RD Sharma Solutions For Class 10 Maths – Chapter wise Free PDF Download Updated for (2021-22)
RD Sharma Solutions for Class 10 Maths PDF are provided here to help the students in their effective preparation for the exams. The expert faculty at BYJU’S prepare these solutions for the exercise-wise problems after acquiring in-depth knowledge across all the concepts. Students can now solve any problem from the RD Sharma textbook by referring to the RD Sharma Solutions. The main purpose to create 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 examinations is to make sure that they are thorough with the concepts, and 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 underneath. The accurate solutions for the CBSE textbook 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 tackle. The chapters for Class 10 are based on the lessons present in the textbook, ensuring that the students study only 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 would help students gain confidence in solving the different types of questions that might appear in the examination.
RD Sharma Chapter-wise Solutions for Class 10 Maths
In addition, students can access various study materials like worksheets, sample papers, and previous year question papers to secure a good academic rank. Also, the RD Sharma Solutions for Class 10 Sample Papers can be practised timely 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 the problems are advised to follow these solutions on a daily basis and improve skills in Mathematics which are essential from an exam perspective. Diligent practice of these solutions not only clears doubts of students immediately but also boosts confidence in appearing for the board and competitive exams as well.
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 over the concepts under each chapter of the textbook. Further, students solving the problems of RD Sharma textbook using solutions mainly 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 for good scores in exams from the links given here.
RD Sharma Solutions for Class 10 Maths Chapter 1 – Real Numbers
Chapter 1 of RD Sharma textbook 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 short-cuts in solving the problem following the latest CBSE guidelines. PDF format 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 factorized as a product of primes, and this factorization is unique, apart from the order in which the prime factors occur.
Provided here are the links to the exercise-wise solutions to problems of this chapter.
|Chapter 1 – Real Numbers Exercises:|
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. Our faculty at BYJU’S has explained all these concepts in an interactive manner to help students perform well in the exam. The step-wise explanations for each problem help students to gain a 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 polynomial: The representation of linear and quadratic polynomial in a geometric form.
This chapter contains three exercises and their solutions links are provided below.
|Chapter 2 – Polynomials Exercises:|
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, solution 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 is covered in this chapter.
Chapter 3 exercise-wise solutions links are provided here.
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 with confidence. 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 the exercise-wise problems can make use of chapter-wise PDF to understand the topics with ease.
- 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 the 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.
|Chapter 4 – Triangles Exercises:|
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 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 of another angle.
Chapter 5 contains 3 exercises for which the solutions links are as follows.
|Chapter 5 – Trigonometric Ratios Exercises:|
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. BYJU’S has made solutions for the exercise problems after conducting wide research on each concept. Further students can use these solutions while solving chapter-wise problems. RD Sharma Class 10 Solutions contains explanations in understandable language to help students 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.
|Chapter 6 – Trigonometric Identities Exercises:|
RD Sharma Solutions for Class 10 Maths Chapter 7 – Statistics
Chapter 7 of RD Sharma 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 a simple language to enhance conceptual knowledge. Also, the students can access the solutions PDF at ease to improve their speed in solving problems. The objective of providing solutions is to help the students to understand 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 collection, organization, 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 here.
|Chapter 7 – Statistics Exercises:|
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 format 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 marks weightage allotted for each step.
- Quadratic equations: The quadratic polynomials when equated to zero are the quadratic equations.
- Standard form of quadratic equation: ax2 + bx + c = 0.
There are about 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 of any two successive numbers is always a constant. Chapter 9 contains important concepts like general, nth, selection, the sum of terms of an A.P. Students can make use of the RD Sharma Class 10 Solutions PDF prepared by experts at BYJU’S as a reference to perform well in their exams. The PDF is available in both chapter-wise and exercise-wise format 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 first term and d as common difference is an = a + (n-1) d. Here the nth term (an) 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 solutions links for the concepts covered in this chapter are given here.
|Chapter 9 – Arithmetic Progressions Exercises|
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
Circle is nothing but the locus of all points which are equidistant from the centre. The 10th chapter of RD Sharma gives students the concepts of the secant of a circle and tangent to a circle along with their properties. Additionally, problems including circle, triangle, and quadrilateral are tested in the exercise problems. The students referring 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 solutions links are available below.
|Chapter 10 – Circles Exercises|
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 the students who wish to master the steps of the constructions. By regularly practising the exercise-wise problems, students will be able to solve complex problems which would arise 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 the three exercises in this chapter are given below.
|Chapter 11 – Constructions Exercises:|
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 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 would arise in the board exams. Students can also use the PDF to solve problems of RD Sharma 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.
|Chapter 12 – Some Applications Of Trigonometry Exercise:|
Also access the following resources for Class 10 Chapter 12 Some Applications of Trigonometry at BYJU’S:
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 would 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 here.
|Chapter 13 – Probability Exercises:|
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 – Co-ordinate Geometry
Chapter 14 of RD Sharma’s textbook 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 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:
|Chapter 14 – Co-ordinate Geometry Exercises:|
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 solutions of the RD Sharma textbook prepared according to the latest CBSE guidelines. This chapter deals with finding the area of circular regions and two special parts of the circular region known as sector and segment of a circle. The important formulas in finding the areas related to circles and 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 of this chapter are solved by subject experts and the solution links are attached below.
|Chapter 15 – Areas Related To Circles Exercises:|
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, we shall discuss problems on 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. 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 understanding and easier for students. The exercise-wise problems are solved by the experts 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 hereby access the solutions of 3 exercises from the links provided below.
|Chapter 16 – Surface Areas And Volumes Exercises:|
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 as regular practise is required to remember important concepts efficiently. The subject matter experts at BYJU’S design 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 about how to solve 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 concepts of importance and score high in the board exams.