# NCERT Solutions for Class 10 Maths

All ready to appear for your board exam?? Terrifying isn’t it? We understand how tough it gets when you think about the very class that can turn your life in a different direction. Especially when there’s hardly anyone out there to help with the class 10 maths solutions. Here GeeksforGeeks come to save your day. Our NCERT Solutions for Class 10 Maths provided by GeeksforGeeks contains the solutions to the problems described in 15 chapters provided in the NCERT textbook. The solutions help students to build a deeper understanding of the concepts like Polynomials, Linear equations in two variables, Triangles, Circles, etc.

NCERT solutions for class 10 maths provide a comprehensive and step-by-step explanation to every CBSE 10th grade NCERT question. Students can utilize these answers to assist them to go on if they encounter a stumbling block when completing a sum. These NCERT answers for class 10 mathematics are written by a team of subject matter experts in maths who are professionals in their industry. The maths solutions are given in such a way that students not only acquire the answer to a single issue but also have a thorough knowledge of the topic employed in that question.

GeeksforGeeks also covered** **1500+ Most asked Questions of Mathematics, Chapterwise Important Formulas, and many more based on the new Class 10th CBSE curriculum. Students can use these notes and other study materials to help students prepare for their Final Exams.

## Chapter 1: Real Numbers

The chapter covers **NCERT Solutions for class 10 maths chapter 1 – ****Real numbers** which vastly explains the concept of properties of real numbers using Euclid’s Lemma, Fundamental Theorem of Arithmetic.

The first chapter of Class 10 maths has a total of 18 questions, 10 of which are simple, 5 moderate, and 3 of which are lengthy answer-type problems. The problems in Exercises 1.1 and 1.2 are needed to find out the divisibility of integers using Euclid’s division algorithm and the factorization of composite numbers using the fundamental theorem of arithmetic. However, Exercise 1.3 and 1.4 includes the question to prove the roots of any irrational number and decimal expansions of rational numbers.

**NCERT Solutions for Class 10 Maths of Chapter 1 are here:**

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

**More resources for CBSE Class 10 Maths Chapter 1**

## Chapter 2: Polynomials

This chapter covers **NCERT Solutions for class 10 maths chapter 2 ****polynomials** which includes the advanced terminology related to polynomials such as the degree, coefficient, and zeroes of any kind of polynomial. The chapter includes four exercises.

Class 10 Maths NCERT Solutions of Chapter 2 consists of a total of 13 questions, of which 6 are basic questions, 3 are moderate and10 are difficult type questions. Exercises 2.1 and 2.2 consist of problems that need to determine the number of zeroes through a graph and the relation between zeroes and coefficients of a polynomial. While Exercise 2.3 is based on the topic of division algorithm and Exercise 2.4 covers all the topics of the respective chapter.

**NCERT Solutions for Class 10 Maths of Chapter 2 are here:**

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

**More resources for CBSE Class 10 Maths Chapter 2**

## Chapter 3: Pair of Linear Equations in Two Variables

This chapter** ****Pair of Linear Equations in Two Variables** in the 10th NCERT maths solution deals with the concept determination of the solutions of pair of any linear equations in two variables graphically and algebraically. There is a total of seven exercises in the chapter.

Exercises 3.1 and 3.2 contain problems that need to represent the provided form of equations graphically or algebraically. The problems in Exercises 3.3 and 3.4 are to be solved using the substitution and elimination methods. Rest exercises 3.5, 3.6, and 3.7 include the questions from the applications of the linear pair of any linear equations in two variables.

**NCERT Solutions for Class 10 Maths of Chapter 3 are here:**

- NCERT Maths Solutions Class 10 Exercise 3.1 – 3 Questions (2 Short Answers, 1 Long Answer)
- NCERT Maths Solutions Class 10 Exercise 3.2 – 7 Questions (5 Short Answers, 2 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 3.3 – 3 Questions (2 Short Answers, 1 Long Answer)
- NCERT Maths Solutions Class 10 Exercise 3.4 – 2 Questions (2 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 3.5 – 4 Questions (4 Short Answers)
- NCERT Maths Solutions Class 10 Exercise 3.6 – 2 Questions (2 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 3.7 – 8 Questions (1 Short Answer, 7 Long Answers)

**More resources for CBSE Class 10 Maths Chapter 3**

## Chapter 4: Quadratic Equations

The chapter **Quadratic equations** are associated to determine the roots of quadratic equations and change the world problem into quadratic equations itself. NCERT solutions for class 10 maths chapter 4 have four exercises, that consist of 24 well-structured questions. They further comprise 10 easy-level problems, 6 mid-level problems, and 8 difficult-type questions.

Exercises 4.1 and 4.2 are based on the basic idea of quadratic equations and the construction of the equation from the problem statement. Further, Exercises 4.3 and 4.4 deals with the problems of the determination of roots using the method of completing the square and its application.

**NCERT Solutions for Class 10 Maths of Chapter 4 are here:**

- NCERT Maths Solutions Class 10 Exercise 4.1 – 2 Questions (1 Short Answer, 1 Long Answer)
- NCERT Maths Solutions Class 10 Exercise 4.2 – 6 Questions (6 Short Answers)
- NCERT Maths Solutions Class 10 Exercise 4.3 – 11 Questions (8 Short Answers, 3 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 4.4 – 5 Questions (2 Short Answers, 3 Long Answers)

**More resources for CBSE Class 10 Maths Chapter 4**

## Chapter 5: Arithmetic Progressions

This chapter deal with the concepts of the **Arithmetic Progression (AP)**, determination of the nth term of a series, the sum of the first n terms of a series, and applications of AP in everyday life. The chapter primarily consists of four exercises, exercises 5.1 and 5.2 deal with the basic introduction to the AP while exercises 5.3 and 5.4 comprise the problem that needs to determine the sum of the first term n terms of an AP and its applications.

**NCERT Solutions for Class 10 Maths of Chapter 5 are here:**

- NCERT Maths Solutions Class 10 Exercise 5.1 – 4 questions (1 Short Answer, 3 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 5.2 – 20 questions (10 Short Answers, 10 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 5.3 Set 1, Set 2 – 20 Questions (7 Short Answers, 13 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 5.4 – 5 Questions (5 Long Answers)

**More resources for CBSE Class 10 Maths Chapter 5**

## Chapter 6: Triangles

The chapter covers **NCERT Solutions for class 10 maths Chapter 6 – ****Triangles** in this class which gives detailed knowledge about the triangles with the concept of similarity and congruence of triangles, and theorems related to them. This chapter covers concepts primarily in six exercises.

There are a total of 65 questions in Class 10 Maths Chapter 6 NCERT Solutions. These comprise of 30 difficult questions, 25 medium, and 10 easy problems. Exercise 6.1 covers the basics of triangles. However, exercises 6.2, 6.3, and 6.4 contain problems on the topic of the similarity of triangles and theorems related to it. Further, Exercises 6.5 and 6.6 emphasize on congruence of triangles and their application.

**NCERT Solutions for Class 10 Maths of Chapter 6 are here:**

- NCERT Maths Solutions Class 10 Exercise 6.1 – 3 Questions (3 Short Answers)
- NCERT Maths Solutions Class 10 Exercise 6.2 – 10 Questions (9 Short Answers, 1 Long Answer)
- NCERT Maths Solutions Class 10 Exercise 6.3 Set 1, Set 2 – 16 Questions (12 Short Answers, 4 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 6.4 – 9 Questions (7 Short Answers, 2 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 6.5 Set 1, Set 2 – 17 Questions (15 Short Answers, 2 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 6.6 – 10 Questions (5 Short Answers, 5 Long Answers)

**More resources for CBSE Class 10 Maths Chapter 6**

## Chapter 7: Coordinate Geometry

As the name of the chapter suggests, the **Coordinate geometry**, therefore this chapter deals with the problems in the coordinate system such as determining the distance between any two points in the system, coordination of the point of a line divided into two halves, section formula, and areas of the triangle.

NCERT Solutions of Chapter 7 coordinate geometry includes a total of 33 questions out of which 15 are of a medium level, 10 are easy and 8 are difficult problems. Exercise 7.1 are from the introduction of the chapter and the distance while exercises 7.2, 7.3, and 7.4 are from the section formula and its practical application.

**NCERT Solutions for Class 10 Maths of Chapter 7 are here:**

- NCERT Maths Solutions Class 10 Exercise 7.1 – 10 Questions (3 Short Answers, 7 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 7.2 – 10 Questions (2 Short Answers, 8 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 7.3 – 5 Questions (2 Short Answers, 3 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 7.4 – 8 Questions (3 Short Answers, 5 Long Answers)

**More resources for CBSE Class 10 Maths Chapter 7**

## Chapter 8: Introduction to Trigonometry

The chapter **Introduction to Trigonometry** studies the ratio of the right angles with the acute angles of any right-angled triangle. The problems from this chapter are based on the trigonometric ratios of specific angles, trigonometric identities, and trigonometric ratios of complementary angles.

Exercise 8.1 is based on the introduction of the trigonometric ratio and their calculation with the help of Pythagoras theorem; Exercise 8.2 is based on the calculation of some specific angles like 0 degrees, 30 degrees, 45 degrees, and 90 degrees and the use of the trigonometric table; Exercise 8.3 is based on the concept of complementary angles and Exercise 8.4 is based on the concept of trigonometric identities.

**NCERT Solutions for Class 10 Maths of Chapter 8 are here:**

- NCERT Maths Solutions Class 10 Exercise 8.1 – 11 Questions (8 Short Answers, 3 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 8.2 – 4 Questions (2 Short Answers, 2 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 8.3 – 7 Questions (5 Short Answers, 2 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 8.4 – 5 Questions (3 Short Answers, 2 Long Answers)

**More resources for CBSE Class 10 Maths Chapter 8**

- CBSE Class 10 Maths Notes Chapter 8
Class 10 RD Sharma Solutions Introduction to TrigonometryChapter 1andChapter 2All important formulas for Chapter 8

## Chapter 9: Some Applications of Trigonometry

This chapter deals with the study of the practical **application of trigonometry** in real life. The topic discusses the line of sight, angle of deviation, angle of elevation, and angle of depression. The exercise in this chapter is based on the introduction of the application of trigonometry to calculate the heights and distances of various objects without actually measuring them.

There are 16 questions in Chapter 9 that deal with various problems that happen in everyday life. 7 of the questions are simple, 5 are difficult, and 4 are of medium difficulty. The chapter explains how to apply trigonometry to real-life examples in order to calculate the height and distance between two objects that are far apart.

**NCERT Solutions for Class 10 Maths of Chapter 9 are here:**

**More resources for CBSE Class 10 Maths Chapter 9**

## Chapter 10: Circles

This chapter deals with the concept of the **tangent of a circle**. The topic discusses the brief introduction of the circle, tangent to a circle, and a number of tangents from a point on a circle. There are 17 questions in class 10 maths chapter 10 out of which 4 are of an intermediate level, 3 are easy and 10 are difficult problems that challenge a student’s conceptual understanding.

Exercise 10.1 is based on the introduction of the circle and calculation of tangents to a circle and Exercise 10.2 is based on the calculation of the number of tangents from a point on a circle.

**NCERT Solutions for Class 10 Maths of Chapter 10 are here:**

- NCERT Maths Solutions Class 10 Exercise 10.1 – 4 Questions (2 Short Answers, 2 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 10.2 – 16 Questions (2 Short Answers, 14 Long Answers)

**More resources for CBSE Class 10 Maths Chapter 10**

**Chapter 11: Constructions**

In chapter 11 **Constructions**, Students will learn how to construct various figures using tools such as a compass and ruler. They learn how to divide a line segment into the necessary ratio and use various strategies to generate a tangent to a circle. There are two exercises in NCERT Solutions for Class 10 Maths of Chapter 11.

Chapter 11 contains 14 problems, eight of which test a student’s critical thinking, three of which are easy, and three of which are in the intermediate level sums. Exercise 11.1 consists of problems based on the Division of Line Segment in Given Ratio. While, the second exercise, Exercise 11.2 includes problems based on the constructions of Tangents to a Circle.

**NCERT Solutions for Class 10 Maths of Chapter 11 are here: **

- NCERT Maths Solutions Class 10 Exercise 11.1 – 7 Questions (7 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 11.2 – 7 Questions (7 Long Answers)

**More resources for CBSE Class 10 Maths Chapter 11**

## Chapter 12: Areas Related to Circles

**Circles** are some of the commonly found shapes in our surroundings. By merging lines and other shapes within circles, students will learn how to measure the areas of different segments using theorems and the number Pi.

The chapter Areas Related to Circles from Class 10, deals with determining the area and circumference of a circle using the standard formulas. It also includes questions on finding the area of composite figures, along with the area enclosed within a sector, and a segment.

**NCERT Solutions for Class 10 Maths of Chapter 12 are here:**

- NCERT Maths Solutions Class 10 Exercise 12.1 – 5 Questions (5 Short Answers)
- NCERT Maths Solutions Class 10 Exercise 12.2 Set 1, Set 2 – 14 Questions (9 Short Answers, 5 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 12.3 Set 1, Set 2 – 16 Questions (9 Short Answers, 7 Long Answers)

**More resources for CBSE Class 10 Maths Chapter 12**

## Chapter 13: Surface Areas and Volumes

NCERT solutions for class 10 maths chapter 13 **Surface areas and volumes** deal with the TSA (total surface area), LSA/CSA (lateral or curved surface area), and volume of various composite figures. The questions also need you to transfer a solid shape from one form to another and make assumptions.

In **NCERT Solutions of Class 10 Chapter 13**, there is a total of five exercises. These exercises consist of 38 well-structured problems from easy to difficult levels questions. Thus these problems will help students to learn the formulas and concepts of Surface Area and Volume. The first two exercises, which are Exercise 13.1 and 13.2 deals with the problems based on the basics of Surface Areas and Volumes. However, further exercises deal with concepts of cylinder and cone, Conversion of solids, and practical applications of Volumes of a combination of solids.

**NCERT Solutions for Class 10 Maths of Chapter 13 are here:**

- NCERT Maths Solutions Class 10 Exercise 13.1 – 9 Questions (2 Short Answers, 7 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 13.2 – 8 Questions (1 Short Answer, 7 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 13.3 – 9 Questions (9 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 13.4 – 5 Questions (5 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 13.5 – 7 Questions (7 Long Answers)

**More resources for CBSE Class 10 Maths Chapter 13**

**Chapter 14: Statistics**

In** Class 10 Mathematics NCERT solutions chapter 14 ****Statistics **students will learn how to apply statistical concepts such as mean, mode, standard deviation, and the graphical representation of cumulative frequency distribution. There are a total of four exercises in Class 10 Maths NCERT.

**NCERT Solutions for Class 10 Maths of Chapter 14 **have a total of 28 questions. Of which 5 are easy, 15 are intermediate, and 8 are difficult questions that test a student’s calculating speed and accuracy.

**NCERT Solutions for Class 10 Maths of Chapter 14 are here:**

- NCERT Maths Solutions Class 10 Exercise 14.1 – 9 Questions (9 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 14.2 – 6 Questions (6 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 14.3 – 7 Questions (7 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 14.4 – 3 Questions (3 Long Answers)

**More resources for CBSE Class 10 Maths Chapter 14**

**Chapter 15: Probability**

The last chapter deals with **Probability**. The chapter starts with the theoretical approach to probability. Subsequently, the chapter explains the difference between experimental probability and theoretical probability. There are only two exercises in this chapter that covers the various problems to explain them effectively.

The probability of an event happening, elementary event concepts, and the complement of events are the topics covered under NCERT solutions for class 10 maths chapter 15. The chapter has a total of 30 questions. 7 can be easily solved by using the given formula, 10 are of intermediate level, and 13 require careful concentration as they are of a higher level.

**NCERT Solutions for Class 10 Maths of Chapter 15 are here:**

- NCERT Maths Solutions Class 10 Exercise 15.1 Set 1, Set 2 – 25 Questions (22 Short Answers, 3 Long Answers)
- NCERT Maths Solutions Class 10 Exercise 15.2 – 5 Questions (5 Short Answers)

**More resources for CBSE Class 10 Maths Chapter 15**

**Important Resources for CBSE Class 10th provided by GeeksforGeeks:-**

**CBSE Class 10 Maths Notes****RD Sharma Solutions Maths Class 10****CBSE Class 10 Maths Formulas****CBSE Physics Class 10 Notes****CBSE Class 8 Chemistry Notes**

## Frequently Asked Questions (FAQs)

**Question 1: What are some important formulas from Class 10 Maths NCERT?**

**Answer:**

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}= a^{2}+ b^{2}+ 2ab- (a + b) (a-b) = a
^{2}– b^{2}- (a – b)
^{2}= a^{2}+ b^{2}– 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-

- sin
^{2}θ + cos^{2}θ = 1- cosec
^{2}θ = 1 + cot^{2}θ- sec
^{2}θ = 1 + tan^{2}θ

Formulas for Circles are-

- Circumference = 2πr
- Area = πr
^{2}

**Question 2: Why it is important to study Class 10 maths Notes for CBSE Exams?**

**Answer:**

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.

**Question 3: Why are NCERT Solutions for Class 10 Maths Important?**

**Answer:**

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.

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