# NCERT Solutions for Class 10 Maths (Updated 2023-24) - Download PDF

## Related Materials

 NCERT Syllabus For Class 10 Mathematics NCERT Books For Class 10 Mathematics NCERT Notes For Class 10 Mathematics NCERT Exemplar Solutions For Class 10 Mathematics

## NCERT solutions for class 10 maths - chapter wise

Here students can find class 10 maths all chapter name and NCERT solutions. Prcatice these class 10th maths ncert solutions to commad and indepth understanding of the concepts.

 Chapter No. Chapter Name 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

How to use maths ncert solutions class 10 ?

• Go to the chapter that you wish to check.
• Click on the link given for that particular chapter of class 10 maths.
• The chapter page with solutions of NCERT class 10 maths will open.
• Check the questions and solutions given in the NCERT class 10 maths.

Chapter 1 Real Numbers: In class 10 maths NCERT solutions Chapter 1, you are going to learn about Euclid’s Division Lemma and this concept is used to find the HCF, LCM, the relation between HCF and LCM and the fundamental theorem of arithmetic. Euclid’s Division Lemma will also be required if you want to prove that the given number is rational or irrational and the given rational number is terminating or non terminating repeating. There are many real-life examples of LCM and HCF mentioned in the NCERT class 10 maths solutions. There are a total of 4 exercises with a total of 48 questions in this chapter. Students can fine these exercises as well as ncert maths solutions class 10 in this page.

Real Numbers Class 10 Maths NCERT Book Chapter 1 Topics

• Euclid's division algorithm
• Prime factorization
• Highest common factor
• Prime factorization
• Prime & composite numbers
• Rational & irrational numbers

## NCERT Solutions For Class 10 Maths Chapter 1 Exercises

• Class 10 Maths Chapter 1 Real Numbers Exercise 1.1
• Class 10 Maths Chapter 1 Real Numbers Exercise 1.2
• Class 10 Maths Chapter 1 Real Numbers Exercise 1.3
• Class 10 Maths Chapter 1 Real Numbers Exercise 1.4

Chapter 2 Polynomials: The NCERT 10 maths solution Chapter 2 starts with an explanation of polynomials referring to the previous classes and then explains the geometrical interpretation of the zeroes of the polynomial. Then it gives the relation between zeroes and the coefficient of a given polynomial and also explains how to carry out the polynomial divisions. You have to be good in class 9 maths chapter polynomial to beat this one. In NCERT solutions class 10 maths chapter 2 polynomials, step by step explanation is given in the answers of all 4 exercises including the optional exercise.

Polynomials Class 10 Maths NCERT Book Chapter 2 Topics

• The degree of a polynomial
• Number of zeroes in a quadratic polynomial
• The sum & product of quadratic polynomial
• Division algorithm
• The number of zeroes in a cubic polynomial

## NCERT Solutions For Class 10 Maths Chapter 2 Exercises

• Polynomials Class 10 Exercise 2.1
• Polynomials Class 10 Exercise 2.2
• Polynomials Class 10 Exercise 2.3
• Polynomials Class 10 Exercise 2.4

Chapter 3 Pair of Linear Equations in Two Variables: There are many real-life examples that can be formulated in linear equations in two variables. Let's take an example to understand: If a person buys some pens and pencils at a total of 41 Rs and the price of a pen and a pencil are 5 Rs and 4 Rs respectively. Then the statement can be represented as Many such problems are mentioned in the class 10 NCERT maths solutions. The NCERT maths class 10 solution Chapter 3 covers various algebraic methods to solve a given pair of linear equations and a geometrical way of solving the pair of linear equations.

Pair Of Linear Equations In Two Variables Class 10 Maths Chapter 3 Topics

• Solving a linear equation with two variables.
• Representation of linear equation in a graph.
• Solutions of linear equations using the graph.
• Algebraic interpretation of linear equations.
• Formation of linear equations using statements.

## NCERT Solutions For Class 10 Maths Chapter 3 Exercises

• Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.1
• Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.2
• Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.3
• Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.4
• Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.5
• Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.6
• Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.7

Chapter 4 Quadratic Equations: We get a quadratic equation if a quadratic polynomial is equated to zero with the condition that the coefficient of the variable with power two is not equal to zero. The main content of the NCERT class 10 maths solutions Chapter 4 includes the various methods of solving the quadratic equations and how to determine the consistency of quadratic equations from the value of discriminants. Every year around 8 to 10 marks questions come from this chapter only. In solutions of NCERT for class 10 maths chapter 4 quadratic equation, all the 4 exercises consisting of 46 questions are covered.

Quadratic Equations Class 10 Maths Chapter 4 Topics

• Representation of situation in a quadratic equation.
• Checking if an equation is quadratic or not.
• Solving a quadratic equation using factorization/ roots of quadratic solutions.
• The solution of the quadratic equation using completing the square method.
• Solving a quadratic equation using the Sridharacharya formula.
• Product of roots in a quadratic equation.
• Sum of roots in a quadratic equation.

## NCERT Solutions For Class 10 Maths Chapter 4 Exercises

• NCERT Class 10 Maths Chapter 4 Exercise 4.1
• NCERT Class 10 Maths Chapter 4 Exercise 4.2
• NCERT Class 10 Maths Chapter 4 Exercise 4.3
• NCERT Class 10 Maths Chapter 4 Exercise 4.4

Chapter 5 Arithmetic Progressions: Any number series having the same difference between two immediate terms is called arithmetic progression. For example- 2, 5, 8, 11 is an arithmetic progression as the difference everywhere is 3. Every year around questions of 8 to 10 marks come from this chapter only. In this particular chapter, you will learn to solve questions related to nth /last term and questions related to the sum of an arithmetic progression. Also, some questions are based on the usage of both the concepts together. There are some real-life situations mentioned in the NCERT maths class 10 solutions. Studying a chapter by correlating to real-life examples will be interesting. In NCERT solutions class 10 maths chapter 5 arithmetic progression, we are covering all the 4 exercises including an optional exercise.

## NCERT Solutions For Class 10 Maths Chapter 5 Exercises

• Class 10 Maths Chapter 5 Exercise 5.1
• Class 10 Maths Chapter 5 Exercise 5.2
• Class 10 Maths Chapter 5 Exercise 5.3
• Class 10 Maths Chapter 5 Exercise 5.4

Chapter 6 Triangles: A closed shape made using three straight lines is known as geometry. The NCERT Class 10 Chapter 6 starts with an explanation of the difference between the congruent figures and similar figures. In this particular chapter, we will learn the similarity of triangles, criteria for similarity, area of triangles and understanding of Pythagoras theorem using the similarity of triangles. There are many interesting examples that can be solved using the similarity of triangles. In the solutions of this particular chapter, you will get solutions to all the 6 exercises including optional exercise consisting of 90 questions. All of the exercise including ex 6.3 class 10 are listed below.

Triangles Class 10 Maths Chapter 6 - Topics

• Similarity of triangles
• Theorems based on similar triangles
• Areas of similar triangles
• Theorems related to Trapezium
• Pythagoras theorem

## NCERT Solutions For Class 10 Maths Chapter 6 Exercises

• Triangles Class 10 Exercise 6.1
• Triangles Class 10 Exercise 6.2
• Triangles Class 10 Exercise 6.3
• Triangles Class 10 Exercise 6.4
• Triangles Class 10 Exercise 6.5
• Triangles Class 10 Exercise 6.6

Chapter 7 Coordinate Geometry: This is one of the NCERT maths class 10 solutions chapters which you will use in almost all the areas your higher studies, whether it is science, commerce or arts. In class 10 maths, this chapter holds some specific kind of concepts and questions and if you do them well, then the things will become easy for you in the examination. The NCERT solutions for class 10 maths chapter 7 coordinate geometry include the distance formulae, section formulae and the concept of finding the area of triangles if the coordinate of the vertex is given. The NCERT solutions for Class 10 Maths Chapter 7 to all the 4 exercises including an optional exercise consisting total of 45 questions are explained in a step by step manner. Students can practice these exercise i.e. exercise 7.1 class 10 and exercise 7.2 class 10 which all are listed below.

## NCERT Solutions For Class 10 Maths Chapter 7 Exercises

• Coordinate Geometry Class 10 Exercise 7.1
• Coordinate Geometry Class 10 Exercise 7.2
• Coordinate Geometry Class 10 Exercise 7.3
• Coordinate Geometry Class 10 Exercise 7.4

Chapter 8 Introduction to Trigonometry: The chapter has originated from the right angle triangle. The properties, formulas, and ratios of trigonometry can be derived using length, breadth, and height of the right-angle triangle. In this chapter, there are a total of 4 exercises and questions of these exercises are mainly based on finding trigonometric ratios of the sides of a right-angled triangle. The class 10 NCERT maths solutions of this chapter cover important concepts to find trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles and trigonometric identities.

## NCERT Solutions For Class 10 Maths Chapter 8 Exercises

• Trigonometry Class 10 Exercise-8.1
• Trigonometry Class 10 Exercise-8.2
• Trigonometry Class 10 Exercise-8.3
• Trigonometry Class 10 Exercise-8.4

Chapter 9 Some Applications of Trigonometry: This chapter is just an extension of the concepts used in chapter 8. This is the application based chapter which tells us the usage of trigonometry in real life. "Trigonometry" unit holds 12 marks out of 80 marks in the CBSE final maths paper and we can expect one question of 3 or 4 marks from this chapter. In maths NCERT solutions class 10 Chapter 9, we will learn how trigonometry is helpful in finding the distance and height of different objects without actually measuring them. This chapter has only 1 exercise for which answers are there in solutions of NCERT for class 10 maths chapter 9 some applications of trigonometry. students can practice all exercise including exercise 9.1 class 10 to get deeper knowledge of the concepts.

Chapter 10 Circles: A circle is nothing but a closed figure with a collection of points in a plane that are at a specific distance (radius) from a fixed point (center). This chapter is an important part of geometry along with triangles. This chapter in class 10 maths is an extension of class 9 maths chapter circles. In this chapter, we will discuss tangent to a circle and number of tangents from a point on the circle. The chapter holds good weightage in the board examinations. Every year approximately 10 to 12 marks questions come from this chapter only. The solution of NCERT class 10 maths covers all 2 exercises consisting of overall 26 questions.

## NCERT Solutions For Class 10 Maths Chapter 10 Exercises

• Circles Class 10 Exercise-10.1
• Circles Class 10 Exercise-10.2

Chapter 11 Constructions: The NCERT solutions for Class 10 Maths Chapter 11, deals with the problem constructions. It is also known as a geometrical drawing which deals with constructing geometric figures using some specific geometric tools. It is a part of the geometry unit and geometry holds 15 marks in the final CBSE exams and construction is a scoring topic for students. In this chapter, there is a total of 2 exercises with 14 questions. In the first exercise, we will learn how to divide a line segment and in the second exercise, we will learn the construction of tangents to a circle.

## NCERT Solutions For Class 10 Maths Chapter 11 Exercises

• Constructions Class 10 NCERT Exercise 11.1
• Constructions Class 10 NCERT Exercise 11.2

Chapter 12 Areas Related to Circles: In this maths ncert solutions class 10 chapter, we will deal with areas related to circles. This chapter is a part of the Mensuration unit, which holds 10 marks in the CBSE Class 10 final exam. In this chapter, there are 3 exercises with 35 questions in them. In this chapter, we will learn the perimeter and area of a circle, areas of sector and segment of a circle, areas of combinations of plane figures. In NCERT solutions for class 10 maths chapter 12 areas related to circles, detailed solutions to each question are given.

Circles Class 10 NCERT Topics

• Tangent to a Circle
• Radius and Tangent Relation
• Tangent From External Point to the Circle

## NCERT Solutions For Class 10 Maths Chapter 12 Exercises

• Area Related to Circle Exercise 12.1
• Area Related to Circle Exercise 12.2
• Area Related to Circle Exercise 12.3

Chapter 13 Surface Areas and Volumes: This comes under mensuration. We have already done some part of the mensuration in the class 9 maths. In NCERT solutions for Class 10 Maths Chapter 13, we will discuss how to find surface areas and volumes of combinations, which are formed by two or more than two of the basic solids such as cone, cuboid, cylinder, sphere, and hemisphere. Apart from all these shapes, a new shape frustum will be introduced here in this particular chapter. In this chapter, there are a total of 5 exercises with 38 questions in them. In all the exercises, we will deal with questions on finding surface areas and volumes of solids.

## NCERT Solutions For Class 10 Maths Chapter 13 Exercises

• Surface Areas and Volumes Exercise 13.1 Solutions
• Surface Areas and Volumes Exercise 13.2 Solutions
• Surface Areas and Volumes Exercise 13.3 Solutions
• Surface Areas and Volumes Exercise 13.4 Solutions
• Surface Areas and Volumes Exercise 13.5 Solutions

Chapter 14 Statistics: In the previous class, we have learned about data representation and have solved many calculations based questions on that. Statistics is also somehow related to data handling. In NCERT solutions for Class 10 Maths Chapter 14, the questions will be based on data and we will discuss how to find the measures of central tendency namely, mean, mode and median from the ungrouped data to that of grouped data. In this chapter, there are a total of 4 exercises with 25 questions. In NCERT Class 10 Maths Chapter 14 Statistics, you will also get to know about the concept of cumulative frequency, its distribution and how to draw cumulative frequency curves. Students can practice exercise such as exercise 14.1 class 10 that are listed below to get in-depth understanding of concepts.

## NCERT Solutions For Class 10 Maths Chapter 14 Exercises

• Statistics Exercise 14.1
• Statistics Exercise 14.2
• Statistics Exercise 14.3
• Statistics Exercise 14.4

Chapter 15 Probability: Probability is one of the newest concepts you will learn here in class 10 mathematics. In the previous class, you have learned about empirical probabilities or experimental probabilities of events that are based on the results of actual experiments. In this NCERT class 10 maths, we will discuss the theoretical probability (also called classical probability) of an event, and solve simple questions based on this concept. In NCERT solutions for class 10 maths chapter 15 probability, solutions of 2 exercises including optional exercise consisting of overall 68 questions are covered.

## NCERT Solutions For Class 10 Maths Chapter 15 Exercises

• Probability Class 10 Ex 15.1
• Probability Class 10 Ex 15.2

## How NCERT Solutions for Class 10 Will be Beneficial for You?

• NCERT solutions class 10 maths will help you in the completion of homework as well as for better scores in the board examinations.
• Using these solutions you can observe and learn the steps to solve some typical kind of questions.
• The class 10 NCERT maths solutions will help you in creating a strong base of mathematics and will help to face competitive examinations in the future.
• Along with maths, you can also learn the NCERT solution for class 10 science.

#### Also Check NCERT Books and NCERT Syllabus here

• NCERT Books Class 10 Maths
• NCERT Syllabus Class 10 Maths
• NCERT Books Class 10
• NCERT Syllabus Class 10