# NCERT Solutions for Class 10 Maths

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.

### Chapter 1: Real Numbers

The chapter Real numbers vastly explain the concept of properties of real numbers using Euclid’s Lemma, Fundamental Theorem of Arithmetic. This chapter mainly covered in four exercises, the problems in Exercise 1.1 and 1.2 are needed to find out the divisibility of integers using Euclid’s division algorithm and 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 number irrational and decimal expansions of rational numbers.

### Chapter 2: Polynomials

This chapter includes the advanced terminology related to polynomials such as the degree, coefficient, zeroes of any kind of polynomial. The chapter includes four exercises out of which, Exercise 2.1 and 2.2 consists 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.

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

This chapter deals with the concept determination of the solutions of pair of any linear equations in two variables graphically and algebraically. There are total 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.

### 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. This chapter in total has four exercises out of which Exercises 4.1 and 4.2 are based on the basic idea of quadratic equations and 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.

### 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 first n terms of a series, and applications of AP in every-day life. The chapter primarily consists of four exercises, exercises 5.1 and 5.2 deal with the basic introduction with 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.

- Exercise 5.1
- Exercise 5.2
- Exercise 5.3 Set 1, Set 2
- Exercise 5.4

### Chapter 6: Triangles

The chapter Triangles in this class gives detailed knowledge about the triangles with the concept of similarity and congruence of triangles, and theorems related to it. This chapter covers concepts primarily in six exercises out of which exercise 6.1 covers the basics of the triangles. However, exercises 6.2, 6.3, and 6.4 contain problems from the topic of similarity of triangles and theorem related to it. Further, Exercises 6.5 and 6.6 emphasize on congruence of triangles and their application.

- Exercise 6.1
- Exercise 6.2
- Exercise 6.3 Set 1, Set 2
- Exercise 6.4
- Exercise 6.5 Set 1, Set 2
- Exercise 6.6

### Chapter 7: Coordinate Geometry

As the name of the chapter suggests, 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, coordinate of the point of a line divided in a given ratio, section formula, and areas of the triangle. This chapter includes total four exercises out of which the problems in 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.

### Chapter 8: Introduction to Trigonometry

This chapter deals with the study of 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. There are four exercises in this chapter, in which 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 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.

### Chapter 9: Some Applications of Trigonometry

This chapter deals with the study of the practical application of trigonometry in our 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.

### 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. 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.

**Chapter 11: Constructions**

This chapter deals with the study of the concept of the geometrical construction of lines, circles, and triangles. The topic discusses the division of any line segment in internal ratio, tangents to a

### Chapter 12: Areas Related to Circles

- Exercise 12.1
- Exercise 12.2 Set 1, Set 2
- Exercise 12.3 Set 1, Set 2

### Chapter 13: Surface Areas and Volumes

**Chapter 14: Statistics**

The chapter statistics explains the arrangement of an ungrouped set of information or data to a grouped data numerically. There are total four exercises in the chapter in

**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 only two exercises in this chapter that covers the various problems to explain them effectively.

- Exercise 15.1 Set 1, Set 2
- Exercise 15.2