HCF × LCM equals the product of the numbers
Answer
C. HCF × LCM = product of two positive integers
Explanation
HCF × LCM = product of two positive integers. 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).
Q11MCQ1 markEasy
Choose the correct statement related to Terminating decimals in the chapter Real Numbers.
A. Terminating decimals: denominator 2^m 5^n after simplifying
B. A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors
C. Euclid’s algorithm finds HCF
D. This happens only in a laboratory and never in daily life
Answer
A. Terminating decimals: denominator 2^m 5^n after simplifying
Explanation
Terminating decimals: denominator 2^m 5^n after simplifying. 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).
Q12MCQ1 markEasy
Choose the correct statement related to Real Numbers in the chapter Real Numbers.
A. √2, √3, √5 are irrational
B. If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal
C. This idea is not part of the NCERT chapter
D. Every composite number can be expressed as a product of primes, unique except for the order of factors
Answer
A. √2, √3, √5 are irrational
Explanation
√2, √3, √5 are irrational. 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).
Q14MCQ1 markEasy
Choose the correct statement related to Fundamental Theorem of Arithmetic in the chapter Real Numbers.
A. If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal
B. This happens only in a laboratory and never in daily life
C. HCF is the product of smallest powers and LCM the product of greatest powers of common primes
D. Every composite number can be expressed as a product of primes, unique except for the order of factors
Answer
D. 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.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q15MCQ1 markModerate
Choose the correct statement related to HCF and LCM in the chapter Real Numbers.
A. For two positive integers, HCF × LCM equals the product of the numbers
B. Real numbers include all rationals and irrationals and fill the number line
C. Every composite number can be expressed as a product of primes, unique except for the order of factors
D. √2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0
Answer
A. For two positive integers, HCF × LCM equals the product of the numbers
Explanation
For two positive integers, HCF × LCM equals the product of the numbers. 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).
Q16MCQ1 markEasy
Choose the correct statement related to Terminating decimal 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. Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b)
D. For two positive integers, HCF × LCM equals the product of the numbers
Answer
A. A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors
Explanation
A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors. 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).
Q18MCQ1 markEasy
Choose the correct statement related to Irrational 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. Real numbers include all rationals and irrationals and fill the number line
C. If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal
D. Terminating decimals: denominator 2^m 5^n after simplifying
Answer
A. √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).
Q19MCQ1 markEasy
Choose the correct statement related to Euclid’s algorithm in the chapter Real Numbers.
A. Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b)
B. Fundamental Theorem of Arithmetic (statement)
C. √2, √3, √5 are irrational
D. √2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0
Answer
A. Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b)
Explanation
Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b). 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).
Q20MCQ1 markModerate
Choose the correct statement related to Prime factorisation in the chapter Real Numbers.
A. HCF is the product of smallest powers and LCM the product of greatest powers of common primes
B. Euclid’s algorithm finds HCF
C. HCF × LCM = product of two positive integers
D. Euclid’s algorithm finds HCF by repeated division: HCF(a,b)=HCF(b,a mod b)
Answer
A. HCF is the product of smallest powers and LCM the product of greatest powers of common primes
Explanation
HCF is the product of smallest powers and LCM the product of greatest powers of common primes. 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).
Q211 Mark1 markEasy
Define or state: Real number.
Answer
Real numbers include all rationals and irrationals and fill the number line.
Explanation
A one-mark answer should use the textbook term and one clear fact — not a long paragraph.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q221 Mark1 markEasy
Define or state: Real Numbers.
Answer
Fundamental Theorem of Arithmetic (statement).
Explanation
A one-mark answer should use the textbook term and one clear fact — not a long paragraph.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q231 Mark1 markEasy
Define or state: Real Numbers.
Answer
HCF × LCM = product of two positive integers.
Explanation
A one-mark answer should use the textbook term and one clear fact — not a long paragraph.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q241 Mark1 markEasy
Define or state: Terminating decimals.
Answer
Terminating decimals: denominator 2^m 5^n after simplifying.
Explanation
A one-mark answer should use the textbook term and one clear fact — not a long paragraph.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q251 Mark1 markModerate
Define or state: Real Numbers.
Answer
√2, √3, √5 are irrational.
Explanation
A one-mark answer should use the textbook term and one clear fact — not a long paragraph.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q261 Mark1 markEasy
Define or state: Real Numbers.
Answer
Euclid’s algorithm finds HCF.
Explanation
A one-mark answer should use the textbook term and one clear fact — not a long paragraph.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q271 Mark1 markEasy
Define or state: Fundamental Theorem of Arithmetic.
Answer
Every composite number can be expressed as a product of primes, unique except for the order of factors.
Explanation
A one-mark answer should use the textbook term and one clear fact — not a long paragraph.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q281 Mark1 markEasy
Define or state: HCF and LCM.
Answer
For two positive integers, HCF × LCM equals the product of the numbers.
Explanation
A one-mark answer should use the textbook term and one clear fact — not a long paragraph.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q291 Mark1 markEasy
Define or state: Terminating decimal.
Answer
A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors.
Explanation
A one-mark answer should use the textbook term and one clear fact — not a long paragraph.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q301 Mark1 markModerate
Define or state: Non-terminating repeating.
Answer
If q has a prime factor other than 2 or 5, p/q has a non-terminating repeating decimal.
Explanation
A one-mark answer should use the textbook term and one clear fact — not a long paragraph.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
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).
Q494 Mark4 marksModerate
Write a long answer on Real Numbers. Include definition, explanation and one application.
Answer
Real Numbers — HCF × LCM = product of two positive integers. 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).
Q504 Mark4 marksModerate
Write a long answer on Terminating decimals. Include definition, explanation and one application.
Answer
Terminating decimals — Terminating decimals: denominator 2^m 5^n after simplifying. 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).
Q514 Mark4 marksModerate
Write a long answer on Real Numbers. Include definition, explanation and one application.
Answer
Real Numbers — √2, √3, √5 are irrational. 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).
Q524 Mark4 marksDifficult
Write a long answer on Real Numbers. Include definition, explanation and one application.
Answer
Real Numbers — Euclid’s algorithm finds HCF. 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).
Q534 Mark4 marksModerate
Write a long answer on Fundamental Theorem of Arithmetic. Include definition, explanation and one application.
Answer
Fundamental Theorem of Arithmetic — Every composite number can be expressed as a product of primes, unique except for the order of 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).
Q544 Mark4 marksModerate
Write a long answer on HCF and LCM. Include definition, explanation and one application.
Answer
HCF and LCM — For two positive integers, HCF × LCM equals the product of the numbers. 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).
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).
Q61Assertion and Reason1 markModerate
Assertion (A): Fundamental Theorem of Arithmetic (statement).
Reason (R): Real Numbers is a key idea in the chapter Real Numbers.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q62Assertion and Reason1 markModerate
Assertion (A): HCF × LCM = product of two positive integers.
Reason (R): Real Numbers is a key idea in the chapter Real Numbers.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q63Assertion and Reason1 markModerate
Assertion (A): Terminating decimals: denominator 2^m 5^n after simplifying.
Reason (R): Terminating decimals is a key idea in the chapter Real Numbers.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q64Assertion and Reason1 markDifficult
Assertion (A): √2, √3, √5 are irrational.
Reason (R): Real Numbers is a key idea in the chapter Real Numbers.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q65Assertion and Reason1 markModerate
Assertion (A): Euclid’s algorithm finds HCF.
Reason (R): Real Numbers is a key idea in the chapter Real Numbers.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q66Assertion and Reason1 markModerate
Assertion (A): Every composite number can be expressed as a product of primes, unique except for the order of factors.
Reason (R): Fundamental Theorem of Arithmetic is a key idea in the chapter Real Numbers.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q67Assertion and Reason1 markModerate
Assertion (A): For two positive integers, HCF × LCM equals the product of the numbers.
Reason (R): HCF and LCM is a key idea in the chapter Real Numbers.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 10 · Subject: Mathematics · Chapter: Real Numbers · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q68Assertion and Reason1 markDifficult
Assertion (A): A rational p/q in lowest terms has a terminating decimal if q has only 2 and/or 5 as prime factors.
Reason (R): Terminating decimal is a key idea in the chapter Real Numbers.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
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).
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).
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 “Revision Notes” 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.
