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Ncert Books Class 10 Maths Chapter 1 Free Download
Ncert Books Class 10 Maths Chapter 1 Free Download
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FAQs on Ncert Books Class 10 Maths Chapter 1 Free Download
1. What are the most important topics in Class 10 Maths Chapter 1, Real Numbers, for the board exams 2025-26?
For the CBSE Class 10 board exams 2025-26, the most important topics in Real Numbers are:
- The Fundamental Theorem of Arithmetic and its application in finding the HCF and LCM of integers.
- Proving the irrationality of numbers, such as √2, √3, √5, and expressions like 5 - 2√3.
- Solving word problems based on HCF and LCM, which test practical application.
- Understanding the conditions for a rational number's decimal expansion to be terminating or non-terminating repeating.
2. What is the expected marks weightage for the Real Numbers chapter in the Class 10 Maths exam?
The chapter Real Numbers is part of the 'Number Systems' unit, which typically carries a weightage of around 6 marks in the CBSE Class 10 Maths board examination. Questions can be a mix of MCQs, short answer (2 marks), and long answer (3 or 5 marks) questions, making it a high-scoring and important chapter.
3. Which types of questions are most frequently asked from Real Numbers in board exams?
The most frequently asked questions from this chapter include:
- 2-Mark Questions: Finding the HCF and LCM of two numbers using the prime factorisation method and verifying the formula HCF × LCM = Product of the two numbers.
- 3-Mark Questions: Proving that a number like √5 is irrational. These are very common and require a precise, step-by-step proof by contradiction.
- 5-Mark Questions: These are often application-based word problems (HOTS) that require you to determine whether to calculate HCF or LCM to find the solution. For example, questions involving circular paths, alarm bells, or stacking items.
4. Why is the Fundamental Theorem of Arithmetic considered a cornerstone for solving important questions in this chapter?
The Fundamental Theorem of Arithmetic is crucial because it states that every composite number can be uniquely expressed as a product of primes. This isn't just a theoretical statement; it is the fundamental principle behind the most common method for calculating HCF and LCM. Almost every important computational problem in this chapter, especially finding HCF and LCM of larger numbers, relies directly on applying this theorem through prime factorisation.
5. How are HCF and LCM concepts applied to solve real-world word problems, which are often asked as important questions?
These concepts are applied to find solutions in different scenarios:
- HCF (Highest Common Factor) is used to find the 'greatest' or 'maximum' number for tasks like arranging items into groups or finding the largest size of tile to pave a floor without wastage. Look for keywords like 'maximum', 'greatest', or 'largest'.
- LCM (Least Common Multiple) is used to find the 'minimum' time or quantity when events repeat at different intervals. For example, finding when two bells will ring together again or when runners on a circular track will meet at the starting point. Look for keywords like 'minimum', 'least', 'next time', or 'together'.
6. What is a common mistake students make when writing the proof of irrationality for a number like √3, and how can it be avoided?
A very common mistake is an incomplete or unclear conclusion. Students often correctly show that if √3 = a/b, then both 'a' and 'b' must be multiples of 3. However, they fail to explicitly state that this contradicts the initial assumption that 'a' and 'b' are co-prime (have no common factors other than 1). To avoid this and score full marks, always end your proof with a clear statement: "This contradicts our assumption that a and b are co-prime. Therefore, our initial assumption was wrong, and √3 is irrational."
7. How important is it to practise questions from the NCERT Exemplar for the Real Numbers chapter?
Practising questions from the NCERT Exemplar for Real Numbers is highly recommended. The Exemplar contains Higher Order Thinking Skills (HOTS) questions and complex MCQs that go beyond the basic textbook exercises. Solving these questions is crucial for tackling the more challenging and tricky problems that may appear in the board exam, helping you to build a deeper conceptual understanding and aim for a top score.
8. How can mastering the important questions from Real Numbers help in scoring 90+ in the Class 10 Maths exam?
Mastering the important questions from Real Numbers is a key step towards a 90+ score for several reasons. Firstly, it is a relatively easy and high-scoring chapter, allowing you to secure a quick 6 marks with confidence. Secondly, the concepts of HCF and LCM and prime factorization are foundational and have applications in other chapters like Polynomials. Securing full marks in this first chapter builds momentum and a strong problem-solving mindset for the rest of the syllabus.
