NCERT Class 10 Math Chapter 1: वास्तविक संख्याएँ PDF Download

NCERT Class 10 Math Chapter 1 वास्तविक संख्याएँ (Real Numbers) introduces students to important concepts like Euclid’s division lemma, the Fundamental Theorem of Arithmetic, prime factorisation, and the properties of irrational and rational numbers. This chapter is a foundation for advanced concepts in higher classes and also plays a big role in board exam preparation.

NCERT Class 10 Math Chapter 1 वास्तविक संख्याएँ (Real Numbers) introduces students to important concepts like Euclid’s division lemma, the Fundamental Theorem of Arithmetic, prime factorisation, and the properties of irrational and rational numbers. This chapter is a foundation for advanced concepts in higher classes and also plays a big role in board exam preparation. It builds a strong base by connecting earlier knowledge of numbers with new techniques of solving real-life mathematical problems.

I chose to write about this chapter because it is one of the most scoring topics in Class 10 Mathematics. Students often underestimate real numbers, but questions from this chapter appear regularly in board exams. By understanding topics such as Euclid’s lemma, HCF, LCM, and proof of irrational numbers, students can gain confidence in both objective and descriptive questions. Moreover, these concepts are not just theoretical but have practical applications in fields like cryptography, coding, and advanced number theory. Knowing them early gives students an advantage in competitive exams like JEE and other entrance tests. That is why it is important to learn this chapter properly and have easy access to the NCERT PDF for revision.

Key Topics in Chapter 1 वास्तविक संख्याएँ

This chapter covers:

Euclid’s Division Lemma – A method for finding HCF of two numbers
Fundamental Theorem of Arithmetic – Unique factorisation into primes
HCF and LCM using prime factorisation – Practical use in problem solving
Proofs of irrational numbers – Like √2, √3, √5 are irrational
Decimals of Rational Numbers – Terminating and non-terminating recurring decimals
Relationship between HCF and LCM – Formula: HCF × LCM = Product of numbers

Why this chapter is important

Frequently asked in CBSE Class 10 Board exams
Base for higher mathematics and competitive exams
Easy to understand and score full marks if practised well
Encourages logical reasoning and proof-writing ability

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You can download NCERT Class 10 Math Chapter 1: वास्तविक संख्याएँ PDF from this website.

NCERT Class 10 Math Chapter 14: प्रायिकता PDF Download

NCERT Class 10 Math Chapter 14 प्रायिकता (Probability) introduces students to the concept of chance and likelihood of events. In this chapter, students learn how to calculate the probability of simple events using the formula P(E) = Number of favourable outcomes ÷ Total number of outcomes. The chapter deals with real-life examples like tossing a

NCERT Class 10 Math Chapter 14 प्रायिकता (Probability) introduces students to the concept of chance and likelihood of events. In this chapter, students learn how to calculate the probability of simple events using the formula P(E) = Number of favourable outcomes ÷ Total number of outcomes. The chapter deals with real-life examples like tossing a coin, rolling a dice, or drawing cards, which makes the subject more interesting and practical. Since probability questions are common in board exams and are generally considered easy, this chapter is highly important for scoring well.

I am writing about this topic because probability is not only an important part of the Class 10 syllabus but also a concept that students will use in higher studies and real life. From predicting weather conditions to calculating risks in business, probability plays a key role. Many students initially find it confusing, but NCERT presents it in a simple and easy-to-understand manner. By practising from the NCERT book, students can build a strong foundation and develop confidence in solving probability problems. Having the PDF makes it easier for learners to access the chapter anytime, revise formulas, and attempt practice questions before exams.