Real Numbers CBSE Class 10 PYQ Chapter Wise (2016–2026)

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Answer first

Real Numbers PYQs (previous year questions) for CBSE Class 10: Real Numbers (Mathematics) had 23 questions across the 40 official CBSE Class 10 papers we tagged (2016–2026), and appeared in 7 of them. Asked in 7 of 10 years. The concepts asked in the most papers: HCF and LCM, Irrational Numbers, Prime Numbers.

Year-wise question count

Asked in 7 of 10 years.

Most-asked concepts

Sorted by the number of papers a concept appeared in.

How to practise Real Numbers PYQs

1. Start with the concepts at the top of the table. They have come back the most.
2. Solve one year’s Real Numbers questions from the official PDF against the clock, then check the answer listed below.
3. Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
4. Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.

Questions by year

Each line gives the question number and paper, type, concept, our one-line summary, with a link to the official PDF.

CBSE Class 102026

• Q.1 (Mathematics Standard (30/1/1)) · MCQ · HCF and LCM: HCF of 960 and 432 PDF
• Q.2 (Mathematics Standard (30/1/1)) · MCQ · Prime Numbers: Classify the natural number 2 PDF
• Q.3 (Mathematics Standard (30/1/1)) · MCQ · Fundamental Theorem of Arithmetic: Last digit of 6 to the power n PDF
• Q.26 (Mathematics Standard (30/1/1)) · Short answer · Irrational Numbers: Prove root 3 is irrational PDF

CBSE Class 102025

• Q.6 (Mathematics Standard (30/1/1)) · MCQ · HCF and LCM: Evaluate n minus 7m from HCF and LCM of 98 and 28 PDF
• Q.9 (Mathematics Standard (30/1/1)) · MCQ · Odd and Even Numbers: Condition on n for a sum of powers of -1 to vanish PDF
• Q.14 (Mathematics Standard (30/1/1)) · MCQ · Rational Numbers: Identify a rational number between two irrationals PDF
• Q.29 (Mathematics Standard (30/1/1)) · Short answer · Irrational Numbers: Prove a given surd is irrational PDF

CBSE Class 102024

• Q.5 (Mathematics Standard (30/1/1)) · MCQ · HCF and LCM: LCM of two numbers given in prime-power form PDF
• Q.25 (Mathematics Standard (30/1/1)) · Very short answer · Irrational Numbers: Prove 5 - 2 root 3 is irrational PDF
• Q.27 (Mathematics Standard (30/1/1)) · Short answer · HCF and LCM: Minimum rooms for equal-size single-subject groups PDF

CBSE Class 102023

• Q.20 (Mathematics Standard (30/1/1)) · Assertion-Reason · Irrational Numbers: Assertion-reason on rationality of a right triangle's perimeter PDF
• Q.24 (Mathematics Standard (30/1/1)) · Very short answer · HCF and LCM: Greatest number dividing 85 and 72 with given remainders PDF
• Q.27 (Mathematics Standard (30/1/1)) · Short answer · Irrational Numbers: Prove root 5 is irrational PDF

CBSE Class 102020

• Q.2 (Mathematics Standard (30/1/1)) · MCQ · Prime Numbers: Number of factors of a prime number PDF
• Q.5 (Mathematics Standard (30/1/1)) · MCQ · HCF and LCM: HCF and LCM of 12, 21 and 15 PDF
• Q.35 (Mathematics Standard (30/1/1)) · Long answer · Euclid's Division Lemma: Show a square is never of form 5q+2 or 5q+3 PDF

CBSE Class 102019

• Q.6 (Mathematics (30/1/1)) · Very short answer · Rational Numbers: A rational number between root 2 and root 3 PDF
• Q.7 (Mathematics (30/1/1)) · Short answer · Euclid's Division Algorithm: HCF of 1260 and 7344 by Euclid's algorithm PDF
• Q.13 (Mathematics (30/1/1)) · Short answer · Irrational Numbers: Prove root 2 is irrational PDF

CBSE Class 102018

• Q.2 (Mathematics (30/1)) · Very short answer · HCF and LCM: HCF of smallest prime and smallest composite number PDF
• Q.7 (Mathematics (30/1)) · Short answer · Irrational Numbers: Prove 5 + 3 root 2 is irrational PDF
• Q.13 (Mathematics (30/1)) · Short answer · HCF and LCM: HCF and LCM of 404 and 96 with product check PDF

Other Mathematics chapters

• Polynomials PYQs
• Pair of Linear Equations in Two Variables PYQs
• Quadratic Equations PYQs
• Arithmetic Progressions PYQs
• Triangles PYQs
• Coordinate Geometry PYQs
• Introduction to Trigonometry PYQs
• Some Applications of Trigonometry PYQs
• Circles PYQs
• Constructions PYQs
• Areas Related to Circles PYQs
• Surface Areas and Volumes PYQs
• Statistics PYQs
• Probability PYQs

FAQ

How many Real Numbers questions come in CBSE Class 10?

In the official papers we tagged: 4 in 2026, 4 in 2025, 3 in 2024, 3 in 2023, 3 in 2020, 3 in 2019 and 3 in 2018. Not asked in the other 3 years. That is 23 questions in all, about 7% of Mathematics.

Which Real Numbers topics repeat in CBSE Class 10?

Asked in the most papers: HCF and LCM, Irrational Numbers, Prime Numbers. The concept table lists every one with its count.

Are these official CBSE Class 10 questions?

Yes. Every question is from an official CBSE Class 10 paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.