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NCERT Solutions for Class 10 Maths

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NCERT Solutions for Class 10 Maths provides a comprehensive and step-by-step explanation of every 10th-grade NCERT question. Students can utilize these answers to assist them to go on if they encounter a stumbling block when solving a problem. This Class 9 NCERT solution covers all the chapters in the NCERT book like Real Numbers, Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions, and many more with solutions for all the relevant exercises.

NCERT Solutions for Class 10 Maths

These NCERT Solutions for Class 9 are written by a team of subject matter experts in maths who are professionals in their industry. The 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.

Class 10 Maths Solutions : Chapters List (1 to 15)

The below table contains the NCERT solutions chapter-wise(1 to 15) list for Class 10 Maths:-

NCERT Solution for Class 10 Maths Chapters List

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

NCERT Solutions for Class 10 Maths 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.

Class 10 Maths NCERT Solutions Chapter 1 Exercises:

More resources for Class 10 Maths Chapter 1 Real Numbers

NCERT Solutions for Class 10 Maths 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 and 10 are difficult-to-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.

Class 10 Maths NCERT Solutions Chapter 2 Exercises:

More resources for Class 10 Maths Chapter 2 Polynomials

NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables

This NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables 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.

Class 10 Maths NCERT Solutions Chapter 3 Exercises

More resources for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

NCERT Solutions for Class 10 Maths Chapter 4 – Quadratic Equations

This NCERT Solutions for Class 10 Maths Chapter 4 – Quadratic Equations 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 deal with the problems of the determination of roots using the method of completing the square and its application.

Class 10 Maths NCERT Solutions Chapter 4 Exercises

More resources for Class 10 Maths Chapter 4 Quadratic Equations

NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions

This NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions deals with the concepts of the Arithmetic Progression (AP), the 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.

Class 10 Maths NCERT Solutions Chapter 5 Exercises

More resources for Class 10 Maths Chapter 5 Arithmetic Progression(AP)

NCERT Solutions for Class 10 Maths 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 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 them. Further, Exercises 6.5 and 6.6 emphasize on congruence of triangles and their application.

Class 10 Maths NCERT Solutions Chapter 6 Exercises

More resources for Class 10 Maths Chapter 6 Triangles

NCERT Solutions for Class 10 Maths Chapter 7 – Coordinate Geometry

This NCERT Solutions for Class 10 Maths Chapter 7 – Coordinate Geometry 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.

Class 10 Maths NCERT Solutions Chapter 7 Exercises

More resources for Class 10 Maths Chapter 7 Coordinate Geometry

NCERT Solutions for Class 10 Maths Chapter 8 – Introduction to Trigonometry

The NCERT Solutions for Class 10 Maths Chapter 8 – 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. 

Class 10 Maths NCERT Solutions Chapter 8 Exercises

More resources for Class 10 Maths Chapter 8 Introduction to Trigonometry

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

This NCERT Solutions for Class 10 Maths Chapter 9 – Some Applications of Trigonometry 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.

Class 10 Maths NCERT Solutions Chapter 9 Exercises

  • NCERT Maths Solutions Class 10 Exercise 9.1 Set 1, Set 2 – 16 Questions (16 Long Answers)

More resources for Class 10 Maths Chapter 9 Some Application of Trigonometry

NCERT Solutions for Class 10 Maths Chapter 10 – Circles

This NCERT Solutions for Class 10 Maths Chapter 10 – Circles deals with the concept of the tangent of a circle. The topic discusses the brief introduction of the circle, the tangent to a circle, and the 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 the 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.

Class 10 Maths NCERT Solutions Chapter 10 Exercises

More resources for Class 10 Maths Chapter 10 Circles

NCERT Solutions for Class 10 Maths Chapter 11 – Constructions

In NCERT Solutions for Class 10 Maths 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 Segments in the Given Ratio. While, the second exercise, Exercise 11.2 includes problems based on the constructions of Tangents to a Circle.

Class 10 Maths NCERT Solutions Chapter 11 Exercises

More resources for Class 10 Maths Chapter 11 Constructions

NCERT Solutions for Class 10 Maths Chapter 12 – Areas Related to Circles

NCERT Solutions for Class 10 Maths Chapter 12 – Areas Related to Circles 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.

Class 10 Maths NCERT Solutions Chapter 12 Exercises

More resources for Class 10 Maths Chapter 12 Areas Related to Circles

NCERT Solutions for Class 10 Maths 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 level 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 deal 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.

Class 10 Maths NCERT Solutions Chapter 13 Exercises

More resources for Class 10 Maths Chapter 13 Surface Areas and Volumes

NCERT Solutions for Class 10 Maths Chapter 14 – Statistics

In NCERT Solutions for Class 10 Maths 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.

Class 10 Maths NCERT Solutions Chapter 14 Exercises

More resources for Class 10 Maths Chapter 14 Statistics

NCERT Solutions for Class 10 Maths Chapter 15 – Probability

The last chapter NCERT Solutions for Class 10 Maths Chapter 15 – Probability 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.

Class 10 Maths NCERT Solutions Chapter 15 Exercises

More resources for Class 10 Maths Chapter 15 Probability

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

FAQs on NCERT Solutions for Class 10 Maths

Q1: 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 = a2 + b2 + 2ab
  • (a + b) (a-b) = a2 – b2
  • (a – b)2 = a2 + b2 – 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-

  • sin2θ + cos2θ = 1
  • cosec2θ = 1 + cot2θ 
  • sec2θ = 1 + tan2θ 

Formulas for Circles are-

  • Circumference = 2πr
  • Area = πr2

Q2: 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.

Q3: 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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Last Updated : 15 May, 2023
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