## NCERT Solutions forÂ Class 10 Maths Chapterwise – Free PDF Download

**NCERT Solutions For Class 10 Maths** chapters 1 to 15 are provided here. These solutions are curated by our expert faculties to help students in their board exam preparations. The students looking for the answers for Class 10 Maths NCERT questions can download all chapter-wise pdf to find a better approach to solve them.

The solutions to the problems present in the NCERT books are undoubtedly the best study material a student can get hold of. These NCERT SolutionsÂ will also help students to have a deeper understanding of concepts covered in Class 10 Maths textbook. PractisingÂ the textbook questions will help the students to analyze their level of preparation and the understanding of concepts. The solutions to these questions present in the textbooks can help students to clear their doubts easily. Check out the chapter-wise **NCERT Maths Solutions for Class 10** PDFs in English medium from the links provided below:

- Chapter 1 Real Numbers
- Chapter 2 Polynomials
- Chapter 3 Pair of Linear Equations in Two Variables
- Chapter 4 Quadratic Equations
- Chapter 5 Arithmetic Progressions
- Chapter 6 Triangles
- Chapter 7 Coordinate Geometry
- Chapter 8 Introduction to Trigonometry
- Chapter 9 Some Applications of Trigonometry
- Chapter 10 Circles
- Chapter 11 Constructions
- Chapter 12 Areas Related to Circles
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability

The solution list comprises of all the chapter-wise answers to the questions present in the **NCERT Book for Class 10 Maths** written in a very clear and lucid manner, keeping in the objective of textbooks. The students can refer to the NCERT Solutions for Class 10 as their additional references and study materials. Practising textbook exercises will surely help the students in their preparation for the examination.

### NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

In chapter 1 of class 10, students will explore real numbers and irrational numbers. 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, 0â‰¤r<b”. TheÂ 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, rational number and decimal expansion of rational number is explained with the help of theorem.

Chapter 1 Exercises |
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â˜žExercise 1.1 – 5 Questions (4 Long Answers, 1 Short Answer)
â˜žExercise 1.2 – 7 Questions (4 Long Answers, 3 Short Answers) â˜žExercise 1.3 – 3 Questions (3 Short Answers) â˜žExercise 1.4 – 3 Questions (3 Short Answers) |

### NCERT Solutions for Class 10 MathsÂ Chapter 2 Polynomials

In Polynomials, the chapter begins with the definition of degree of the polynomial, linear polynomial, quadratic polynomial and cubic polynomial. This chapter has a total of 4 exercises including the optional exercise. Exercise 2.1 includes the questions on finding the number of zeroes through a graph. It requires the understanding of Geometrical Meaning of the Zeroes of a Polynomial. Exercise 2.2 is based on the Relationship between Zeroes and Coefficients of a Polynomial where students have to find the zeros of a quadratic polynomial and in some of the questions they have to find the quadratic polynomial. In exercise 2.3, the concept of division algorithm is defined and students will find the questions related to it. The optional exercise i.2 2.4 consists of the questions from all the concepts of chapter 2.

Chapter 2 Exercises |
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â˜žExercise 2.1 – 1 Question (1 Short Answer)
â˜žExercise 2.2 – 2 Questions (2 Short Answers) â˜žExercise 2.3 – 5 Questions (2 Short Answers, 3 Long Answers) â˜žExercise 2.4 – 5 Questions (2 Short Answers, 3 Long Answers) |

### NCERT Solutions for Class 10 MathsÂ Chapter 3 Pair of Linear Equations in Two Variables

This chapter explains the concept of Pair of Linear Equations in Two Variables. This chapter has a total of 7 exercises and in these exercises, different methods of solving the pair of linear equations are described. Exercise 3.1 describes how to represent a situation algebraically and graphically. The exercise 3.2 explains the methods of solving the pair of the linear equation through Graphical Method. Exercise 3.3, 3.4, 3.5, 3.6 describes the Algebraic Method, Elimination Method,Â Cross-Multiplication Method,Â Substitution Method respectively. Exercise 3.7 is an optional exercise which contains all types of questions. Students must practice these exercises to master the method of solving the linear equations.

Chapter 3 Exercises |
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â˜žExercise 3.1 – 3 Questions (2 Short Answers, 1 Long Answer)
â˜žExercise 3.2 – 7 Questions (5 Short Answers, 2 Long Answers) â˜žExercise 3.3 – 3 Questions (2 Short Answers, 1 Long Answer) â˜žExercise 3.4 – 2 Questions (2 Long Answers) â˜žExercise 3.5 – 4 Questions (4 Short Answers) â˜žExercise 3.6 – 2 Questions (2 Long Answers) â˜žExercise 3.7 – 8 Questions (1 Short Answer, 7 Long Answers) |

### NCERT Solutions for Class 10 MathsÂ Chapter 4 Quadratic Equations

In this chapter, students will get to know the standard form of writing a quadratic equation. Then this chapter will explain the method of solving the quadratic equation through the factorization method and completing the square method. The chapter ends with the topic on finding the nature of roots which states that, a quadratic equation axÂ² + bx + c = 0 has

- Two distinct real roots, if bÂ² – 4ac > 0
- Two equal roots, if bÂ² – 4ac = 0
- No real roots, ifÂ bÂ² – 4ac < 0

Chapter 4 Exercises |
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â˜žExercise 4.1 – 2 Questions (1 Short Answer, 1 Long Answer)
â˜žExercise 4.2 – 6 Questions (6 Short Answers) â˜žExercise 4.3 – 11 Questions (8 Short Answers, 3 Long Answers) â˜žExercise 4.4 – 5 Questions (2 Short Answers, 3 Long Answer) |

### NCERT Solutions for Class 10 MathsÂ Chapter 5 Arithmetic Progressions

This chapter introduces students to a new topic that isÂ Arithmetic Progression i.e AP. This chapter constitutes a total of 4 exercises. In exercise 5.1, students will find the questions related to representing a situation in the form of AP, finding the first term and difference of an AP, finding out whether a series is AP or not. Exercise 5.2 includes the questions on finding out the nth term of an AP by using the following formula;

a_{nÂ }= a + (n-1) d

The next exercise i.e 5.3, contains the questions on finding the sum of first n terms of an AP. The last exercise includes higher-level questions based on AP to enhance students analytical and power solving skills.

Chapter 5 Exercises |
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â˜žExercise 5.1 – 4 questions (1 MCQ and 3 Long Answers)
â˜žExercise 5.2 – 20 questions (1 fill in the blanks, 2 MCQâ€™s, 7 Short Answers, 10 Long Answers) â˜žExercise 5.3 – 20 Questions (3 fill in the blanks, 4 daily life examples, and 13 Long Answers) â˜žExercise 5.4 – 5 Questions (5 Long Answers) |

### NCERT Solutions for Class 10 MathsÂ Chapter 6 Triangles

In chapter 6 of class 10 CBSE maths, students will study those figures which have the same shape but not necessarily the same size. The chapter starts with the concept of a similar and congruent figure. It further explains the condition for the similarity of two triangles and theorems related to the similarity of triangles. After that, the areas of similar triangles have been explained with a theorem. At the end of this chapter, the Pythagoras Theorem and converse of Pythagoras Theorem is described.

Chapter 6 Exercises |
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â˜žExercise 6.1 – 3 Questions (3 Short Answers)
â˜žExercise 6.2 – 10 Questions (9 Short Answers, 1 Long Answer) â˜žExercise 6.3 – 16 Questions (12 Short Answers, 4 Long Answers) â˜žExercise 6.4 – 9 Questions (7 Short Answers, 2 Long Answers) â˜žExercise 6.5 – 17 Questions (15 Short Answers, 2 Long Answers) â˜žExercise 6.6 – 10 Questions (5 Short Answers, 5 Long Answers) |

### NCERT Solutions for Class 10 MathsÂ Chapter 7 Coordinate Geometry

In this chapter, students will learn how to find the distance between two points whose coordinates are given, and to find the area of the triangle formed by three given points. Along with this students will also study how to find the coordinates of the point which divides a line segment joining two given points in a given ratio. For this students will get introduced to Distance Formula, Section Formula and Area of a Triangle in this chapter.

Chapter 7 Exercises |
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â˜žExercise 7.1 – 10 Questions (3 Short Answers, 7 Long Answer)
â˜žExercise 7.2 – 10 Questions (2 Short Answers, 8 Long Answer) â˜žExercise 7.3 – 5 Questions (2 Short Answers, 3 Long Answer) â˜žExercise 7.4 – 8 Questions (3 Short Answers, 5 Long Answer) |

### NCERT Solutions for Class 10 MathsÂ Chapter 8 Introduction to Trigonometry

This chapter will introduce students to Trigonometry. They will study some ratios of a right triangle with respect to its acute angles, called trigonometric ratios of the angles. The chapter also defines the trigonometric ratios for angles of 0^{0} and 90^{0}. Further, students will also know how to calculate trigonometric ratios for some specific angles and establish some identities involving these ratios, called trigonometric identities.

Chapter 8 Exercises |
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â˜žExercise 8.1 – 11 Questions (8 Short Answers, 3 Long Answers)
â˜žExercise 8.2 – 4 Questions (2 Short Answers, 2 Long Answers) â˜žExercise 8.3 – 7 Questions (5 Short Answers, 2 Long Answers) â˜žExercise 8.4 – 5 Questions (2 Short Answers, 2 Long Answers, 1 MCQ) |

### NCERT Solutions for Class 10 MathsÂ Chapter 9 Some Applications of Trigonometry

This chapter is the continuation of the previous chapter as here the student will study the application of trigonometry. It is used in geography, navigation, construction of maps, determining the position of an island in relation to the longitudes and latitudes. In this chapter, students will see how trigonometry is used for finding the heights and distances of various objects, without actually measuring them. They will get introduced to the term line of sight, angle of elevation, angle of depression.

Chapter 9 Exercise |
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â˜žExercise 9.1 – 16 Questions (16 Long Answers) |

### NCERT Solutions for Class 10 MathsÂ Chapter 10 Circles

In earlier classes, students have studied about a circle and various terms related to a circle like a chord, segment, arc etc. In this chapter, students will study the different situations that arise when a circle and a line are given in a plane. So, they will get through with the concept of Tangent to a Circle and Number of Tangents from a Point on a Circle.

Chapter 10 Exercises |
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â˜žExercise 10.1 – 4 Questions (1 Short Answer, 1 fill in the blanks, 2 Long Answers)
â˜žExercise 10.2 – 13 Questions (2 Short Answers, 14 Long Answers) |

### NCERT Solutions for Class 10 MathsÂ Chapter 11 Constructions

In this chapter consist of a total of 2 exercises. Whatever students have learned about construction in earlier classes will also help them. In exercise 11.1, students will study how to divide a line segment. Whereas in exercise 11.2 they will study the construction of tangents to a circle. Method and steps for construction are explained and also some example are given to make it more clear to the students.

Chapter 11 Exercises |
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â˜žExercise 11.1 – 7 Questions (7 Long Answers)
â˜žExercise 11.2 – 7 Questions (7 Long Answers) |

### NCERT Solutions for Class 10 MathsÂ Chapter 12 Areas Related to Circles

This chapter begins with the concepts of perimeter and area of a circle. Using this concept the chapter further explains, how to find the area of sector and segment of a circular region. Moreover, students will get to know how to find the areas of some combinations of plane figures involving circles or their parts.

Chapter 12 Exercises |
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â˜žExercise 12.1 – 5 Questions (5 Short Answers)
â˜žExercise 12.2 – 14 Questions (9 Short Answers, 5 Long Answers) â˜žExercise 12.3 – 16 Questions (9 Short Answers, 7 Long Answers) |

### NCERT Solutions for Class 10 MathsÂ Chapter 13 Surface Areas and Volumes

In chapter 13, there are a total of 5 exercises. The first exercise consists of the questions based on finding the surface area of an object formed by combining any two of the basic solids i.e cuboid, cone, cylinder, sphere and hemisphere. In exercise, 13.2 questions are based on finding the volume of objects formed by combining any two of a cuboid, cone, cylinder, sphere and hemisphere. The exercise 13.3 deals with the questions in which solid is converted from one shape to another. The exercise 13.4 is based on finding the volume, curved surface area and total surface area of a frustum of a cone. The last exercise is optional and has high-level questions based on all the topics of this chapter.

Chapter 13 Exercises |
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â˜žExercise 13.1 – 9 Questions (2 Short Answers, 7 Long Answers)
â˜žExercise 13.2 – 8 Questions (1 Short Answer, 7 Long Answers) â˜žExercise 13.3 – 9 Questions (9 Long Answers) â˜žExercise 13.4 – 5 Questions (5 Long Answers) â˜žExercise 13.5 – 7 Questions (7 Long Answers) |

### NCERT Solutions for Class 10 MathsÂ Chapter 14 Statistics

Here students will learn the numerical representation of ungrouped data to grouped data and finding theÂ Mean, Mode and Median. Also, the concept of cumulative frequency, cumulative frequency distribution and how to draw cumulative frequency curves will be explained.

Chapter 14 Exercises |
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â˜žExercise 14.1 – 9 Questions (9 Long Answers)
â˜žExercise 14.2 – 6 Questions (6 Long Answers) â˜žExercise 14.3 – 7 Questions (7 Long Answers) â˜žExercise 14.4 – 3 Questions (3 Long Answers) |

### NCERT Solutions for Class 10 MathsÂ Chapter 15 Probability

The last chapter deals with the probability. The chapter starts with the theoretical approach of probability. Then the chapter explains the difference betweenÂ experimental probability and theoretical probability. There are various examples given to explain it in a better way. So, before going through the exercise problems students must solve the examples of CBSE Maths first.

Chapter 15 Exercises |
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â˜žExercise 15.1 – 25 Questions (22 Short Answers, 3 Long Answers)
â˜žExercise 15.2 – 5 Questions (5 Short Answers) |

### Benefits ofÂ NCERT Solutions Class 10 Maths:

The class 10 NCERT maths solutions given here in PDFs have several benefits like:

- The solutions given here are very easy to understand.
- Solutions are provided in steps for better understanding.
- Diagrams are given to help the students in visualizing the solutions.
- All the questions from each chapter are covered.

The students are advised to prepare all the chapters covered in the solution modules which will eventually help them to have a deeper knowledge of concepts. For effective preparations, it is important for students to understand all the steps provided in the solutions.

### How CBSE 10 Maths Solutions of NCERT Helpful for Board Exams?

CBSE Class 10 Maths is an important subject for students. Here we have provided complete assistance to students for its preparation. Class 10 is the first benchmark for any student that will reflect in the future records of achievement. CBSE always prescribes the NCERT books for board exam preparation.

Exam preparation is a rigorous process that requires an overall understanding of individual chapters. This process demands hard work towards studies and an effective approach to getting through the solutions. This significant role is played by class 10 NCERT solutions to equip students in the preparation of competitive entrance exams. NCERT books are best known for putting forth the concepts in a simple way for better understanding. NCERT Class 10 books for mathematics are written in the most lucid and clear manner that helps to break the complex problems in the most efficient way.

Keep visiting to get complete chapter-wise solutions in PDF for all the classes. Students can even download BYJU’S App to get a personalized learning experience and prepare for the exams more effectively.

## Frequently Asked Questions on NCERT Solution for Class 10 Maths

### Where to download NCERT Solutions for Class 10 Maths?

The NCERT Solutions for Class 10 Maths can be referred to online as well as downloaded from the BYJUâ€™S website. The detailed answers for all the questions present in the NCERT textbook of Class 10 Maths are solved by subject experts at BYJUâ€™S as per the NCERT guidelines.

### How many chapters are present in NCERT Class 10 Maths?

A total of 15 chapters are present in the NCERT Class 10 Maths. Chapter 1-Real Numbers, Chapter 2-Polynomials, Chapter 3-Pair of Linear Equations in Two Variables, Chapter 4-Quadratic Equations, Chapter 5-Arithmetic Progressions, Chapter 6-Triangles, Chapter 7-Coordinate Geometry, Chapter 8-Introduction to Trigonometry, Chapter 9-Some Applications of Trigonometry, Chapter 10-Circles, Chapter 11-Constructions, Chapter 12-Areas Related to Circles, Chapter 13-Surface Areas and Volumes, Chapter 14-Statistics, Chapter 15-Probability are the chapters in Class 10 Maths NCERT.

### Which is the best resource for Class 10 board exam preparation?

NCERT books are undoubtedly the best resource for CBSE board exam preparation. But then again, simply mugging up the concepts given in the NCERT books a few weeks before the exams will help the students with nothing. Students should be thorough with the NCERT Solutions well ahead of the board exam, giving them ample time to practice more questions from other reference books such as RS Aggarwal, RD Sharma etc. Students can now move ahead and solve the sample papers as well as previous year question papers to get an idea of the question paper pattern.

### Which is the official website for NCERT?

http://ncert.nic.in/ is the official webise of NCERT. The NCERT provides various study materials like textbooks, syllabus and much more to help the students as well as teachers.