Class 10 Chapter 1: Real Numbers PYQs
Practise chapter-wise CBSE previous-year questions with focused topics and exam-ready solutions.
Use these previous-year questions to revise Euclid’s division algorithm, the Fundamental Theorem of Arithmetic, HCF and LCM, and irrational numbers. Work through the topic links to identify recurring CBSE question patterns, practise proof and calculation methods, and check your final reasoning against exam-ready solutions for timed board practice.
Choose a topic to practise
CBSE Board Exam Blueprint & Topic Weightage: Real Numbers
In the Class 10 CBSE Board Examination, Real Numbers constitutes the entire Unit 1: Number Systems, contributing 6 marks to the 80-mark theory paper. Historically, board questions follow a consistent and dependable pattern:
- Section A (1 Mark MCQ): Questions testing the Fundamental Theorem of Arithmetic, prime factorisation exponents (such as finding the sum of exponents of prime factors), or applying the relationship \(\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b\).
- Section B or C (2 or 3 Marks): Rigorous proof of irrationality for numbers like \(\sqrt{2}\), \(\sqrt{3}\), \(\sqrt{5}\), or composite forms such as \(3 + 2\sqrt{5}\) using proof by contradiction.
- Word Problems (3 Marks): Real-life synchronization problems (e.g., bells tolling together, traffic lights, morning walks along circular paths) requiring the calculation of HCF or LCM.
Key Revision Tips for Board Examinations
When proving that a number is irrational, clearly state the initial assumption that \(p/q\) is in simplest form where \(p\) and \(q\) are co-prime positive integers with \(q \neq 0\). Showing that \(p\) and \(q\) share a common factor contradicts the assumption of co-primality. In prime factorisation questions, always express your final answers in standard canonical prime power format.