# RD Sharma Class 10 Solutions

RD Sharma Solutions for class 10 provides prime reference material to the students to get a strong grip over the concepts under each chapter of the textbook. As Class 10 mathematics is categorized into various important topics such as Algebra, Geometry, and Trigonometry, which are standing pillars of mathematics therefore in order To provide the best way to help students we have provided the RD Sharma Solution, which can be looked upon anytime whenever any doubt arises.

### Chapter 1: Real Numbers

The chapter real number in this book gives the knowledge about two very important properties of positive integers, namely Euclid’s division algorithm related to the divisibility of integers and Euclid’s lemma. Some problems are related to the Fundamental Theorem of Arithmetic which is related to the multiplication of positive integers. Various theorems for irrational numbers are also covered in total six exercises present in this chapter.

- Exercise 1.1 Set 1, Set 2
- Exercise 1.2 Set 1, Set 2
- Exercise 1.3
- Exercise 1.4
- Exercise 1.5
- Exercise 1.6

### Chapter 2: Polynomials

There are 3 exercises present in this chapter. This chapter helps to find quadratic polynomials, verify the relationship between the zeroes and the coefficients of given quadratic polynomials. Some questions to perform divisions of given polynomials or find all the zeros of a polynomial are also asked in this chapter.

- Exercise 2.1 Set 1, Set 2
- Exercise 2.2
- Exercise 2.3

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

In this chapter basically, the graphical and algebraic methods of solution of a pair of linear equations are covered, and when the graphical method is not suitable, substitution or elimination methods are used. Further, the questions need to solve using cross-related multiplication methods, and those pairs of equations which are not linear are solved by first reducing them to linear form by making some suitable substitutions. There are total eleven exercises based on the mentioned topics.

- Exercise 3.1
- Exercise 3.2 Set 1, Set 2, Set 3
- Exercise 3.3 Set 1, Set 2
- Exercise 3.4 Set 1, Set 2
- Exercise 3.5 Set 1, Set 2, Set 3
- Exercise 3.6 Set 1, Set 2
- Exercise 3.7
- Exercise 3.8
- Exercise 3.9
- Exercise 3.10
- Exercise 3.11 Set 1, Set 2

### Chapter 4: **Triangles **

There are seven exercises based on the topics like types of triangles, to prove congruence and similarity of triangles based on several criteria. This chapter also helps to solve questions based on the Basic proportionality theorem and Pythagoras theorem.

- Exercise 4.1
- Exercise 4.2
- Exercise 4.3
- Exercise 4.4
- Exercise 4.5 Set 1, Set 2
- Exercise 4.6 Set 1, Set 2
- Exercise 4.7 Set 1, Set 2

### Chapter 5: Trigonometric Ratios

This Chapter has a total of three exercises in which one needs to determine the values of trigonometric ratios in a triangle when the measurement of sides is given, or other trigonometric ratios for a triangle are given. It also helps to determine the values of the trigonometric equation prepared with related trigonometric ratio terms. There are some questions that ask to prove some trigonometric ratio relationships, and some need you to evaluate the given equations based on trigonometric ratios.

### Chapter 6: Trigonometric Identities

This topic of trigonometry is basically defined as an equation involving trigonometric ratios of an angle, which can be used to express and determine one trigonometric ratio in terms of other trigonometric ratios. Further, this chapter helps to learn the solutions of various equations involving trigonometric ratios of an angle where one trigonometric identity is proved first, and then it is used to prove further trigonometric identities. The solutions are determined by proving equality between the left-hand side and right-hand side equation. There are 2 exercises only that are based on the mentioned topics.

- Exercise 6.1 Set 1, Set 2, Set 3
- Exercise 6.2

### Chapter 7: **Statistics **

There are total six exercises in this book in the present chapter. The questions are based on the direct calculation of mean, assumed mean and calculation of mean with step-deviation methods. Also, the median calculation with Class intervals, types of cumulative frequency distribution, and graphical representation of the median has also been dealt in a clear manner. Further, this chapter explains the methods of estimating mode from a set of grouped data, ungrouped data, finding mode without class intervals, graphical representation of mode, and calculation of central tendency.

- Exercise 7.1 Set 1, Set 2
- Exercise 7.2
- Exercise 7.3 Set 1, Set 2
- Exercise 7.4 Set 1, Set 2
- Exercise 7.5 Set 1, Set 2
- Exercise 7.6

### Chapter 8: Quadratic Equations

The Quadratic Equations covered in the present book include various types of questions, which are based on the determination of quadratic equations, formulation of quadratic equations, various methods of finding zeros, or roots of quadratic equations like factorisation, completing the square, and using the quadratic formula. There are a total of 13 exercises based on such topics.

- Exercise 8.1
- Exercise 8.2
- Exercise 8.3 Set 1, Set 2
- Exercise 8.4
- Exercise 8.5
- Exercise 8.6 Set 1, Set 2
- Exercise 8.7 Set 1, Set 2
- Exercise 8.8
- Exercise 8.9
- Exercise 8.10
- Exercise 8.11
- Exercise 8.12
- Exercise 8.13

### Chapter 9: Arithmetic Progressions

The questions related to this chapter are asked in a total of six exercises. This chapter gives an overview of arithmetic progressions, nth term of an AP, and the sum of the first n given terms of an arithmetic progression. Some questions in this chapter are based on the fact that successive terms are found by adding a fixed number to the preceding terms etc.

- Exercise 9.1
- Exercise 9.2
- Exercise 9.3
- Exercise 9.4 Set 1, Set 2
- Exercise 9.5
- Exercise 9.6 Set 1, Set 2, Set 3

### Chapter 10: Circles

There are two exercises in this chapter that are based on the properties of circles and tangents to a circle, tangents of a circle, number of tangents passing from a given point on the circle. This chapter also contains the problems related to the fact that tangent to a circle is perpendicular to the radius at the point of contact and lengths of the two tangents from an external point to a circle are equal.

- Exercise 10.1
- Exercise 10.2 Set 1, Set 2

**Chapter 11: Constructions**

The chapter Construction chapter helps to learn how to construct geometrical shapes along with providing mathematical reasoning behind working of such constructions, construct a triangle which is similar to a triangle given already according to the given scale factor. Also, helps to understand the construction of the tangents to a circle from a point outside it in different steps using a ruler and a compass.

- Exercise 11.1
- Exercise 11.2 Set 1, Set 2
- Exercise 11.3

### Chapter 12: Some Applications of Trigonometry

There is only one exercise in this Chapter. That needs to solve questions based on concepts of trigonometry, determination of – the height of the object, the distance between two objects, the length of the horizontal level, and the angle of elevation or depression.

### Chapter 13: Probability

The chapter Probability in this book has 2 exercises only. The problems in these exercises are based on the basic concepts of probability, some significant concepts of probability that include the theoretical approach to probability, random experiments, the meaning of events, the possible outcome of an event, elementary and complimentary events, and compound events.

- Exercise 13.1 Set 1, Set 2
- Exercise 13.2

**Chapter 14: **Coordinate Geometry

In the Coordinate Geometry chapter, there are five exercises. The questions from the topic coordinate geometry help to solve different questions on locating the coordinates, determining the distance from a point, calculating the distance between two points, dividing a line segment into two parts in a given ratio, and determination of the area of the triangle.

- Exercise 14.1
- Exercise 14.2 Set 1, Set 2, Set 3
- Exercise 14.3 Set 1, Set 2, Set 3
- Exercise 14.4
- Exercise 14.5 Set 1, Set 2, Set 3

**Chapter 15: **Areas Related To Circles

There are 4 exercises that help to determine the circumference and area of circles using the formula when the radius or diameter is given. It also helps to determine the length or angle of the arc subtended on the perimeter of a given circle. Some questions of the exercises are based on the determination of the areas of major and minor segments given in a circle applying different formulas.

- Exercise 15.1 Set 1, Set 2
- Exercise 15.2
- Exercise 15.3
- Exercise 15.4 Set 1, Set 2, Set 3

**Chapter 16: **Surface Areas And Volumes

In this Chapter, there are a total three exercises that explain the three-dimensional geometrical figures. It helps to learn how to calculate the surface area and volume of objects formed by the combination of any two of the basic solid shapes like cuboid, cone, cylinder, sphere, and hemisphere. This also gives the knowledge of the frustum of the right circular cone surface area and its volume.