 # Ncert Solutions For Class 10 Maths

Here are the NCERT Solutions for Class 10 Maths for all exercises from Chapters 1 to 15. These NCERT solutions have been prepared by our expert faculty to help the students in their board exam preparation. Students looking for NCERT Solutions for Class 10 Maths can download all chapter-wise PDF to find a better approach to solve the problems.

Answers to questions present in NCERT books are undoubtedly the best study material that a student can get hold of. These CBSE NCERT Solutions for Class 10 Maths 2021 will also help students to build a deeper understanding of the concepts covered in the Class 10 Maths textbook. Practicing the questions from the textbook will help the students to analyze their level of preparation and knowledge of the concepts. The NCERT solutions of these questions present in the books can help the students to clear their doubts quickly.

### Class 10 Maths Solutions PDf Updated for 2021 Session

The Class 10 Maths Ncert book Contain 15 Chapters. Just click on the chapter-wise links given below to practice the NCERT Solutions for the respective chapter. #### Class 10 Maths Solutions Chapter Details and Exercises

All the chapter-wise answers to the questions present in NCERT Book for Class 10 Maths are written in a very precise and clear manner, keeping the objective of textbooks in the solution list. Students can refer to the NCERT Solutions for Class 10 as their additional reference and study material. Practicing textbook exercises will definitely help the students to prepare for the exam.

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 1

In Chapter 1 of Class 10, students will explore real numbers and irrational numbers. The chapter begins with Euclid’s division lemma which states that “Given positive integers a and b, there exist unique integers q and r that satisfy a = bq + r, 0≤r<b”. 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.

Topic Covered in this Chapter:

Euclid’s Division Lemma, Fundamental Theorem of Arithmetic – After reviewing the work done earlier followed by illustration and inspiration through statements and examples, proofs of irrationality of 2, 3, 5, terminating/reference to non-recurring recurring decimals Decimal representation of rational numbers in.

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

In polynomials, the chapter begins with the definitions of degrees of polynomials, linear polynomials, quadratic polynomials, and cubic polynomials. There are total 4 exercises in this chapter including one optional exercise. Exercise 2.1 includes questions on finding the number of zeros through a graph. This requires an understanding of the geometric meaning of the zeroes of a polynomial.

Chapter 2 Polynomials

Exercise 2.2 is based on the relation between zeroes and coefficients of a polynomial where students have to find the zeroes of a quadratic polynomial and in some questions they have to find the quadratic polynomial. In Exercise 2.3, the concept of division algorithm is defined and students will find questions related to it. Optional Exercises, 2.4 contains questions from all the concepts of Chapter 2.

Topic Covered In This Chapter:

Zeroes of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statements and simple problems on division algorithms for polynomials with real coefficients.

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

This chapter explains the concept of a pair of linear equations in two variables. There are total 7 exercises in this chapter and in these exercises various methods of solving a pair of linear equations have been described. Exercise 3.1 describes how to represent a situation algebraically and graphically. Exercise 3.2 explains the methods of solving a pair of linear equations by the graphical method.

Chapter 3 Pair of Linear Equations in Two Variables

Exercises 3.3, 3.4, 3.5 and 3.6 describe the algebraic method, elimination method, cross-multiplication method, substitution method respectively. Exercise 3.7 is an optional exercise consisting of all types of questions. Students should practice these exercises to master the method of solving linear equations.

Topics Covered In This Chapter:

Pair of Linear Equations in Two Variables and Graphical Method of their Solution, Consistency/Anomaly. Algebraic conditions for the number of solutions. Solve a pair of linear equations in two variables algebraically – by substitution, by deletion and by the method of cross multiplication. Simple situational problems. Simple problems on reducing linear equations to reducible equations.

NCERT Solutions for Class 10 Math Chapter 4 Quadratic Equations

In this lesson, students will learn the standard form of writing a quadratic equation. In this chapter, the method of solving quadratic equation through factorization method and completing the square method has been explained. The chapter ends with the topic of finding out the nature of roots, which states that the quadratic equation ax² + bx + c = 0.

Two different real roots, if b² – 4ac > 0
Two equal roots, if b² – 4ac = 0
There is no real root, if b² – 4ac < 0

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progression Progress

This chapter introduces the students to a new topic which is Arithmetic Progression, i.e. AP. There are total 4 exercises in the chapter. In Exercise 5.1, students will get questions related to representing a situation in the form of an AP, finding the first term and difference of an AP, finding whether a series is an AP or not. Exercise 5.2 consists of questions to find the nth term of an AP using the following formula;

a = a + (n – 1) d

The next exercise, i.e., 5.3, consists of questions on finding the sum of the first n terms of an AP. The final exercise includes high-level questions based on AP to enhance the analytical and problem-solving skills of the students.

NCERT Solutions for Class 10 Maths Chapter 6 Triangles

In Chapter 6 of Class 10 CBSE Maths, students will study figures that have the same shape but not necessarily the same size. The chapter begins with the concept of a similar and congruent figure. It further explains the condition of the theorems relating to the similarity of two triangles and the similarity of triangles. After that the areas of similar triangles are explained by a theorem.

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

In this lesson, students will learn how to find the distance between two points whose coordinates are given and find the area of a triangle formed by three given points. Along with this, students will also study how to find the coordinates of the point which bisects the line segment joining two given points in a given ratio. For this purpose, students will be introduced to the distance formula, segment formula, and area of a triangle in this chapter.

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

This chapter will introduce students to trigonometry. They will study some ratios with respect to acute angles of a right triangle, called trigonometric ratios of angles. The chapter also defines trigonometric ratios for angles 00 and 900. In addition, students will also learn how to calculate trigonometric ratios for certain angles and establish certain identities involving these ratios, called trigonometric identities.

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

This chapter is a continuation of the previous chapter as here students will study the applications of trigonometry. It is used in geography, navigation, making maps, determining the position of an island with respect to longitude and latitude. In this lesson, students will see how trigonometry is used to find the height and distance of various objects without actually measuring them. They will be introduced to the line of sight, angle of elevation, angle of depression.

NCERT Solutions for Class 10 Maths Chapter 10 Circles

In previous classes, students have studied about a circle and various terms related to a circle like a chord, segment, arc, etc. In this chapter, students will study the various situations that arise when a circle and a line are given together. Airplane. Hence, they will be fully familiar with the concept of tangents to a circle and the number of tangents to a point on a circle.

NCERT Solutions for Class 10 Maths Chapter 11 Constructions

There are total 2 exercises in this chapter. What students have learned about construction in previous classes will also help them. In Exercise 11.1, students will study how to divide a line segment, while in Exercise 11.2 they will study the construction of tangents to a circle. The methods and steps of construction are explained and some examples are also given to make it clear to the students.

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

This chapter begins with the concepts of circumference and area of a circle. Using this concept, the chapter further explains how to find the sector and the area of the segment of a circular region. In addition, students will gain clarity in finding the areas of some combinations of plane figures containing circles or their parts.

NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes

There are total 5 exercises in Chapter 13. The first exercise consists of questions based on finding the surface area of an object formed by mixing any two 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 cuboid, cone, cylinder, sphere, and hemispheres. Exercise 13.3 deals with questions in which a solid is changed from one shape to another.

Question 13.4 is based on finding the volume, curved surface area, and total surface area of the frustum of a cone. The last exercise is optional and contains high-level questions based on all the topics of this chapter.

NCERT Solutions for Class 10 Maths Chapter 14 Statistics

Here, students will learn numerical representation of ungrouped data and find the mean, mode and median for grouped data. Also, the concept of cumulative frequency, cumulative frequency distribution and how to draw a cumulative frequency curve will be explained.

NCERT Solutions for Class 10 Maths Chapter 15 Probability

The last chapter deals with probability. The chapter begins with a theoretical approach to probability. Next, the chapter explains the difference between experimental probability and theoretical probability. Various examples are given to explain it effectively. Therefore, before going through the practice problems students must first solve the CBSE Maths examples.

#### CBSE Class 10 Maths Exam Pattern 2020-2021

The Central Board of Secondary Education conducts the CBSE Class 10 Maths exam for a total of 100 marks, where 80 marks are allotted for theory paper and 20 marks for internal assessment. By going through the CBSE Maths Exam Pattern 2020-2021 for Class 10, students can understand how marks are awarded for every answer step by step. Every year the board releases the sample paper and marking scheme before the board exam so that the students can be well aware of the exam pattern and question paper design.

The students who are appearing in the exam have to go through the marking scheme 2020-2021. As per the revised pattern of CBSE, 25% questions from theory paper are objective type questions. While the number of questions has increased, marks per question have been reduced, maximum number of questions have been converted to objective type or very few answer type. Here, you can find the CBSE Class 10 Maths Exam Pattern.

 CBSE Class 10 Maths (Basic and Standard Paper) Marking Scheme Sections No. of Questions Marks per Question Total Marks Section A 20 Questions 1 Mark 20 Section B 6 Questions 2 Marks 12 Section C 8 Questions 3 Marks 24 Section D 6 Questions 4 Marks 24 Total 40 Questions 80

#### Frequently Asked Questions on NCERT Solutions for Class 10 Maths

• How to understand the important concepts covered in NCERT Solutions for Class 10 Maths?

Students who aspire to get good marks in class 10 exam are advised to download NCERT solutions from Utopper. The solutions are designed with utmost care by a group of faculty having vast experience in the concerned subject. Each minute detail is explained in an interactive manner to make it easy for the students during learning. Step wise solutions have been prepared keeping in mind the allotted marks as per CBSE guidelines.

• Will NCERT Solutions for Class 10 Maths help me to solve problems easily?

Class 10 exams are one of the turning points in the life of students. Mathematics is the subject which mainly consists of numerical and understanding of concepts which helps to score more marks. Students are advised to understand the syllabus of the first academic year and learn the concepts based on them for better performance. Solving textbook problems by citing solutions will improve logical thinking and analytical skills in students.

• Where do I get NCERT Solutions for Class 10 Maths PDF?

Students can get NCERT Solutions for Class 10 Maths PDF at Utopper. The solutions are prepared by subject experts keeping in mind the comprehension ability of the students. The main objective of creating solutions is to help students learn complex concepts without any difficulty. Students can also cross-check their answers while solving textbook problems to get an idea about other ways to answer questions efficiently.

• Are NCERT Solutions for Class 10 Maths Useful for Students Under CBSE Board?

Some of the uses of NCERT Solutions for Class 10 Maths are given below –
1. It builds a strong foundation of fundamental concepts and improves confidence to face board exams.
2. The method of solving complex problems can be learned easily.
3. It is an ideal study material for students to complete their assignments on time and score more marks in board exams.

• Are Utopper NCERT Solutions for Class 10 Maths important?

Utopper’s NCERT Solutions for Class 10 Maths are designed in such a way that students can understand the concepts and clear their doubts instantly. The solutions include comprehensive explanations to make the topic more interesting for the students. The PDF of the solution can be accessed by the students of Utopper and can be used to improve their conceptual knowledge.

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