NCERT Solutions For Class 10 Maths for all the exercises from Chapters 1 to 15 are provided here. These solutions are curated by our expert faculty to help students in their board exam preparations. Students looking for the answers for Class 10 Maths NCERT textual questions can download all chapter-wise pdf to find a better approach to solve the problems.
The answers to the questions present in the NCERT books are undoubtedly the best study material a student can get hold of. These CBSE NCERT Solutions will also help students to build a deeper understanding of concepts covered in Class 10 Maths textbook. Practising the textbook questions will help students 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.
The solution 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 lucid manner, maintaining 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 Exercises are given below.
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, 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, rational number and decimal expansion of rational numbers are explained with the help of theorem.
|NCERT Solutions for Class 10 Maths Chapter 1 Exercises|
|☛ Exercise 1.1 – 5 Questions (4 Long Answers, 1 Short Answer)
☛ Exercise 1.2 – 7 Questions (4 Long Answers, 3 Short Answers)
☛ Exercise 1.3 – 3 Questions (3 Short Answers)
☛ Exercise 1.4 – 3 Questions (3 Short Answers)
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 an 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, 2.4 consists of the questions from all the concepts of Chapter 2.
|NCERT Solutions for Class 10 Maths Chapter 2 Exercises|
|☛ Exercise 2.1 – 1 Question (1 Short Answer)
☛ Exercise 2.2 – 2 Questions (2 Short Answers)
☛ Exercise 2.3 – 5 Questions (2 Short Answers, 3 Long Answers)
☛ Exercise 2.4 – 5 Questions (2 Short Answers, 3 Long Answers)
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, Cross-Multiplication Method, 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.
|NCERT Solutions for Class 10 Maths Chapter 3 Exercises|
|☛ Exercise 3.1 – 3 Questions (2 Short Answers, 1 Long Answer)
☛ Exercise 3.2 – 7 Questions (5 Short Answers, 2 Long Answers)
☛ Exercise 3.3 – 3 Questions (2 Short Answers, 1 Long Answer)
☛ Exercise 3.4 – 2 Questions (2 Long Answers)
☛ Exercise 3.5 – 4 Questions (4 Short Answers)
☛ Exercise 3.6 – 2 Questions (2 Long Answers)
☛ Exercise 3.7 – 8 Questions (1 Short Answer, 7 Long Answers)
Chapter 4 – Quadratic Equations
In this chapter, students will get to know the standard form of writing a quadratic equation. The chapter goes on to 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 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 Solutions for Class 10 Maths Chapter 4 Exercises|
|☛ Exercise 4.1 – 2 Questions (1 Short Answer, 1 Long Answer)
☛ Exercise 4.2 – 6 Questions (6 Short Answers)
☛ Exercise 4.3 – 11 Questions (8 Short Answers, 3 Long Answers)
☛ Exercise 4.4 – 5 Questions (2 Short Answers, 3 Long Answer)
Chapter 5 – Arithmetic Progressions
This chapter introduces students to a new topic that is 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;
an = 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.
|NCERT Solutions for Class 10 Maths Chapter 5 Exercises|
|☛ Exercise 5.1 – 4 questions (1 Short Answer, 3 Long Answers)
☛ Exercise 5.2 – 20 questions (10 Short Answers, 10 Long Answers)
☛ Exercise 5.3 – 20 Questions (7 Short Answer, 13 Long Answers)
☛ Exercise 5.4 – 5 Questions (5 Long Answers)
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.
|NCERT Solutions for Class 10 Maths Chapter 6 Exercises|
|☛ Exercise 6.1 – 3 Questions (3 Short Answers)
☛ Exercise 6.2 – 10 Questions (9 Short Answers, 1 Long Answer)
☛ Exercise 6.3 – 16 Questions (12 Short Answers, 4 Long Answers)
☛ Exercise 6.4 – 9 Questions (7 Short Answers, 2 Long Answers)
☛ Exercise 6.5 – 17 Questions (15 Short Answers, 2 Long Answers)
☛ Exercise 6.6 – 10 Questions (5 Short Answers, 5 Long Answers)
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 purpose, students will get introduced to Distance Formula, Section Formula and Area of a Triangle in this chapter.
|NCERT Solutions for Class 10 Maths Chapter 7 Exercises|
|☛ Exercise 7.1 – 10 Questions (3 Short Answers, 7 Long Answer)
☛ Exercise 7.2 – 10 Questions (2 Short Answers, 8 Long Answer)
☛ Exercise 7.3 – 5 Questions (2 Short Answers, 3 Long Answer)
☛ Exercise 7.4 – 8 Questions (3 Short Answers, 5 Long Answer)
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 00 and 900. Further, students will also know how to calculate trigonometric ratios for some specific angles and establish some identities involving these ratios, called trigonometric identities.
|NCERT Solutions for Class 10 Maths Chapter 8 Exercises|
|☛ Exercise 8.1 – 11 Questions (8 Short Answers, 3 Long Answers)
☛ Exercise 8.2 – 4 Questions (2 Short Answers, 2 Long Answers)
☛ Exercise 8.3 – 7 Questions (5 Short Answers, 2 Long Answers)
☛ Exercise 8.4 – 5 Questions (3 Short Answers, 2 Long Answers)
Chapter 9 – Some Applications of Trigonometry
This chapter is the continuation of the previous chapter as here the students will study the applications 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.
|NCERT Solutions for Class 10 Maths Chapter 9 Exercises|
|☛ Exercise 9.1 – 16 Questions (16 Long Answers)|
Chapter 10 – Circles
In earlier classes, students have studied about a circle and various terms related to a circle such as 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.
|NCERT Solutions for Class 10 Maths Chapter 10 Exercises|
|☛ Exercise 10.1 – 4 Questions (2 Short Answer, 2 Long Answers)
☛ Exercise 10.2 – 13 Questions (2 Short Answers, 14 Long Answers)
Chapter 11 – Constructions
This chapter consists 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. Methods and steps for construction are explained and also some examples are additionally given to make it more clearer to the students.
|NCERT Solutions for Class 10 Maths Chapter 11 Exercises|
|☛ Exercise 11.1 – 7 Questions (7 Long Answers)
☛ Exercise 11.2 – 7 Questions (7 Long Answers)
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 clarity on finding the areas of some combinations of plane figures involving circles or their parts.
|NCERT Solutions for Class 10 Maths Chapter 12 Exercises|
|☛ Exercise 12.1 – 5 Questions (5 Short Answers)
☛ Exercise 12.2 – 14 Questions (9 Short Answers, 5 Long Answers)
☛ Exercise 12.3 – 16 Questions (9 Short Answers, 7 Long Answers)
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.
|NCERT Solutions for Class 10 Maths Chapter 13 Exercises|
|☛ Exercise 13.1 – 9 Questions (2 Short Answers, 7 Long Answers)
☛ Exercise 13.2 – 8 Questions (1 Short Answer, 7 Long Answers)
☛ Exercise 13.3 – 9 Questions (9 Long Answers)
☛ Exercise 13.4 – 5 Questions (5 Long Answers)
☛ Exercise 13.5 – 7 Questions (7 Long Answers)
Chapter 14 – Statistics
Here students will learn the numerical representation of ungrouped data to grouped data and finding the Mean, Mode and Median. Also, the concept of cumulative frequency, cumulative frequency distribution and how to draw cumulative frequency curves will be explained.
|NCERT Solutions for Class 10 Maths Chapter 14 Exercises|
|☛ Exercise 14.1 – 9 Questions (9 Long Answers)
☛ Exercise 14.2 – 6 Questions (6 Long Answers)
☛ Exercise 14.3 – 7 Questions (7 Long Answers)
☛ Exercise 14.4 – 3 Questions (3 Long Answers)
Chapter 15 – Probability
The last chapter deals with Probability. The chapter starts with the theoretical approach of probability. Subsequently, the chapter explains the difference between experimental probability and theoretical probability. There are various examples given to explain it in an effective way. So, before going through the exercise problems students must solve the examples of CBSE Maths first.
|NCERT Solutions for Class 10 Maths Chapter 15 Exercises|
|☛ Exercise 15.1 – 25 Questions (22 Short Answers, 3 Long Answers)
☛ Exercise 15.2 – 5 Questions (5 Short Answers)
Benefits of 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.
Students are advised to prepare all the chapters covered in the solution modules which will eventually help them to gain a deeper knowledge of concepts. For effective preparations, it is essential for students to understand all the steps provided in the solutions.
How are 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 Maths 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 BYJU’S website. The detailed answers for all the questions present in the NCERT textbook of Class 10 Maths are solved by subject experts at BYJU’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 website of NCERT. The NCERT provides various study materials like textbooks, syllabus and much more to help the students as well as teachers.
What is meant by a pair of linear equations in two variables?
An equation in the form of ax+by+c, where a,b and c are real numbers and a,b are not equal to zero, is called a linear equation in two variables. Whereas in pairs of linear equations in two variables, we deal with two such equations. The solution of such equations is a point on the line representing the equation. This topic is widely explained in Class 10 Maths Chapter 3. Find the solutions to the questions given in the NCERT textbook at BYJU’S.