‘रचना-प्रयोग’ का मुख्य उद्देश्य क्या है?

व्याकरण का व्यावहारिक प्रयोग सिखाना

‘द्वितीयः’ किस प्रकार की संख्या है?

क्रमवाचक (दूसरा)

CBSE · Board years

CBSE Class 10 — Notes, Chapters & Practice Quizzes

Your Class 10 year, organised — chapter notes, board-style questions and a practice quiz for every chapter.

7 subjects 143 chapters 149 practice quizzes NCERT syllabus

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sin²θ means (sinθ)², not sin(θ²). A pure notation trap that changes the value.

Class 10 Mathematics — Chapter-wise Notes & Quizzes

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Mathematics · 14 chapters

Summary, key terms, extra questions with answers and a practice quiz with AI diagnosis for each.

Chapter 1: Real NumbersClass 10 Mathematics — summary, notes, extra questions & NCERT solutions

Short notes — the whole chapter on one page

Every formula, worked example and diagram in the chapter — on a single sheet.

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Which theorem states that every composite number can be expressed as a unique product of primes?

Summary

This chapter builds the foundation of number theory for Class 10. The Fundamental Theorem of Arithmetic states that every composite number can be expressed as a unique product of primes, which lets us find the HCF and LCM of numbers through prime factorisation. A key relationship is that for any two positive integers, \(\text{HCF} \times \text{LCM}\) equals the product of the numbers. The chapter also revisits irrational numbers, proving results such as the irrationality of \(\sqrt{2}\) using the method of contradiction. Together these ideas sharpen the understanding of how integers and primes underpin the rest of arithmetic and algebra.

Fundamental Theorem of ArithmeticHCF and LCM by prime factorisationIrrational numbersProofs of irrationality

Key terms

Fundamental Theorem of Arithmetic

Every composite number has a unique prime factorisation.

HCF

The highest common factor (greatest common divisor) of given numbers.

LCM

The lowest common multiple of given numbers.

Irrational number

A number that cannot be written as a ratio of two integers.

Extra questions & answers

EXERCISE 1.1

EXERCISE 1.2

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HCF × LCM = product of two numbers

Number aNumber bHCF

LCM =36

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Fundamental Theorem of Arithmetic

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Every composite number has a unique prime factorisation.

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Practice quiz · Real Numbers

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Real Numbers

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Maths 10 Qs · ~10 min

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Your Class 10 board-year rhythm

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