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Chapter Wise NCERT Solutions for Class 10 Maths

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NCERT Solutions for Class 10 Maths covering all exercises from Chapters 1 to 15. Our team of expert faculty has carefully curated these solutions to aid students in their exam preparations.

By downloading the chapter-wise PDFs of CBSE NCERT Solutions for Class 10, students can access comprehensive guidance to tackle the problems effectively.

The solutions for Class 10 NCERT maths are tailored for the 2023-24 session and are crafted to assist students in comprehending and solving textbook problems.

NCERT Solutions for Class 10 Maths

The provided answers to the questions in NCERT books serve as excellent study material for students. This page includes all the questions and answers with proper explanations from the CBSE class 10th NCERT math Books.

With this Class 10 Maths NCERT Solutions, students can gain a deeper understanding of the textbook concepts. Practicing these 10th class Maths textbook questions will enable students to assess their preparation level and grasp of the subject matter.

Moreover, the solutions to these questions help students swiftly clarify any doubts they may have. By utilizing these solutions, students can approach their studies with greater confidence and ensure a solid foundation in Mathematics for their academic journey.

NCERT Solutions for Class 10 Maths Chapter-Wise

Solutions for Class 10 NCERT Maths provides an chapter-wise solutions to all the problems as per the NCERT textbooks. These solutions are written in a clear and concise style, and they also include helpful hints and tips.

By working on these NCERT solutions for Class 10 Maths, students can get an idea about how to solve the problems and grasp basic concepts better and faster. It’s also a perfect guide to help students score good marks in CBSE board examinations.

To practice or see the chapter-wise solutions for Class 10 NCERT Maths, simply click on the chapter-wise links given below.

Here are the chapters from the NCERT Class 10 Maths textbook 2023-24 academic year. Also, Take a look at the Class 10 Maths syllabus to see what topics you will learn and in what order.

NCERT Solutions for Class 10 Maths Free PDF Download

NCERT Solutions of Class 10 Maths list comprises all the chapter-wise answers to the questions present in the NCERT Book for Class 10 Maths, written in a very precise and easy manner, maintaining the objective of textbooks.

The students can refer to the NCERT Solutions for Class 10 as their additional references and study materials. Practicing NCERT textbook solutions exercise will surely help the students in their preparation for the CBSE Class 10th examination.

Solutions for Class 10 NCERT Maths Chapter 1 – Real Numbers

In NCERT Solutions for Class 10 Maths Chapter 1, students will explore real numbers and irrational numbers. In Class 10 Maths, the chapter starts with the Euclid’s Division Lemma, which states that “Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0≤r<b”.

The Euclid’s Division algorithm is based on this lemma and is used to calculate the HCF of two positive integers. Then, the Fundamental Theorem of Arithmetic is defined, which is used to find the LCM and HCF of two positive integers. After that, the concept of an irrational number, a rational number and the decimal expansion of rational numbers are explained with the help of the theorem in NCERT Class 10 Chapter 1 Real Numbers.

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

Class 10 Maths NCERT Solutions Chapter 1 Exercises

More resources for Class 10 Maths Chapter 1 Real Numbers

NCERT Solutions for Class 10 Maths Chapter 2 – Polynomials

Solutions for Class 10 NCERT Maths Chapter 2, Polynomials, presents a comprehensive study of algebraic expressions with a specific focus on polynomials. The NCERT Solutions offered in this chapter elucidate advanced terminologies like degree, coefficient, and zeroes associated with polynomials. With four exercises to reinforce learning, the chapter caters to students at different proficiency levels.

In Class 10 Maths, the chapter begins by defining the degree of a polynomial and explaining linear, quadratic, and cubic polynomials, laying a solid groundwork for further exploration. Exercise 2.1 challenges students to deduce zeroes from graphical representations, honing their analytical skills. In Exercise 2.2, they explore the relationship between zeroes and coefficients, deepening their understanding of polynomial properties.

The division algorithm is introduced in Exercise 2.3, elucidating its significance and application in polynomial division. The optional Exercise 2.4 encompasses all chapter concepts, providing a comprehensive review for students seeking additional practice.

Overall, NCERT Class 10 Chapter 2 Polynomials provide a well-structured learning experience, empowering students to grasp the intricacies of polynomials and apply their knowledge confidently in various mathematical scenarios.

Class 10 Maths NCERT Solutions Chapter 2 Exercises

More resources for Class 10 Maths Chapter 2 Polynomials

Solutions for Class 10 NCERT Maths Chapter 3 – Pair of Linear Equations in Two Variables

In NCERT Solutions for Class 10 Maths Chapter 3, Pair of Linear Equations in Two Variables, students are introduced to the concept of solving linear equations with two variables both graphically and algebraically. In Class 10 Mathematics, the NCERT Class 10 Chapter 3 Pair of Linear Equations in Two Variables comprises seven exercises that progressively cover various methods of solving these equations.

Exercises 3.1 and 3.2 focus on representing equations in both graphical and algebraic forms, serving as foundational exercises to develop a solid understanding of the topic. Exercises 3.3 and 3.4 introduce the Substitution and Elimination methods, respectively, enabling students to solve equations using these techniques.

Moving forward, Exercises 3.5 and 3.6 elaborate on the Cross-Multiplication and Substitution methods, respectively, providing students with a comprehensive toolkit to tackle diverse linear equations.

Exercise 3.7, an optional exercise, consolidates all the methods introduced in the previous exercises, offering students the opportunity to practice and strengthen their problem-solving skills.

Class 10 Maths NCERT Solutions Chapter 3 Exercises

More resources for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

NCERT Solutions for Class 10 Maths Chapter 4 – Quadratic Equations

In Solutions for Class 10 NCERT Maths Chapter 4, students will explore the standard form of writing a Quadratic Equation. The chapter proceeds to elucidate two essential methods of solving quadratic equations: the factorization method and the completing the square method.

As the Class 10 Mathematicschapter progresses, students will encounter the topic of finding the nature of roots, where they learn that a quadratic equation in the form of ax² + bx + c = 0 will have:

Two distinct real roots if b² – 4ac > 0

Two equal roots if b² – 4ac = 0

No real roots if b² – 4ac < 0.

The NCERT Class 10 Chapter 4 Quadratic Equations comprises four exercises with a total of 24 well-structured questions, thoughtfully categorized into 10 easy-level problems, 6 mid-level problems, and 8 difficult-type questions. These exercises offer students an opportunity to apply the learned concepts and enhance their problem-solving skills in quadratic equations.

Class 10 Maths NCERT Solutions Chapter 4 Exercises

More resources for Class 10 Maths Chapter 4 Quadratic Equations

NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions

In this Solutions for Class 10 NCERT Maths chapter 5, students are introduced to the concept of Arithmetic Progression (AP). In Class 10 Maths, the NCERT Class 10 Chapter 5 Arithmetic Progressions consists of four exercises, each catering to different aspects of AP. Exercise 5.1 covers questions related to representing situations as AP, finding the first term and difference of an AP, and determining whether a series is an AP or not.

In Exercise 5.2, students will explore how to find the nth term of an AP using the formula: an = a + (n-1) d. Moving on to Exercise 5.3, students will encounter questions focused on calculating the sum of the first n terms of an AP. Finally, the last exercise, 5.4, challenges students with higher-level questions that aim to enhance their analytical and problem-solving skills in the context of AP.

With these exercises, students will develop a comprehensive understanding of Arithmetic Progressions and gain proficiency in various aspects of this essential mathematical concept.

Class 10 Maths NCERT Solutions Chapter 5 Exercises

More resources for Class 10 Maths Chapter 5 Arithmetic Progression(AP)

Solutions for Class 10 NCERT Maths Chapter 6 – Triangles

In NCERT Solutions for Class 10 Maths Chapter 6, Triangles, students will explore comprehensive NCERT Solutions that delve into the intricacies of triangles, focusing on concepts of similarity and congruence.

In Class 10 Mathematics, the NCERT Class 10 Chapter 6 Triangles commences with a thorough explanation of similar and congruent figures, followed by discussions on conditions for triangle similarity and related theorems. Additionally, the chapter covers the computation of areas of similar triangles with a relevant theorem. 

Towards the conclusion, students will encounter the Pythagoras Theorem and the Converse of Pythagoras Theorem, crucial topics that demonstrate the practical applications of triangles in various scenarios. By engaging with this chapter, students will develop a profound understanding of triangles, their properties, and the theorems that govern their geometric relationships, laying a strong foundation for future mathematical explorations.

Class 10 Maths NCERT Solutions Chapter 6 Exercises

More resources for Class 10 Maths Chapter 6 Triangles

NCERT Solutions for Class 10 Maths Chapter 7 – Coordinate Geometry

In the solutions for class 10 NCERT maths chapter 7 on Coordinate Geometry, students will acquire essential skills in finding the distance between two points with known coordinates and calculating the area of a triangle formed by three given points.

Additionally, students will explore methods to determine the coordinates of a point that divides a line segment joining two given points in a specified ratio. In Class 10 Mathematics, the NCERT Class 10 Chapter 7 Coordinate Geometry introduces fundamental concepts such as the Distance Formula, Section Formula, and Area of a Triangle.

Through these concepts, students will gain valuable insights into the geometric properties of points and lines in a coordinate plane, enabling them to solve a wide range of problems involving coordinates and distances.

Class 10 Maths NCERT Solutions Chapter 7 Exercises

More resources for Class 10 Maths Chapter 7 Coordinate Geometry

Solutions for Class 10 NCERT Maths Chapter 8 – Introduction to Trigonometry

In NCERT solutions for class 10 maths chapter 8, Introduction to Trigonometry, students will delve into the fundamentals of Trigonometry, exploring the ratios of right angles with the acute angles of a right-angled triangle. The NCERT Class 10 Chapter 8 Trigonometry introduces students to the concept of Trigonometry, where they will study the ratios associated with the acute angles of a right triangle, known as trigonometric ratios. 

Furthermore, the trigonometric ratios for angles of 0° and 90° are defined, providing students with a strong foundation in trigonometric concepts. In Class 10 Maths, the chapter also explores the calculation of trigonometric ratios for specific angles and establishes important identities involving these ratios, referred to as trigonometric identities.

By mastering the content of this chapter, students will gain valuable skills in trigonometry, enabling them to solve a variety of mathematical problems involving angles and triangles.

Class 10 Maths NCERT Solutions Chapter 8 Exercises

More resources for Class 10 Maths Chapter 8 Introduction to Trigonometry

Solutions for Class 10 NCERT Maths Chapter 9 – Some Applications of Trigonometry

This NCERT solutions for class 10 maths chapter 9 serves as a continuation of the previous one, delving into the practical applications of trigonometry. Students will explore the diverse real-world uses of trigonometry, ranging from geography and navigation to map construction and determining positions based on longitudes and latitudes. In Class 10 Maths, the NCERT Class 10 Chapter 9 Some Applications of Trigonometry focuses on how trigonometry enables the calculation of heights and distances of objects without the need for direct measurement. 

Students will be introduced to key terminologies like “line of sight,” “angle of elevation,” and “angle of depression,” which play crucial roles in trigonometric applications. Through this exploration, students will gain a deeper appreciation for the versatility and relevance of trigonometry in solving real-life problems and making accurate measurements in various fields.

Class 10 Maths NCERT Solutions Chapter 9 Exercises

  • NCERT Maths Solutions Class 10 Exercise 9.1 Set 1, Set 2 – 16 Questions (16 Long Answers)

More resources for Class 10 Maths Chapter 9 Some Application of Trigonometry

NCERT Solutions for Class 10 Maths Chapter 10 – Circles

In previous classes, students have familiarized themselves with the concept of a circle and its related terms, including chords, segments, and arcs. However, in this solutions for class 10 NCERT maths chapter 10, the focus shifts to exploring various scenarios that arise when a circle and a line intersect on a plane.

In class 10 Maths, NCERT class 10 chapter 10 Circles will delve into the concept of tangents to a circle and the determination of the number of tangents from a point on a circle. Through this study, they will gain a comprehensive understanding of the interactions between circles and lines, enabling them to identify and work with tangents in different geometric situations.

This chapter equips students with valuable insights into the geometric properties of circles and lines, broadening their mathematical knowledge and problem-solving skills in the realm of plane geometry.

Class 10 Maths NCERT Solutions Chapter 10 Exercises

More resources for Class 10 Maths Chapter 10 Circles

NCERT Solutions for Class 10 Maths Chapter 11 – Constructions

In this solutions for class 10 maths NCERT chapter 11, students will find two exercises dedicated to the topic of construction. Their prior knowledge of construction from earlier classes will prove beneficial in mastering these exercises.

In Exercise 11.1, students will learn the art of dividing a line segment using specific methods and steps NCERT Class 10 Chapter 11 Constructions. In Exercise 11.2, the focus shifts to the construction of tangents to a circle, where students will be guided through the necessary procedures. 

Throughout these exercises, detailed explanations and illustrative examples are provided to ensure students grasp the construction techniques effectively. By engaging with this Class 10 Maths chapter, students will enhance their construction skills, gaining the ability to precisely divide line segments and construct tangents to circles with confidence and accuracy.

Class 10 Maths NCERT Solutions Chapter 11 Exercises

More resources for Class 10 Maths Chapter 11 Constructions

NCERT Solutions for Class 10 Maths Chapter 12 – Areas Related to Circles

The solutions for class 10 maths NCERT chapter 12 commences with an introduction to the fundamental concepts of the perimeter and area of a circle. Building upon this foundation, students of Class 10 Maths will explore the methods to determine the area of a sector and segment within a circular region.

Additionally, the chapter will provide clarity on calculating the areas of various combinations of plane figures that involve circles or their components.

By understanding these principles of NCERT Class 10 Chapter 12 Areas Related to Circles, students will gain a comprehensive understanding of the geometric properties of circles and their relevance in calculating areas of different circular regions and their combinations. This knowledge will enable them to solve complex problems related to circles and other plane figures, further enhancing their mathematical proficiency.

Class 10 Maths NCERT Solutions Chapter 12 Exercises

More resources for Class 10 Maths Chapter 12 Areas Related to Circles

Solutions for Class 10 Maths NCERT Chapter 13 – Surface Areas and Volumes

In NCERT solutions for class 10 maths chapter 13 consists of five exercises that encompass a diverse range of problems related to solid objects. In Exercise 13.1, students will encounter questions requiring them to calculate the surface area of composite objects formed by combining any two basic solids, such as cuboid, cone, cylinder, sphere, and hemisphere.

Exercise 13.2 focuses on finding the volume of objects resulting from the combination of a cuboid, cone, cylinder, sphere, or hemisphere. In Exercise 13.3, students will explore questions involving the transformation of solids from one shape to another. 

The content of Exercise 13.4 centers around the calculation of volume, curved surface area, and total surface area of a frustum of a cone. For those seeking an extra challenge, the last exercise of NCERT Class 10 Chapter 13 Surface Areas and Volumes offers optional high-level questions that encompass all the topics covered in this chapter.

By engaging with these exercises, students of Class 10 Maths will gain a comprehensive understanding of solid objects and their various properties, developing the necessary skills to solve complex problems involving composite shapes and transformations.

Class 10 Maths NCERT Solutions Chapter 13 Exercises

More resources for Class 10 Maths Chapter 13 Surface Areas and Volumes

NCERT Solutions for Class 10 Maths Chapter 14 – Statistics

In this solutions for class 10 maths NCERT chapter 14, students will delve into the conversion of ungrouped data into grouped data, enabling them to represent numerical information more effectively. They will also learn to calculate the Mean, Mode, and Median of the data, providing valuable insights into the central tendencies of the dataset.

Furthermore, students of Class 10 Maths will explore the concept of cumulative frequency and cumulative frequency distribution, gaining an understanding of how to construct cumulative frequency curves. Through this study of NCERT Class 10 Chapter 14 Statistics, students will enhance their statistical analysis skills and develop a comprehensive understanding of handling and interpreting data in a more organized and insightful manner.

Class 10 Maths NCERT Solutions Chapter 14 Exercises

More resources for Class 10 Maths Chapter 14 Statistics

Solutions for Class 10 NCERT Maths Chapter 15 – Probability

In the final chapter of NCERT solutions for class 10 maths chapter 15 Probability is the focal point of study. It commences by introducing the theoretical aspects of probability, providing students with a foundational understanding of the subject.

Additionally, the NCERT Class 10 Chapter 15 Probability highlights the distinction between experimental probability and theoretical probability, offering various illustrative examples to reinforce the concepts effectively. For Class 10 Maths, Students are encouraged to work through these examples in CBSE Maths before proceeding to the exercise problems. 

This approach ensures that students have a solid grasp of the theoretical concepts and practical applications of probability, equipping them to tackle the exercises with confidence and accuracy. By engaging with this chapter, students will develop a comprehensive understanding of probability and its significance in analyzing real-world situations.

Class 10 Maths NCERT Solutions Chapter 15 Exercises

More resources for Class 10 Maths Chapter 15 Probability

Benefits of Solving NCERT Solutions for Class 10 Maths From GeeksforGeeks

Benefits of Using GeeksforGeeks for Solved paper for class 10 Maths:

  • Comprehensive Coverage: GeeksforGeeks provides in-depth solutions covering all NCERT exercises, ensuring complete understanding.
  • Step-by-Step Guidance: Solutions are presented in a clear, step-wise manner, aiding easy comprehension and problem-solving.
  • Visual Aids: Visual representations and diagrams enhance understanding of complex concepts and geometrical problems.
  • Variety of Approaches: GeeksforGeeks often presents multiple methods to solve problems, broadening problem-solving skills.
  • Practice Questions: Additional practice questions beyond NCERT help reinforce concepts and provide more practice.
  • Interactive Platform: The platform allows doubt clarification through discussions and interaction with experts and peers.
  • Accessibility: Solutions are available online, making it convenient for students to access anytime and anywhere.
  • Concept Reinforcement: GeeksforGeeks helps solidify fundamentals, preparing students for CBSE exams and beyond

CBSE Class 10 Maths Chapter-wise Marks Weightage for 2023-24

UnitUnit NameMarks
INumber Systems06
IIAlgebra20
IIICoordinate Geometry06
IVGeometry15
VTrigonometry12
VIMensuration10
VIIStatistics and Probability11
Total80
Internal Assessment20
Total100

 Internal Assessment Class 10 (2023 -2024)

Type of AssessmentMarks
Written Test and Diverse Evaluation (5+5)10 Marks
Portfolio05 Marks
Laboratory Practical (Engaging in lab activities from recommended resources)05 Marks
Total Score20 Marks

Also, check our Important Related Resources for CBSE Class 10 Maths:

These newly revised and updated NCERT textbook solutions for Class 10 Maths are suitable for students in both Hindi and English mediums. Therefore, Class X Maths Solutions give you a clear idea of the question patterns in your upcoming board exams, making them easier to solve. Through consistent practice with these free Class 10th Maths Solutions, you can achieve a good percentage in your 10th board exams.

FAQs on NCERT Solutions for Class 10 Maths

1. What are some important formulas from Class 10 Maths NCERT?

Here is the list of some important formulas covered in NCERT solutions from Algebra, trigonometry, and circles, for class 10 maths are given below:

Important Algebraic Formulas are-

  • (a + b)2 = a2 + b2 + 2ab
  • (a + b) (a-b) = a2 – b2
  • (a – b)2 = a2 + b2 – 2ab

Formulas of Arithmetic Progressions are-

  • nth term = a + (n-1) d
  • Sum upto nth term = n/2 [2a + (n – 1) d]

Important Trigonometric Formulas are-

  • sin2θ + cos2θ = 1
  • cosec2θ = 1 + cot2θ 
  • sec2θ = 1 + tan2θ 

Formulas for Circles are-

  • Circumference = 2πr
  • Area = πr2

2. Why it is important to study Class 10 maths Notes for CBSE Exams?

Making notes when studying the NCERT Solutions Class 10 Maths is usually a good idea because they serve as guides for pupils while revising the amounts. Furthermore, notes aid students in recalling topics involved in a problem at a glance. This cuts down on the amount of time it takes to go over an issue during an exam.

3. Why are NCERT Solutions for Class 10 Maths Important?

NCERT Solutions for Class 10 Math are essential since they allow students to double-check their responses to exercise problems. These NCERT answers for class 10 math are self-explanatory and give pupils a full overview of the procedures they must take to obtain the correct answer using the most effective way.

4. How to master in Class 10 Maths CBSE?

  • Practice regularly. The more you practice, the better you will become at solving math problems.
  • Make sure you understand the concepts. Don’t just memorize formulas and procedures. Take the time to understand why they work.
  • Get help when you need it. If you’re struggling with a particular concept, don’t be afraid to ask for help from your teacher, a tutor, or a friend.
  • Stay positive. Math can be challenging, but it’s also rewarding. Don’t give up if you don’t understand something right away. Keep practicing and you’ll eventually get it.

5. How do I solve Class 10 Mathematics problems easily?

  • Start by understanding the problem. Read the problem carefully and make sure you understand what it’s asking you to do.
  • Break the problem down into smaller steps. This will make it seem less daunting.
  • Work step-by-step. Don’t try to solve the problem all at once. Take it one step at a time.
  • Check your work. Once you’ve solved the problem, go back and check your work to make sure it’s correct.

6. Where can I download CBSE Class 10 NCERT Mathematics PDF Solutions?

You can download CBSE Class 10 NCERT Mathematics PDF Solutions from the our website and from official website as well of National Council of Educational Research and Training (NCERT).

7. How these NCERT Solutions for class 10 Maths will be beneficial for CBSE Students?

  • NCERT Solutions for class 10 Maths provide step-by-step solutions to all the problems in the NCERT textbooks.
  • These solutions are written in a clear and concise style, and they also include helpful hints and tips.
  • By working on these solutions, students can get an idea of how to solve the problems and grasp basic concepts better and faster.
  • They are also a perfect guide to help students score good marks in CBSE board examinations.

8. Which Textbook is enough for Class 10 Maths Boards Examination?

There are a number of good books available for Class 10 maths. Some of the most popular books include:

  • R.S. Aggarwal: This book is known for its comprehensive coverage of the syllabus. It also includes a large number of practice problems.
  • Titu’s Mathematics: This book is known for its challenging problems. It is a good choice for students who want to prepare for competitive exams.
  • S.L. Loney: This book is known for its clear and concise explanations. It is a good choice for students who want to understand the concepts behind the problems.

9. Is NCERT enough for Class 10 boards Maths 2023?

NCERT textbooks are a good starting point for Class 10 maths. However, if you want to score high marks in the board exams, you should also practice with other books and resources.

10. What are the best reference books for class 10 CBSE?

Some of the best reference books for class 10 CBSE include:

  • R.S. Aggarwal: This book is a good choice for students who want comprehensive coverage of the syllabus.
  • Titu’s Mathematics: This book is a good choice for students who want challenging problems.
  • S.L. Loney: This book is a good choice for students who want clear and concise explanations.
  • Mathematical Olympiads Questions: This book is a good choice for students who want to prepare for competitive exams.

11. How to get maximum marks in maths?

Here are some tips on how to get maximum marks in maths:

  • Start early. Don’t wait until the last minute to start studying for your maths exams.
  • Practice regularly. The more you practice, the better you will become at solving math problems.
  • Get help when you need it. If you’re struggling with a particular concept, don’t be afraid to ask for help from your teacher, a tutor, or a friend.
  • Stay positive. Math can be challenging, but it’s also rewarding. Don’t give up if you don’t understand something right away. Keep practicing and you’ll eventually get it.


12. How to solve the toughest Chapters In Class 10 Maths?

In the NCERT Textbook 2023-24, most chapters are easy to solve, even for average students. Some challenging chapters in Class 10 Maths include Circle, Triangles, Trigonometry, Application of trigonometry, and Surface area and volume. However, with dedicated practice, these chapters can become easier. Ensure you revise these tougher topics 3-4 times before the exam.

13. Are the standard of CBSE 10th Maths Papers little bit higher than the usual school papers?

The question papers in CBSE Board exams are designed to be suitable for all students. The pattern of the 10th Standard Board Examination is simple and easy to understand. Don’t be misled by unnecessary fears. If you practice the entire syllabus diligently, you can achieve excellent marks in the Class 10 Board Exam.



Last Updated : 28 Feb, 2024
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