NCERT solutions for class 10 maths- Are you preparing for class 10 board exams and looking for solutions of NCERT, then you are at the right place. CBSE NCERT solutions class 10 maths are going to help you crack board exams and make learning easier. NCERT class 10 maths contain a total of 15 chapters and all the chapters are important to study. You should not ignore any single chapter because at least one question is sure from each chapter in your boardexams. It is necessary to solve all the exercises including the additional exercises to get a good score. NCERT solutions for class 10 maths will help you understand each question in detail. By solving the entire NCERT maths using CBSE NCERT solutions for class 10 maths and practicing the previous 5 years' questions you can easily score well in board exams. Geometry and trigonometry are one of the most important chapters in this class as most of the students feel troubled in geometry and trigonometry. For saving you from this trouble, here are the NCERT solutions for class 10 maths, you can click on the chapter you wish to study below. Also, in order to study other subjects or even higher classes, you can take help from NCERT solutions that are answered using step by step approach so that you do not miss any step while answering the problems in the examinations.
If we talk about futuristic importance, then most of the students will opt for a competitive examination after their school or graduation. If a student is good in class 10 maths then only a few additional things will be left to study. If you want to check the solutions for science or other subjects of class 10, then click on the link NCERT solutions for class 10.
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NCERT solutions for class 10 maths chapter 1 Real Numbers: In this chapter, you are going to learn about Euclid’s Division Lemma and this concept is used to find the HCF, LCM, the relation between HCF and LCM and fundamental theorem of arithmetic. Euclid’s Division Lemma will also be required if you want to prove that the given number is rational or irrational and the given rational number is terminating or non terminating repeating. There are many real-life examples of LCM and HCF mentioned in the NCERT solutions for class 10 maths. There are a total of 4 exercises with a total of 48 questions in this chapter.
Solutions of NCERT class 10 maths chapter 2 Polynomials: The chapter starts with an explanation of polynomials referring to the previous classes and then explains the geometrical interpretation of the zeroes of the polynomial. Then it gives the relation between zeroes and coefficient of a given polynomial and also explains how to carry out the polynomial divisions. You have to be good in class 9 maths chapter polynomial to beat this one. In NCERT solutions for class 10 maths chapter 2 polynomials, step by step explanation is given in the answers of all 4 exercises including the optional exercise.
CBSE NCERT solutions for class 10 maths chapter 3 Pair of Linear Equations in Two Variables: There are many real-life examples that can be formulated in linear equations in two variables. Let's take an example to understand: If a person buys some pens and pencils at a total of 41 Rs and the price of a pen and a pencil are 5 Rs and 4 Rs respectively. Then the statement can be represented as Many such problems are mentioned in the NCERT solutions for class 10 maths. The chapter covers various algebraic methods to solve a given pair of linear equations and a geometrical way of solving the pair of linear equations.
NCERT solutions for class 10 maths chapter 4 Quadratic Equations: We get a quadratic equation if a quadratic polynomial is equated to zero with the condition that the coefficient of the variable with power two is not equal to zero. The main content of the chapter includes the various methods of solving the quadratic equations and how to determine the consistency of quadratic equations from the value of discriminants. Every year around 8 to 10 marks questions come from this chapter only. In solutions of NCERT for class 10 maths chapter 4 quadratic equation, all the 4 exercises consisting of 46 questions are covered.
Solutions of NCERT class 10 maths chapter 5 Arithmetic Progressions: Any number series having the same difference between two immediate terms is called arithematic progression. For example- 2, 5, 8, 11 is an arithematic progression as the difference everywhere is 3. Every year around questions of 8 to 10 marks come from this chapter only. In this particular chapter, you will learn to solve questions related to nth /last term and questions related to sum of arithematic progression. Also, some questions are based on the usage of both the concepts together. There are some real-life situations mentioned in the NCERT solutions for class 10 maths. Studying a chapter by correlating to real-life examples will be interesting. In NCERT solutions for class 10 maths chapter 5 arithematic progression, we are covering all the 4 exercises including an optional exercise.
CBSE NCERT solutions for class 10 maths chapter 6 Triangles: A closed shape made using three straight lines is known as geometry. The NCERT Class 10 Chapter 6 starts with an explanation of the difference between the congruent figures and similar figures. In this particular chapter, we will learn similarity of triangles, criteria for similarity, area of triangles and understanding of Pythagoras theorem using the similarity of triangles. There are many interesting examples that can be solved using the similarity of triangles. In the solutions of this particular chapter, you will get solutions to all the 6 exercises including optional exercise consisting of 90 questions.
NCERT solutions for class 10 maths chapter 7 Coordinate Geometry: This is one of the chapters which you will use in almost all the areas your higher studies, whether it is science, commerce or arts. In class 10 maths, this chapter holds some specific kind of concepts and questions and if you do them well, then the things will become easy for you in the examination. The NCERT solutions for class 10 maths chapter 7 coordinate geometry include the distance formulae, section formulae and the concept of finding the area of triangles if the coordinate of the vertex is given. The solution to all the 4 exercises including an optional exercise consisting total of 45 questions are explained in a step by step manner.
Solutions of NCERT class 10 maths chapter 8 Introduction to Trigonometry: The chapter has originated from the right angle triangle. The properties, formulas, and ratios of trigonometry can be derived using length, breadth, and height of the right-angle triangle. In this chapter, there are a total of 4 exercises and questions of these exercises are mainly based on finding trigonometric ratios of the sides of a right-angled triangle. The NCERT Solutions for Class 10 Maths of this chapter covers important concepts to find trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles and trigonometric identities.
CBSE NCERT solutions for class 10 maths chapter 9 Some Applications of Trigonometry: This chapter is just an extension of the concepts used in chapter 8. This is the application based chapter which tells us the usage of trigonometry in real life. "Trigonometry" unit holds 12 marks out of 80 marks in the CBSE final maths paper and we can expect one question of 3 or 4 marks from this chapter. In this, we will learn how trigonometry is helpful in finding the distance and height of different objects without actually measuring them. This chapter has only 1 exercise for which answers are there in solutions of NCERT for class 10 maths chapter 9 some applications of trigonometry.
NCERT solutions for class 10 maths chapter 10 Circles: A circle is nothing but a closed figure with a collection of points in a plane that are at a specific distance (radius) from a fixed point (center). This chapter is an important part of geometry along with triangles. This chapter in class 10 maths is an extension of class 9 maths chapter circles. In this chapter, we will discuss tangent to a circle and number of tangents from a point on the circle. The chapter holds good weightage in the board examinations. Every year approximately 10 to 12 marks questions come from this chapter only. The solution of NCERT class 10 maths covers all 2 exercises consisting of overall 26 questions.
Solutions of NCERT class 10 maths chapter 11 Constructions: This chapter, deals with the problem constructions. It is also known as a geometrical drawing which deals with constructing geometric figures using some specific geometric tools. It is a part of the geometry unit and geometry holds 15 marks in the final CBSE exams and construction is a scoring topic for students. In this chapter, there is a total of 2 exercises with 14 questions. In the first exercise, we will learn how to divide a line segment and in the second exercise, we will learn the construction of tangents to a circle.
CBSE NCERT solutions for class 10 maths chapter 12 Areas Related to Circles: In this chapter, we will deal with areas related to circles. This chapter is a part of the Mensuration unit, which holds 10 marks in the CBSE Class 10 final exam. In this chapter, there are 3 exercises with 35 questions in them. In this chapter, we will learn the perimeter and area of a circle, areas of sector and segment of a circle, areas of combinations of plane figures. In NCERT solutions for class 10 maths chapter 12 areas related to circles, detailed solutions to each question are given.
NCERT solutions for class 10 maths chapter 13 Surface Areas and Volumes: This comes under mensuration. We have already done some part of the mensuration in the class 9 maths. In this chapter, we will discuss how to find surface areas and volumes of combinations, which are formed by two or more than two of the basic solids such as cone, cuboid, cylinder, sphere, and hemisphere. Apart from all these shapes, a new shape frustum will be introduced here in this particular chapter. In this chapter, there are a total of 5 exercises with 38 questions in them. In all the exercises, we will deal with questions on finding surface areas and volumes of solids.
Solutions of NCERT class 10 maths chapter 14 Statistics: In the previous class, we have learned about data representation and have solved many calculation based questions on that. Statistics is also somehow related to data handling. In this chapter, the questions will be based on data and we will discuss how to find the measures of central tendency namely, mean, mode and median from the ungrouped data to that of grouped data. In this chapter, there are a total of 4 exercises with 25 questions. In NCERT Class 10 Maths Chapter 14 Statistics, you will also get to know about the concept of cumulative frequency, its distribution and how to draw cumulative frequency curves.
CBSE NCERT solutions for class 10 maths chapter 15 Probability: Probability is one of the newest concept you will learn here in class 10 mathematics. In the previous class, you have learned about empirical probabilities or experimental probabilities of events that are based on the results of actual experiments. In this NCERT class 10 maths, we will discuss the theoretical probability (also called classical probability) of an event, and solve simple questions based on this concept. In NCERT solutions for class 10 maths chapter 15 probability, solutions of 2 exercises including optional exercise consisting of overall 68 questions are covered.
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Q5 Use Euclid’s division lemma to show that the cube of any positive integer is of the form
9m, 9m + 1 or 9m + 8.
6. In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in Fig. Find the area of the design.
Q : 3 In the following APs, find the missing terms in the boxes :
(iv)