RD Sharma Solutions for Class 10 Maths

RD Sharma Solutions for Class 10 Maths – Chapter-wise Free PDF Download, Updated for 2023-24

RD Sharma Solutions for Class 10 Maths PDF are provided here to help the students in their effective preparation for the board exams. The expert faculty at BYJU’S, having in-depth knowledge of all the concepts, prepared these solutions according to the exercise-wise problems in the textbook. Students can now solve any problem from the RD Sharma Textbook by referring to the RD Sharma Solutions. The main purpose of creating such a resource for students is to help them self-analyse their areas of weaknesses and also to help them solve problems of higher difficulty levels in an efficient way.

The most excellent technique in which the students can prepare for their forthcoming board examinations is to make sure that they are thorough with the concepts and that they have the benefit of accurate study materials. Students no longer have to waste their time and effort in finding the solutions of RD Sharma, as we at BYJU’S, have provided the solutions PDF for free in this article. The accurate solutions for the CBSE textbook questions are prepared with utmost care to help students ace the exams with good grades.

The RD Sharma Book for Class 10 is undoubtedly packed with all the essential summaries and explanations that the students need to understand. The chapter-wise solutions for Class 10 are based on the lessons present in the textbook, ensuring that the students study all the relevant topics and concepts with the problems related to the same. These RD Sharma Solutions contain questions with varying levels of difficulty, and the questions are in addition to those present in the RD Sharma Solutions for Class 10 Maths. Practising these solutions will help students gain confidence in solving the different types of questions that might appear in the board examination.

RD Sharma Chapter-wise Solutions for Class 10 Maths

In addition, students can access various study materials like worksheets, sample papers, and previous years’ question papers at BYJU’S to secure a good academic rank. Also, the RD Sharma Solutions for Class 10 Sample Papers can be practised regularly by the students to get familiar with the question paper patterns and different types of questions that might be asked in the exam.

Students can access RD Sharma Class 10 Maths PDF for a better understanding of concepts. Those who are facing difficulty in solving problems are advised to practise these solutions on a daily basis and improve their skills in Mathematics, which are essential from an exam perspective. Diligent practice of these solutions not only clears the doubts of students immediately but also boosts their confidence in appearing for the board and competitive exams.

RD Sharma Class 10 Maths – Exercise-wise Solutions

The PDF format of the solutions can be used as prime reference material by the students to get a strong grip on the concepts in each chapter of the textbook. Further, students solving the problems in the textbook using RD Sharma Solutions improve their problem-solving skills, which are very essential from the exam point of view. Students can make use of RD Sharma Maths Class 10 Solutions PDF Free Download from the links given here to achieve good scores in the board exam.

RD Sharma Solutions for Class 10 Maths Chapter 1 – Real Numbers

Chapter 1 of RD Sharma Solutions helps students comprehend the divisibility of integers and some important properties of integers, like Euclid’s division lemma, Euclid’s division algorithm, and the fundamental theorem of arithmetic. The solutions help students to discover the right method and shortcuts in solving the problem following the latest CBSE guidelines. The PDF of solutions can be downloaded by the students and practised on a regular basis for a good score in the board exams.

• Euclid’s division lemma: If we have two positive integers a and b, there should be whole numbers q and r that satisfy the equation – a = bq + r, where 0 ≤ r < b, where a is the dividend and b is the divisor.
• Euclid’s division algorithm: It is the technique used to determine the HCF of two given positive integers.
• Fundamental theorem of arithmetic: Every composite number can be factorised as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

Provided below are the links to the exercise-wise solutions to problems of Chapter 1.

Also, access the following resources for Class 10 Chapter 1 Real Numbers, at BYJU’S:

• NCERT Solutions for Class 10 Maths Chapter 1 – Real Numbers
• NCERT Exemplar Class 10 Maths Solutions for Chapter 1 – Real Numbers

RD Sharma Solutions for Class 10 Maths Chapter 2 – Polynomials

Polynomials are algebraic expressions that have both variables and coefficients. This chapter has problems based on the concepts like the geometrical representation of linear and quadratic polynomials, the geometric meaning of their zeros, and the relationship between the zeros and coefficients of a polynomial. The expert faculty at BYJU’S has explained all these concepts in an interactive manner to help students perform well in the board exam. The step-wise explanations for each problem help students to gain better conceptual knowledge, which is important from the exam perspective.

• Linear polynomial: A polynomial of degree one, i.e., the highest exponent of the variable is one.
• Quadratic polynomial: A polynomial of degree two, i.e., the highest exponent of the variable is two.
• Geometrical representation of linear and quadratic polynomials: The representation of linear and quadratic polynomials in a geometric form.

This chapter contains three exercises, and their solution links are provided below.

Also, access the following resources for Class 10 Chapter 2 Polynomials, at BYJU’S:

• NCERT Solutions for Class 10 Maths Chapter 2 – Polynomials
• NCERT Exemplar Class 10 Maths Solutions for Chapter 2 – Polynomials

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

The 3rd chapter of RD Sharma Solutions contains problems based on systems of linear equations in two variables, solutions of a system of linear equations in two variables, graphical and algebraic methods of solving a system of linear equations in two variables, as well as their applications. RD Sharma Mathematics Class 10 are well-explained in a simple language that matches the understanding capabilities of students to enhance their exam preparations. The solutions PDF helps students to understand the method of solving complex problems effortlessly.

• Linear equations in two variables: If a, b, and r are real numbers (a and b are not equal to 0), then ax+by = r is called a linear equation in two variables. 
• Graphical and algebraic methods of solving a system of linear equations in two variables: Solving the given linear equation using graphical and algebraic methods.
• Applications of linear equations in two variables: The applications of linear equations in two variables in our daily life are covered in this chapter.

Chapter 3 exercise-wise solution links are provided below.

Also, access the following resources for Class 10 Chapter 3 Pair of Linear Equations in Two Variables, at BYJU’S:

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

RD Sharma Solutions for Class 10 Maths Chapter 4 – Triangles

The exercise-wise problems of Chapter 4 are solved by subject experts at BYJU’S to help students face the exams confidently. The important topics which are covered in this chapter are the similarity of geometric figures, similar triangles and their properties, some basic results on proportionality, and some important theorems and criteria of proportionality. Students who find it difficult to solve exercise-wise problems can make use of chapter-wise PDFs to understand the topics easily. 

• Similarity of geometric figures: Two geometric figures are said to be similar if they have the same sides, angles, or mirrors of the figures.
• Similar triangles: If the two pairs of corresponding angles in two triangles are congruent, then both triangles are said to be similar.
• Proportionality: The equality between two ratios, i.e., a/b = c/d, where a and b are in the same proportion as c and d.

This chapter contains 7 exercises, and their solution links are given below.

Also, access the following resources for Class 10 Chapter 4 Triangles, at BYJU’S:

• NCERT Solutions for Class 10 Maths Chapter 6 – Triangles
• NCERT Exemplar Class 10 Maths Solutions for Chapter 6 – Triangles

RD Sharma Solutions for Class 10 Maths Chapter 5 – Trigonometric Ratios

Trigonometry is an important branch of Mathematics. This chapter throws light on the basic concepts of trigonometry, like trigonometric ratios and the relations between them, trigonometric ratios of some specific angles, and trigonometric ratios of complementary angles. RD Sharma Solutions created by subject experts at BYJU’S can be utilised by students to solve the exercise-wise problems in this chapter. Students are advised to refer to the solutions PDF while solving the problems to gain a grip on the concepts which are important from the exam perspective.

• Trigonometry: It is a branch of Mathematics that deals with the relationship between side lengths and angles of triangles.
• Trigonometric ratios: The six trigonometric ratios are, cosine, sine, cotangent, tangent, secant and cosecant.
• Trigonometric ratios of complementary angles: If the sum of two angles is 90 degrees, then one angle is said to be complementary to another angle.

Chapter 5 contains 3 exercises for which the solution links are as follows.

Also, access the following resources for Class 10 Chapter 5 Trigonometric Ratios, at BYJU’S:

• NCERT Solutions for Class 10 Maths Chapter 8 – Introduction to Trigonometry
• NCERT Exemplar Solutions for Class 10 Maths Chapter 8 – Introduction to Trigonometry and Its Equations

RD Sharma Solutions for Class 10 Maths Chapter 6 – Trigonometric Identities

In this chapter, students will prove some trigonometric identities and use them to prove other useful trigonometric identities. The subject-matter experts at BYJU’S have made solutions for the exercise problems after conducting vast research on each concept. Further, students can refer to these solutions while solving chapter-wise problems. RD Sharma Class 10 Solutions contains explanations in understandable language to help each and every student, irrespective of their intelligence quotient.

• Trigonometric identities: These are equalities that involve trigonometric functions and are true for every value of occurring variables.

Students can access the exercise-wise solutions of Chapter 6 from the links provided below.

RD Sharma Solutions for Class 10 Maths Chapter 7 – Statistics

Chapter 7 of RD Sharma Solutions explains the techniques for finding mean, median, and mode of grouped data, as well as about cumulative frequency graphs of a frequency distribution. The solutions have explanations in simple language to enhance the conceptual knowledge of students. Also, the students can access the solutions PDF easily to practise and improve their speed in solving problems. The objective of providing solutions is to help the students to understand the concepts and topics that are important from the exam point of view. The solutions provided in RD Sharma Mathematics Class 10 help students clear their doubts instantly and score optimum marks in board exams.

• Statistics: The branch of Mathematics dealing with the collection, organisation, analysis, interpretation, and presentation of numerical data is called Statistics.
• Mean: It is done by adding all the numbers in the data set and then dividing by the number of values.
• Median: The middle value when a data set is ordered from least to greatest.
• Mode: The number which occurs most frequently in a data set.
• Frequency distribution: The overview of all different values in some variables and the number of times they occur.

The solutions links of all 6 exercises present in this chapter created by experts at BYJU’S are given below.

Also, access the following resources for Class 10 Chapter 7 Statistics, at BYJU’S:

• NCERT Exemplar Class 10 Maths Solutions for Chapter 13 – Statistics and Probability
• NCERT Solutions for Class 10 Maths Chapter 14 – Statistics

RD Sharma Solutions for Class 10 Maths Chapter 8 – Quadratic Equations

The exercise problems in this chapter mainly deal with various ways of finding their zeros or roots and some applications of quadratic equations in daily life situations. The PDF of solutions is made available in order to boost the exam preparation of students. The solutions cover all the problems from the prescribed textbook according to the latest CBSE syllabus. The problems contain step-wise explanations based on the exam pattern and mark weightage allotted to each step.

• Quadratic equations: The quadratic polynomials, when equated to zero, are quadratic equations.
• Standard form of quadratic equation: ax² + bx + c = 0.

There are 13 exercises in Chapter 8, and students can access the solutions from the links provided below.

Also, access the following resources for Class 10 Chapter 8 Quadratic Equations, at BYJU’S:

• NCERT Solutions for Class 10 Maths Chapter 4 – Quadratic Equations
• NCERT Exemplar Class 10 Maths Solutions for Chapter 4 – Quadratic Equations

RD Sharma Solutions for Class 10 Maths Chapter 9 – Arithmetic Progressions

A sequence is an arrangement of numbers in a definite order according to some rule. Arithmetic Progression is a sequence of numbers in which the difference between any two successive numbers is always a constant. Chapter 9 contains important concepts like general, nth, selection, and the sum of terms of an A.P. Students can make use of the RD Sharma Class 10 Solutions PDF prepared by expert faculty at BYJU’S as a reference to perform well in the board exam. The PDF is available in both chapter-wise and exercise-wise formats based on the requirements of students.

• Arithmetic progression: It is a sequence of numbers where the difference between successive numbers is constant.
• General term of AP: Formula for the nth term of the A.P. with a as the first term and d as the common difference is a_n = a + (n-1) d. Here, the nth term (a_n) is called the general term of AP.
• Sum of terms of AP: It is the sum of the first n terms of the arithmetic sequence.

The exercise solution links for the concepts covered in this chapter are given below.

Also, access the following resources for Class 10 Chapter 9 Arithmetic Progressions, at BYJU’S:

• NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions
• NCERT Exemplar Class 10 Maths Solutions for Chapter 5 – Arithmetic Progressions

RD Sharma Solutions for Class 10 Maths Chapter 10 – Circles

The circle is nothing but the locus of all points which are equidistant from the centre. Chapter 10 of RD Sharma Solutions gives students the concepts of the secant of a circle and tangent to a circle, along with their properties. Additionally, problems related to the circle, triangle, and quadrilateral are tested in the exercise problems. Students who refer to the solutions will get an idea about the steps involved in solving the problems. The solutions are curated by highly experienced faculty at BYJU’S based on the latest syllabus of the CBSE Board.

• Circle: Locus of points equidistant from the centre.
• Secant of a circle: It will intersect the circle at exactly two points.
• Tangent to a circle: A straight line that touches the circle at a single point.

This chapter has 2 exercises, and the solution links are available below.

Also, access the following resources for Class 10 Chapter 10 Circles, at BYJU’S:

• NCERT Solutions for Class 10 Maths Chapter 10 – Circles
• NCERT Exemplar Solutions for Class 10 Maths Chapter 9 – Circles

RD Sharma Solutions for Class 10 Maths Chapter 11 – Constructions

Construction is one of the important concepts in Geometry. Chapter 11 will help students gain knowledge about constructing a triangle similar to a given triangle and tangents to a circle. The steps involved in the construction of geometric figures are explained in an interactive way to help students understand the method easily. The solutions PDF can be downloaded for free by students who wish to master the steps involved in constructions. By regularly practising the exercise-wise problems, students will be able to solve complex problems which would appear in the board exams.

• Constructions: Drawing lines and shapes using various geometrical instruments.
• Angle: The amount of turn between two lines from their common point.
• Length: The size of a line segment is called the length.

The solutions links of all three exercises in this chapter are given below.

Also, access the following resources for Class 10 Chapter 11 Constructions, at BYJU’S:

• NCERT Solutions for Class 10 Maths Chapter 11 – Constructions
• NCERT Exemplar Class 10 Maths Solutions for Chapter 10 – Constructions

RD Sharma Solutions for Class 10 Maths Chapter 12 – Some Applications of Trigonometry

The important concepts based on trigonometric results are explained in an easy and understandable language in this chapter. The main topic based on which the problems are created is regarding heights and distances. The height of certain objects and the distance from a certain point is discussed in brief under each exercise to make students familiar with the type of questions that might be asked in the board exams. Students can also use the PDF of RD Sharma Solutions to solve problems in the textbook and score well.

• Trigonometry: It is a branch of Mathematics that deals with the relationship between angles and side lengths of triangles.
• Height of a triangle: It is the length of a perpendicular line segment that originates on a side and intersects the opposite angle.

Chapter 12 has only one exercise, and its solution link is given below.

Also, access the following resources for Class 10 Chapter 12 Some Applications of Trigonometry, at BYJU’S:

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

RD Sharma Solutions for Class 10 Maths Chapter 13 – Probability

There is always a degree of certainty or uncertainty about what has happened or going to happen. This leads to finding the probability of an occurrence of an event. The branch of Mathematics which deals with numerical descriptions of how likely an event is to occur or how likely a proposition is true is called probability. By using solutions PDF, students will get a quick overview of the concepts which are detailed under each exercise. It’s also a great help for students to practise problems on a daily basis. By solving the textbook problems, students will gain a stronghold on the fundamental concepts, which will be continued in higher classes as well.

• Probability: The numerical description of how likely an event will occur.
• Event: It is an outcome or defined collection of outcomes of a random experiment.

This chapter has two exercises, and the solutions links are provided below.

Also, access the following resources for Class 10 Chapter 13 Probability, at BYJU’S:

• NCERT Solutions for Class 10 Maths Chapter 15 – Probability
• NCERT Exemplar Class 10 Maths Solutions for Chapter 13 – Statistics and Probability

RD Sharma Solutions for Class 10 Maths Chapter 14 – Coordinate Geometry

Chapter 14 of RD Sharma’s Solutions comprises 5 exercises, and the questions cover key concepts like understanding rectangular coordinates, the distance between two points, sections formulae and their applications, collinearity of points, and the area of triangle and quadrilateral. Methods used in solving problems, along with shortcut tips, are well highlighted to help students boost their exam preparations. The solutions PDF contains step-wise explanations of each problem for a better understanding of concepts that are important for the exam.

• Coordinate Geometry: Study of geometry using coordinate systems.
• Distance between two points: The distance between two points in a geometric shape can be determined by using the distance formula, which is an application of the Pythagoras theorem.
• Section formula: It is used to determine the ratio in which a line segment is divided by a point externally or internally.

The solution links for the exercise-wise problems of this chapter are as follows:

Also, access the following resources for Class 10 Chapter 14 Co-ordinate Geometry, at BYJU’S:

• NCERT Solutions for Class 10 Maths Chapter 7 – Coordinate Geometry
• NCERT Exemplar Solutions for Class 10 Maths Chapter 7 – Coordinate Geometry

RD Sharma Solutions for Class 10 Maths Chapter 15 – Areas Related to Circles

Students can now access the chapter-wise RD Sharma Solutions for the textbook questions, prepared according to the latest CBSE syllabus. This chapter deals with finding the area of circular regions and two special parts of the circular region, known as the sector and segment of a circle. The important formulas in finding the areas related to circles and the steps included in them are explained in a comprehensive manner. The students can self-assess their knowledge about the entire chapter by solving problems using the solutions PDF.

• Area of circular regions: The area of a circle is pi times the radius squared.
• Sector: A part of the circle which is made of the arc of the circle along with its two radii.
• Segment: It is the region bounded by the arc and the intercepted arc of the circle. 

All four exercise problems in this chapter are solved by subject experts, and the solution links are attached below.

Also, access the following resources for Class 10 Chapter 15 Areas Related to Circles, at BYJU’S:

• NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles
• NCERT Exemplar Class 10 Maths Solutions for Chapter 11 – Areas Related to Circles

RD Sharma Solutions for Class 10 Maths Chapter 16 – Surface Areas and Volumes

In this chapter, the problems with the conversion of one of these solids into another, as well as finding the surface areas and volumes of a combination of two or more such solids, are discussed. The sum of the areas on a 3-dimensional figure is called the surface area. The space that a substance or shape occupies is called volume. The solutions are well-explained in an interactive manner to make the subject more understandable and easier for students. The exercise-wise problems are solved by the expert faculty at BYJU’S after conducting vast research on each topic. 

• Surface area: The region occupied by the surface of the object.
• Volume: The amount of space that is available in the object.

Students can access the solutions to 3 exercises in this chapter from the links provided below.

Also, access the following resources for Class 10 Chapter 16 Surface Areas and Volumes, at BYJU’S:

• NCERT Solutions for Class 10 Maths Chapter 13 – Surface Areas and Volumes
• NCERT Exemplar Class 10 Maths Solutions for Chapter 12 – Surface Areas and Volumes

Class 10 is a crucial stage in a student’s life, and regular practice is required to remember important concepts efficiently. The subject-matter experts at BYJU’S designed the RD Sharma Solutions for Class 10 with the aim of helping students perform well in the board exams. Numerous examples present before the exercise-wise problems assist students in solving complex questions effortlessly.

Advantages of RD Sharma Solutions for Class 10 Maths

• The chapter-wise and exercise-wise solutions are present with a free download option.
• To enable visual learning skills, pictures are added wherever necessary.
• The solutions are created with utmost care based on the IQ levels of Class 10 students.
• It will help students to know the important concepts from the exam point of view and score high in the board exams.