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NCERT Class 10 Math Chapter 4: द्विघात समीकरण PDF Download

NCERT Class 10 Math Chapter 4: द्विघात समीकरण PDF Download

NCERT Class 10 Math Chapter 4 द्विघात समीकरण (Quadratic Equations) introduces students to one of the most important topics in algebra. A quadratic equation is a polynomial equation of degree two, generally written in the form ax² + bx + c = 0, where a, b, and c are real numbers, and a ≠ 0. This chapter focuses on how to form quadratic equations, solve them using different methods, and apply them in real-life problem situations such as areas, age-related questions, and finance-related problems.

I am writing about this chapter because quadratic equations are a crucial foundation for higher mathematics, especially in Class 11 and 12 where algebra becomes more advanced. Many students initially struggle with the concept because of the formulas involved, but once understood, it becomes a very scoring topic in exams. Quadratic equations are not just limited to academics; they are also used in real life such as calculating projectile motion in physics, analysing business profit or loss, and designing structures in engineering. For Class 10 board exams, this chapter carries significant marks, and mastering it can help students perform better in both school-level and competitive exams. That is why having the NCERT PDF is very useful for regular practice.

Key Topics in Chapter 4 द्विघात समीकरण

This chapter explains quadratic equations step by step. The main topics include:

  • Introduction to Quadratic Equations – Standard form ax² + bx + c = 0
  • Methods of Solving Quadratic Equations
    • Factorisation Method
    • Completing the Square Method
    • Quadratic Formula Method
  • Nature of Roots – Relationship between discriminant (D = b² – 4ac) and types of solutions
  • Word Problems – Application-based questions in geometry, age, and daily life situations

Important Notes for Students

  • If D > 0 → Roots are real and distinct
  • If D = 0 → Roots are real and equal
  • If D < 0 → No real roots (imaginary solutions)
  • Quadratic formula: x = [-b ± √(b² – 4ac)] / 2a

Download PDF

You can download NCERT Class 10 Math Chapter 4: द्विघात समीकरण PDF from the official NCERT website.

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Download NCERT Class 11 Biology Hindi Chapter 1 जीव जगत – Complete PDF and Key Notes

Download NCERT Class 11 Biology Hindi Chapter 1 जीव जगत – Complete PDF and Key Notes

The first chapter of NCERT Class 11 Biology, जीव जगत (The Living World), introduces students to the fascinating diversity of life on Earth. It explains how living organisms are classified, named, and studied scientifically. This chapter is the foundation for all other lessons in biology because it builds the basic understanding of how scientists identify and categorise the immense variety of plants and animals around us.

I chose to write about this topic because “जीव जगत” sets the stage for every biology student stepping into higher secondary education. It answers one of the oldest human questions — “What is life?” Understanding the living world helps students recognise patterns in nature, the importance of biodiversity, and how humans fit into the broader ecological system. Moreover, it’s an important chapter for both CBSE board exams and entrance tests like NEET, where basic concepts of taxonomy and classification are frequently tested.

About Chapter 1: जीव जगत (The Living World)

The chapter begins with a simple question — What makes something living? It goes on to explain that living organisms show growth, reproduction, metabolism, and response to stimuli. The chapter also describes how biologists classify organisms systematically based on shared characteristics.

It introduces the concepts of taxonomy, nomenclature, and the hierarchy of classification — from kingdom to species. Students learn about the contributions of scientists like Carolus Linnaeus, who developed the binomial nomenclature system still used worldwide.

Key Topics Covered in जीव जगत

Here are the main topics that students will study in this chapter:

  • What is living?
  • Diversity in the living world
  • Need for classification
  • Taxonomy and systematics
  • Binomial nomenclature
  • Taxonomical categories and hierarchy
  • Tools for the study of taxonomy (herbaria, museums, zoological parks, and botanical gardens)

Each topic helps students understand how living organisms are grouped and studied, making biology more organised and meaningful.

Important Terms and Definitions

ConceptDescription
TaxonomyThe science of naming, describing, and classifying organisms
SystematicsStudy of relationships among organisms and their evolutionary history
Binomial NomenclatureSystem of naming species with two parts: genus and species name
SpeciesGroup of organisms capable of interbreeding and producing fertile offspring
GenusA group of closely related species

Tools Used in the Study of Taxonomy

To make identification easier, scientists use several resources:

  • Herbarium: Collection of dried plant specimens for study
  • Museum: Preserved animal specimens for reference
  • Botanical Gardens: Living plant collections used for research and education
  • Zoological Parks: Places where animals are kept in natural-like conditions
  • Taxonomic Keys: Guides used to identify organisms based on characteristics

These tools make the process of classification systematic and reliable.

How to Download NCERT Class 11 Biology Chapter 1 PDF in Hindi

Students can easily download the NCERT Class 11 Biology Chapter 1: जीव जगत (The Living World) Hindi PDF from here.

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