Class 10 Maths Chapter 1 Real Numbers Important Questions
Chapter 1 of Class 10 Maths, titled Real Numbers, forms the foundation of number theory in higher classes. Students must understand Euclid’s Division Lemma, Fundamental Theorem of Arithmetic, and concepts like rational and irrational numbers. Practicing important questions from NCERT, CBSE sample papers, and previous year question papers (PYQs) ensures thorough preparation.
In this post, we cover Class 10 Maths Chapter 1 Important Questions categorised into short and long answers based on past trends and NCERT guidelines. You’ll also get marking schemes, stepwise tips to score full marks, and links to helpful resources like chapter-wise formula sheets and exemplar problems. Regular revision using these questions and related MCQs is crucial for both board exams and competitive preparation like JEE Foundation.
Short Answer Type Questions – Real Numbers Class 10
Short answer questions carry 2 to 3 marks and often test your ability to apply definitions and theorems quickly. Here are some commonly asked questions:
- Use Euclid’s Division Lemma to find the HCF of 56 and 72. [3 Marks]
- Prove that √3 is an irrational number. [2 Marks]
- Write the decimal expansion of 1/7 and mention whether it is terminating or non-terminating. [2 Marks]
- Find LCM and HCF of 12 and 18 using prime factorization. [3 Marks]
For detailed solutions, refer to our RD Sharma Class 9 Chapter 1 Solutions and Euclid’s Lemma Explained posts. These concepts lay the base for advanced topics in Class 11 Maths.
Marking Scheme & Tips
- For 2-mark questions, keep your answers concise and to the point.
- Highlight the theorem used – especially when proving irrationality.
- Use clean calculations and box your final answer.
Long Answer Type Questions – Class 10 Real Numbers
These questions carry 4 to 5 marks and require detailed steps. Make sure to practice these well before the exam:
- Use the Fundamental Theorem of Arithmetic to find the HCF of 196 and 38220. [4 Marks]
- Show that any positive odd integer is of the form 6q±1, but not divisible by 3. [5 Marks]
- If HCF(a, b) = 12 and LCM(a, b) = 180, find the product of a and b. [4 Marks]
- Prove that there are infinitely many primes. [5 Marks]
Practice these with hints from the NCERT Exemplar Solutions and our curated list of important theorems and proofs. These questions often reappear in standard sample papers.
Marking Scheme & Tips
- Show each logical step clearly.
- Mention any theorem used and state it properly.
- Label equations and maintain neatness.
How To Prepare for Real Numbers Chapter in Class 10?
Follow these preparation tips for a perfect score in Chapter 1:
- Start with NCERT solutions and examples.
- Watch step-by-step explanations on our video solution page.
- Use Prime Factorization Calculator for practice.
- Practice MCQs and numericals from the Oswaal Question Bank.
FAQs
What are the most important topics in Chapter 1 Real Numbers?
The most important topics include Euclid’s Division Lemma, Fundamental Theorem of Arithmetic, irrational number proofs, and HCF/LCM using prime factorization. Focus on these with practice questions and video explanations.
Where can I get solved questions from RD Sharma and NCERT for Real Numbers?
You can find stepwise RD Sharma solutions at this link and NCERT-based video solutions at our video solutions post.