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# NCERT Solutions Class 10 Maths `

Class 10 Maths syllabus aims at helping you to build a strong base of topics, the basic knowledge about them, making them understand theorems and concepts and testing them enough in the form of exercise and examples in the textbook. The exercises given in the NCERT textbook are designed for the students to use their skills and learnings of each topic to the maximum. Before each exercise, you are also given enough examples to refer to and understand the questions with the help of the step by step explanations provided in the textbooks.

## NCERT Class 10 Maths Chapters

Mentioned down below is NCERT class 10 chapters

• Chapter 1 Real Numbers

• Chapter 2 Polynomials

• Chapter 3 Pair of Linear Equations in Two Variables

• 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 Areas Related to Circles

• Chapter 12 Surface Areas and Volumes

• Chapter 13 Statistics

• Chapter 14 Probability

### NCERT Class 10 Maths Chapter 1 Real Numbers

In Chapter 1 Real Numbers of Class 10, you will explore real numbers and irrational numbers. The chapter begins 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

 Class 10 Maths NCERT  Chapter 1 Real Numbers Exercises NCERT Solutions Real Numbers Class 10 Exercise 1.1 – 5 Questions (4 Long Answers, 1 Short Answer) NCERT Solutions Real Numbers Class 10 Exercise 1.2 – 7 Questions (4 Long Answers, 3 Short Answers) NCERT Solutions Real Numbers Class 10 Exercise 1.3 – 3 Questions (3 Short Answers) NCERT Solutions Real Numbers Class 10 Exercise 1.4 – 3 Questions (3 Short Answers)

### NCERT Class 10 Maths Chapter 2 Polynomials

In chapter 2 Polynomials, it begins with the definition of the degree of the polynomial, linear polynomial, quadratic polynomial and cubic polynomial. This chapter has a total of 4 exercises, including miscellaneous exercise. Exercise 2 includes questions on finding the number of zeroes through a graph. It requires a basic understanding of the Geometrical Meaning of the Zeroes of a Polynomial. Exercise 2.2 is based on the Relationship between Zeroes and Coefficients of a Polynomial, where you 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 the division algorithm is defined, and you will find the questions related to this topic. The optional exercise, 2.4, contains the questions from all the concepts of Chapter 2.

 Class 10 Maths NCERT Chapter 2 Polynomials Exercises NCERT Solutions Polynomials Class 10 Exercise 2.1 – 1 Question (1 Short Answer) NCERT Solutions Polynomials Class 10 Exercise 2.2 – 2 Questions (2 Short Answers) NCERT Solutions Polynomials Class 10 Exercise 2.3 – 5 Questions (2 Short Answers, 3 Long Answers) NCERT Solutions Polynomials Class 10 Exercise 2.4 – 5 Questions (2 Short Answers, 3 Long Answers)

### NCERT Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

This chapter explains the concept of Pair of Linear Equations in Two Variables. This chapter consists of a total of 7 exercises, and in these exercises, different methods of solving the pair of linear equations are described. Exercise 3.1 explains how to represent a situation algebraically and graphically. Exercise 3.2 describes the methods of solving the pair of the linear equation along with the Graphical Method. Exercises 3.3, 3.4, 3.5 and 3.6 describe the Algebraic Method, Elimination Method, Cross-Multiplication Method, and Substitution Method, respectively. Exercise 3.7 is an optional exercise which contains all types of questions. You must practise these exercises to secure good marks in your board exams.

### NCERT Class 10 Maths Chapter 4 Quadratic Equations

In chapter 4 Quadratic Equations, you will get to know the standard form of writing a Quadratic Equation. The chapter goes on to describe the method of solving the quadratic equation through completing the square method and factorization method . It ends with the topic on finding the nature of roots, where you will get to know what is a quadratic equation ax² + bx + c = 0 has

Two distinct real roots, if b² – 4ac > 0

Two equal roots, if b² – 4ac = 0

No real roots, if b² – 4ac < 0

### NCERT Class 10 Maths Chapter 5 Arithmetic Progressions

In this chapter you will introduced to a new topic, Arithmetic Progression, i.e. AP. This chapter has a total of 4 exercises. In Exercise 5.1, the questions related to representing a situation in the form of AP, finding the first term and difference of an AP, and 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:

an = a + (n-1) d

The next exercise, which is 5.3, contains the questions on finding the sum of the first n terms of an AP. The last exercise contains miscellaneous questions which are high level questions based on AP to enhance your problem-solving skills and analytical.

 Class 10 NCERT Chapter 5 Arithmetic Progressions Exercises NCERT Solutions Class 10 Maths Arithmetic Progressions Exercise 5.1 – 4 questions (1 Short Answer, 3 Long Answers) NCERT Solutions Class 10 Maths Arithmetic Progressions Exercise 5.2 – 20 questions (10 Short Answers, 10 Long Answers) NCERT Solutions Class 10 Maths Arithmetic Progressions Exercise 5.3 – 20 Questions (7 Short Answers, 13 Long Answers) NCERT Solutions Class 10 Maths Arithmetic Progressions Exercise 5.4 – 5 Questions (5 Long Answers)

### NCERT Class 10 Maths Chapter 6 Triangles

In Chapter 6 of Class 10 Maths, you will learn about triangles, triangles with same shape but with different angles. This chapter starts with the concept of a similar and congruent figure. It will  explain the condition for the similarity and theorems  of two triangles and theorems related to the similarity of triangles. further, the areas of similar triangles have been explained with a theorem. At the end you will learn about the Pythagoras Theorem and the Converse of Pythagoras Theorem.

Important theorems that you should know thoroughly while preparing for the exam include:

Theorem 1: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Theorem 2: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Theorem 3: If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.

Theorem 4: If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.

Theorem 5: If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

### NCERT  Class 10 Maths Chapter 7 Coordinate Geometry

In chapter 7, you will learn how to find the distance between two points whose coordinates are already given, and to find the area of the triangle formed by three given points. Along with this, you will also know how to find the coordinates of the point which divides a line segment joining two given points in a given ratio.

 Class 10 Maths NCERT Chapter 7 Coordinate Geometry Exercises Coordinate Geometry Class 10 Exercise 7.1 – 10 Questions (3 Short Answers, 7 Long Answers) Coordinate Geometry Class 10 Exercise 7.2 – 10 Questions (2 Short Answers, 8 Long Answers) Coordinate Geometry Class 10 Exercise 7.3 – 5 Questions (2 Short Answers, 3 Long Answers) Coordinate Geometry Class 10 Exercise 7.4 – 8 Questions (3 Short Answers, 5 Long Answers)

## NCERT  Class 10 Maths Chapter 8 Introduction to Trigonometry

Trigonometry Introduced in chapter 8 to the student in NCERT textbook. You will study some ratios of a right triangle with respect to its acute angles called trigonometric ratios of the angles. Also, the trigonometric ratios for angles 0∘ and 90∘. You will also learn to calculate trigonometric ratios for the given angles and also a few trigonometric identities.

 Class 10 Maths NCERT Chapter 8 Exercises  Trigonometry Introduction to Trigonometry Class 10 Exercise 8.1 – 11 Questions (8 Short Answers, 3 Long Answers) Introduction to Trigonometry Class 10 Exercise 8.2 – 4 Questions (2 Short Answers, 2 Long Answers) Introduction to Trigonometry Class 10 Exercise 8.3 – 7 Questions (5 Short Answers, 2 Long Answers) Introduction to Trigonometry Class 10 Exercise 8.4 – 5 Questions (3 Short Answers, 2 Long Answers)

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

This chapter 9 is the continuation of the previous chapter; here, you will study the applications of trigonometry. It is used in so many ways such as: geography, navigation, construction of maps, and determining the position of an island in relation to the latitudes and  longitudes. In this chapter, we will see how trigonometry is used for finding the heights and distances of several objects without actually measuring them.

 Class 10 Maths NCERT Chapter 9 Some Applications of Trigonometry Exercise Some Applications of Trigonometry Class 10 Exercise 9.1 – 16 Questions (16 Long Answers)

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

In chapter 10, you will be introduced to the concept of tangents and the number of tangents from a point on a circle.

Important Theorems –

Theorem 1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Theorem 2: The lengths of tangents drawn from an external point to a circle are equal.

 Class 10 Maths NCERT Chapter 10 Circle Exercises Circles Class 10 Exercise 10.1 – 4 Questions (2 Short Answer, 2 Long Answers) Circles Class 10 Exercise 10.2 – 13 Questions (2 Short Answers, 14 Long Answers)

### NCERT Class 10 Maths Chapter 11 Areas Related to Circles

As per the name of the chapter, it is all about the perimeter and area of a circle. The concepts of finding the area of a sector and segment of a circle are discussed here. Further this chapter explains how to find the area of the figures that contains a circle or part of a circle.

 Class 10 Maths NCERT Chapter 11 Areas Related to Circles Exercises Areas Related to Circles Class 10 Exercise 11.1 – 5 Questions (5 Short Answers) Areas Related to Circles Class 10 Exercise 11.2 – 14 Questions (9 Short Answers, 5 Long Answers) Areas Related to Circles Class 10 Exercise 11.3 – 16 Questions (9 Short Answers, 7 Long Answers)

### NCERT Class 10 Maths Chapter 12 Surface Areas and Volumes

Chapter 13  is about the surface areas and volumes of different shapes and objects. There are a total of 5 exercises in this chapter. Find the surface area of any object which is 2 dimensions or 3 dimensional. The 3 dimensional shapes include cuboid, cone, sphere, hemisphere and cylinder. After that, there are questions on finding the volume of the objects that are made up of two different solid shapes. Also, in this chapter you will get questions on conversion from one shape to another. This chapter disccuss how to find the volume, curvd surface area and total surface area of a frustum of a cone.

 Class 10 Maths Surface Areas and Volumes NCERT Chapter 12 Exercises Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 12.1 – 9 Questions (2 Short Answers, 7 Long Answers) Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 12.2 – 8 Questions (1 Short Answer, 7 Long Answers) Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 12.3 – 9 Questions (9 Long Answers) Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 12.4 – 5 Questions (5 Long Answers) Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 12.5 – 7 Questions (7 Long Answers)

### NCERT Solutions for Class 10 Maths Chapter 13 Statistics

In this chapter 13, you will learn the numerical representation of ungrouped data to grouped data and you will get to know how to find the Mean, Mode and Median. Also, the concept of cumulative frequency, cumulative frequency distribution and how to draw cumulative frequency curves will be clarified.

 Class 10 Maths NCERT Chapter 13 Statistics Exercises NCERT Solutions of Maths Class 10 Statistics Exercise 14.1 – 9 Questions (9 Long Answers) NCERT Solutions of Maths Class 10 Statistics Exercise 14.2 – 6 Questions (6 Long Answers) NCERT Solutions of Maths Class 10 Statistics Exercise 14.3 – 7 Questions (7 Long Answers) NCERT Solutions of Maths Class 10 Statistics Exercise 14.4 – 3 Questions (3 Long Answers)

### NCERT Class 10 Maths Chapter 14 Probability

This is the last chapter of class 10 NCERT Maths which deals with Probability. This chapter starts with the theoretical approach of probability. Later, the chapter explains the difference between experimental probability and theoretical probability. There are several examples given to explain it in an effective way. So, before going through the exercise problems, you must solve the examples of  this book first

 Class 10 Maths NCERT  Chapter 14  Probability Exercises NCERT Solutions of Maths Class 10 Probability Exercise 15.1 – 25 Questions (22 Short Answers, 3 Long Answers) NCERT Solutions of Maths Class 10 Probability Exercise 15.2 – 5 Questions (5 Short Answers)

## Benefits of NCERT Solutions Class 10 Maths

The Class 10 NCERT Solutions of Maths provided on our page in PDFs formate, have several benefits, which include:

• The solutions are easily understandable.

• Solutions are provided for each chapter in steps for better understanding.

• Diagrams are given to help you to understand the solutions better.

• Each questions are from each chapter are covered.

### FAQs

Question 1: How many chapters are in NCERT Math class 10?

Answer: There are a total 15 questions in NCERT Math class 10. Following are the list mentioned

• Chapter 1 Real Numbers

• Chapter 2 Polynomials

• Chapter 3 Pair of Linear Equations in Two Variables

• 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 Areas Related to Circles

• Chapter 12 Surface Areas and Volumes

• Chapter 13 Statistics

• Chapter 14 Probability

Question 2: What is Quadratic Equation?