NCERT Solutions

As the saying goes, “Mathematics is the music of Reason” and this is exactly what maths is doing which is building up your reasoning skills. It’s not that you are just preparing maths for your exam but maths is preparing you for a bigger exam i.e. LIFE. NCERTBOOKS.GURU has compiled the most accurate and comprehensive solutions for class 10 Maths NCERT solutions.

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NCERT Solutions for Class 10 Maths PDF Free Download Chapter-wise

• Chapter 1 Real Numbers
• Chapter 2 Polynomials
• Chapter 3 Pair of Linear Equations in Two Variables
• Chapter 4 Quadratic Equations
• Chapter 5 Arithmetic Progression
• Chapter 6 Triangles
• Chapter 7 Coordinate Geometry
• Chapter 8 Introduction to Trigonometry
• Chapter 9 Some Applications of Trigonometry
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Area Related to Circles
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

Euclid’s division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of results – irrationality of √2, √3, √5, decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

Zeros of a polynomial. The relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.

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

Pair of linear equations in two variables and their graphical solution. Geometric representation of different possibilities of solutions/inconsistency.Algebraic conditions for a number of solutions. A solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method. Simple situational problems must be included. Simple problems on equations reducible to linear equations.

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations

Standard form of a quadratic equation ax² + bx + c = 0, (a ≠ 0). A solution of the quadratic equations (only real roots) by factorization, by completing the square and by using the quadratic formula. The relationship between discriminant and the nature of roots.Situational problems based on quadratic equations related to day to day activities to be incorporated.

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions

The motivation for studying Arithmetic Progression Derivation of the nth term and some of the first n terms of A.P. and their application in solving daily life problems.

NCERT Solutions for Class 10 Maths Chapter 6 Triangles

Definitions, examples, counter examples of similar triangles.

1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.
7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
9. (Prove) In a triangle, if the square on one side is equal to some of the squares on the other two sides, the angles opposite to the first side is a right angle.

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

Lines (In two-dimensions) Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

1. Introduction to Trigonometry Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0^o and 90^o. Values (with proofs) of the trigonometric ratios of 30^o, 45^o and 60^o. Relationships between the ratios.

2. Trigonometric Identities Proof and applications of the identity sin²A + cos²A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

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

Heights and Distances: Angle of elevation, Angle of Depression Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30^o, 45^o, 60^o.

NCERT Solutions for Class 10 Maths Chapter 10 Circles

Tangent to a circle at, the point of contact.

1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2. (Prove) The lengths of tangents drawn from an external point to a circle are equal.

NCERT Solutions for Class 10 Maths Chapter 11 Constructions

1. Division of a line segment in a given ratio (internally).
2. Tangents to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.

NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles

Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter/circumference of the above  said plane figures. (In calculating the area of a segment of a circle, problems should be restricted to a central angle of 60°, 90°, and 120° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken).

NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes

1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.2. Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with the combination of not more than two different solids be taken).

NCERT Solutions for Class 10 Maths Chapter 14 Statistics

Mean, median and mode of grouped data (a bimodal situation to be avoided). Cumulative frequency graph.

NCERT Solutions for Class 10 Maths Chapter 15 Probability

The classical definition of probability. Simple problems on single events (not using set notation).

All the 15 chapters have been covered in the most systematic manner following the latest standards followed by NCERT i.e. National Council for education and Research Training.

NCERT text books are being followed and adopted across all the major CBSE and State schools in India. Without covering NCERT textbooks, your preparation for Board Exam is incomplete.

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Class 10 Maths NCERT Solutions Chapter 15: All the Solutions pertaining to NCERT Class 10 Maths Chapter Probability acts as a Study Material to students preparing for their board exams. Prepare effectively for the exam by downloading the free PDF for NCERT Solutions Maths Class 10 Chapter 15. Subject experts prepared the NCERT Solutions for Class 10 Maths Probability as per the latest NCERT Textbooks to assist the students in scoring max. marks. Furthermore, Maths Class 10 Chapter 15 Probability Solutions are provided in Hindi and English Mediums for your comfort.

Solutions to all the questions are given in a detailed way so that it is easy for you to understand. Go through the Topics and Subtopics list existing here for the CBSE Class 10 Maths Chapter Probability so that you will have an idea of what to cover during your preparation. Revise the concepts thoroughly and excel in the board examination with the NCERT Class 10 Maths Solutions Chapter 15 Probability. Complete your assignments and homework in time with the NCERT Solutions provided for all the exercises(15.1, 15.2).

Topics and Subtopics listed for Class 10 Maths Chapter Probability

Name of the Section	Name of the Topic
15	Probability
15.1	Introduction
15.2	A theoretical approach
15.3	Summary

NCERT Solutions for Class 10 Maths Chapter 15 – Probability

We tried providing the Class 10 Maths NCERT Solutions Chapter Probability and they will be of extreme help during your preparation for the board exams. Step by step solutions provided for CBSE Class 10 Maths Probability will make complex fundamentals too simple. All the Important Questions, Multiple Choice Questions, Notes prepared here aids you in scoring you maximum marks. Get to know the methods used for solving the problems and apply them further in your board examination so that you won’t feel any difficulty.

Class	10
Subject	Maths
Book	Mathematics
Chapter Number	15
Chapter Name	Probability

Class 10 Maths NCERT Solutions Chapter 15 Probability Ex 15.1

Class 10 Maths NCERT Solutions Chapter 15 Probability Ex 15.2

NCERT Class 10 Maths Solutions Chapter 15 – Solved Exercises

Download the Class 10 Maths NCERT Solutions for Probability PDF and avail it offline so that it stays handy for you to practice. All the Questions given related to Probability are in a detailed manner and simple to understand. We gave the NCERT Solutions with an aim to help students understand difficult problems too with ease. You can practice the Maths Class 10 NCERT Solutions Chapter 15 Probability Exercises 15.1, 15.2 to know the various kind of questions being asked in exams.

Total Weightage from NCERT Class 10 Maths Chapter 15 Probability is 4 Marks. Out of which there will be 2 two mark questions. You need to concentrate on problems related to dice, cards, coin. All three topics are important and you will get questions mostly on this.

After going through the Class 10 Maths NCERT Solutions you will get in-depth knowledge on Chapter Probability. Clarify all your doubts by referring to the CBSE Maths Class 10 Solutions Chapter Probability. Revise the Complete Syllabus by making use of Multiple Choice Questions, Important Questions as well as Formulas prevailing on this page.

We believe the information shared related to Class 10 Maths NCERT Solutions Chapter 15 helps you stay updated and top in board exams. If you have any queries or doubts feel free to reach us via the comment section and we will be of your help at the soonest possible.

Class 10 Maths NCERT Solutions Chapter 14: Students can get through the concepts well with the chapter 14 statistics solutions. Make your preparation effective with the stepwise solutions provided for all the Exercises(14.1, 14.2, 14.3, 14.4). On Practicing the CBSE Class 10 Maths Chapter 14 Statistics you can score max. marks as it has more weightage. Apart from this, we tried providing you the handy NCERT Solutions for Class 10 Maths Chapter 14 Statistics in both Hindi and English Mediums. Have an insight into Topics and Subtopics that comes under CBSE Class 10 Maths Chapter Statistics. Our experts prepared the Class 10 Maths Statistics Solutions by adhering to the Latest NCERT Syllabus and Guidelines. Download the Maths Class 10 NCERT Solutions Chapter 14 PDF and avail it as often you wish. Students following UP, MP, CBSE, Gujarat, Bihar Boards Curriculum can use these NCERT Solutions as all of them prefer NCERT Textbooks. Brainstorm and Mindmap the Formulas, Notes, Important Questions prevailing here in order to score maximum marks. Topics and Subtopics for Class 10 Maths Chapter 14 Statistics

Name of the Section	Name of the Topic
14	Statistics
14.1	Introduction
14.2	Mean of Grouped Data
14.3	Mode of Grouped Data
14.4	Median of Grouped Data
14.5	Graphical Representation of Cumulative Frequency Distribution
14.6	Summary

NCERT Solutions for Class 10 Maths Chapter 14 – Statistics

Students can refer to the NCERT Class 10 Maths Solutions for Statistics at any point of time during their preparation and it can be of great help. You will get an elaborate explanation for everything so that you will not face any difficulty in solving the complex problems too. Practice number of Exemplar Problems, Multiple Choice Questions for various topics that come under Chapter Statistics so that it is easy for you to clear the exam.

Class	10
Subject	Maths
Book	Mathematics
Chapter Number	14
Chapter Name	Statistics

Class 10 Maths NCERT Solutions Chapter 14 Statistics Ex 14.1

Class 10 Maths NCERT Solutions Chapter 14 Statistics Ex 14.2

Class 10 Maths NCERT Solutions Chapter 14 Statistics Ex 14.3

Class 10 Maths NCERT Solutions Chapter 14 Statistics Ex 14.4

NCERT Solutions Class 10 Maths Chapter 14 – Solved Exercises

CBSE Class 10 Maths Chapter 14 Statistics Exercise Solutions(14.1,14.2,14.3, 14.4) gives you a complete grip on concepts. All the Solutions given here contain a detailed explanation and can help during your revision thereby you can score good marks. Brush up the concepts and brainstorm related formulas before attempting the exam as they can be of great help in your examination.

Total Weightage from the Class 10 Maths Chapter Statistics is 7 Marks. You will have a 3 Mark Question and 4 Mark Question from this chapter. Important Topics you need to pay attention is finding mean, median, mode and the other is finding x or y value if mean and median are given.

Study Materials, Notes, Important Questions, Exemplar Problems prevailing here related to NCERT Class 10 Maths Solutions help you revise the entire syllabus thoroughly. You can rely on the Maths Class 10 NCERT Solutions for Statistics as they are up to date and prepared as per the guidelines of Latest NCERT Textbooks followed by many boards.

Hope, we have provided adequate data regarding Class 10 Maths NCERT Solutions Chapter 14. If you feel any information to be added do revert back to us with the necessary suggestions and we will try to add them.

Class 10 Maths NCERT Solutions Chapter 13: Detailed solutions for all the exercises(13.5,13.4,13.3, 13.2, 13.1) in Chapter 13 are provided here for your convenience. Make use of the CBSE Class 10 Maths Solutions Surface Areas and Volumes given in  PDF format which is easy to download. Apart from this, you will get to know about the Exemplar Problems, Important Questions and notes in regards to CBSE NCERT Class 10 Maths Chapter 13 Surface Areas and Volumes. Avail the Class 10 Maths NCERT Solutions for Surface Areas and Volumes In both Hindi and English Mediums. You can even have an overview of the Topics and Subtopics that fall under Surface Areas and Volumes.

All the Maths Class 10 NCERT Solutions Chapter 13 is solved and explained in a detailed way. The NCERT Solutions prepared by our experts are in the Context of NCERT Syllabus and guidelines followed by most of the boards like UP, MP, Bihar, Gujarat, CBSE. Class 10 Maths NCERT Solutions for Surface Areas and Volumes present here act as a reference for students preparing for their board examination. Revise and solve the important questions with the handy NCERT Solutions made available for you.

Topics and Subtopics of Class 10 Maths Surface Areas and Volumes

Name of the Section	Name of the Topic
13	Surface Areas ad Volumes
13.1	Introduction
13.2	Surface Area of a Combination of Solids
13.3	Volume of a Combination of Solids
13.4	Conversion of Solid from one shape to another
13.5	Frustum of a Cone
13.6	Summary

NCERT Class 10 Maths Solutions Chapter 13 – Surface Areas and Volumes

You can have Class 10 Maths NCERT Solutions Chapter 13 all in one place. You need not search anywhere as you will have a glimpse of everything like questions, exemplar problems, Formulas related to CBSE Class 10 Maths Chapter 13 Surface Areas and Volumes. Get to know the detailed explanation for all the Exercises 13.1, 13.2, 13.3, 13.4, 13.5 by referring further. Practice all of the Solutions and gain confidence so that you clear the board examination with ease.

Class	10
Subject	Maths
Book	Mathematics
Chapter Number	13
Chapter Name	Surface Areas and Volumes

Class 10 Maths NCERT Solutions Chapter 13 Surface Areas and Volumes Ex 13.1

Class 10 Maths NCERT Solutions Chapter 13 Surface Areas and Volumes Ex 13.2

Class 10 Maths NCERT Solutions Chapter 13 Surface Areas and Volumes Ex 13.3

Class 10 Maths NCERT Solutions Chapter 13 Surface Areas and Volumes Ex 13.4

Class 10 Maths NCERT Solutions Chapter 13 Surface Areas and Volumes Ex 13.5

Maths NCERT Solutions Class 10 Chapter 13 – Solved Exercises

NCERT Class 10 Maths Chapter 13 deals with the questions on finding the Surface areas and volumes of different shapes such as Cone, Cylinder, Sphere, etc. In addition, to these, you will find problems on the conversion of solid from one shape to another shape and finding the surface area and volumes of the new shape formed. Students will understand the concepts of areas and volumes better with the detailed NCERT Class 10 Maths Solutions of Chapter 13.

Total Weightage from the Chapter Surface Areas and Volumes is 7 Marks. You will get one 3 Mark Question and one 4 Mark Question from this Chapter. Frustum of Cone is an important topic in this Chapter so practice it well. Step by step solutions provided for CBSE Class 10 Maths Chapter 13 helps the students complete their assignments and homework in time.

Download the CBSE Maths Class 10 Solutions Chapter 13 Surface Areas and Volumes PDF that helps you in efficient preparation for the board examination. Quality Solutions prepared here as per the Latest NCERT Syllabus and Textbooks will help you in acquiring max. marks.

We wish the step by step Class 10 Maths NCERT Solutions Chapter 13 provided above help you tackle the NCERT Syllabus and crack the Board Examination with ease. For further queries do reach us via the comment section and we will try our best to resolve them at the earliest.

Class 10 Maths NCERT Solutions Chapter 12: Students can take help from the NCERT Class 10 Maths Chapter 12 Solutions existing here for their board examination. Go through the concepts, important questions, and formulas that come under the CBSE Class 10 Maths Areas related to Circles and score good marks. Avail the Topics and Subtopics that fall under the NCERT Class 10 Maths Chapter 12 Areas related to Circles. To make it convenient for you we have jotted down the Maths NCERT Class 10 Solutions Chapter 12 in both Hindi and English Mediums.

Solutions by our experts are prepared strictly following the standards and guidelines as per the Latest NCERT Syllabus and Textbooks. You can avail the Maths Class 10 NCERT Solutions Areas related to Circles PDF and use it offline whenever you wish to practice. Revise and Complete all the CBSE Class 10 Maths NCERT Solutions Chapter 12 here to have a better understanding of concepts. Get to know the detailed and step by step solutions for NCERT Class 10 Maths Chapter 12  by going through further.

Topics and Subtopics of NCERT Class 10 Maths Areas related to Circles

Name of the Section	Name of the Topic
12	Areas Related to Circles
12.1	Introduction
12.2	Perimeter and Area of Circle – A Review
12.3	Areas of Sector and Segment of a Circle
12.4	Areas of Combinations of Plane Figures
12.5	Summary

NCERT Class 10 Maths Solutions Chapter  12 – Areas Related to Circles

Class 10 Maths NCERT Solutions Chapter 12 Areas Related to Circles prevailing here helps you practice all the concepts with ease and score well in the Board Examination. Make use of the Study Material, Notes, and Important Questions regarding the CBSE Class 10 Maths Chapter Areas Related to Circles and understand the concepts in a better way. You will understand how to approach and solve the problem after practicing various questions.

Class	10
Subject	Maths
Book	Mathematics
Chapter Number	12
Chapter Name	Areas Related to Circles

Class 10 Maths NCERT Solutions Chapter 12 Areas related to Circles Ex 12.1

Class 10 Maths NCERT Solutions Chapter 12 Areas related to Circles Ex 12.2

Class 10 Maths NCERT Solutions Chapter 12 Areas related to Circles Ex 12.3

NCERT Solutions Class 10 Maths Chapter 12 – Solved Exercises

Areas Related to Circles Solutions Class 10 Maths is useful in your exam preparation and revision. You can brush up the concepts with the Study Material, Important Questions, Exemplar Problems related to Chapter 12. Moreover, you can have an idea of what type of questions will appear in the examination thereby score max. marks.

NCERT Maths Class 10 Solutions for Exercises 12.1, 12.2, 12.3, 12.4 prevailing here in an elaborate manner makes it simple for you to understand even complex fundamentals. Total weightage from Class 10 Maths Chapter 12 is 3 Marks and it is a 3 Mark Question. CBSE Chapter 12 Areas related to circles include questions like how to find the area of different circular shaped objects. One can solve questions from this chapter easily if they are aware of the basics of circles and areas related to circles.

Start solving problems by understanding the concept and paying attention to accuracy as well as speed so that it becomes simple for you in the Board Examination. Improve your conceptual knowledge by practicing more questions that come under this chapter. This way, your confidence is also built and you will score the maximum marks in the Board Exam.

Hoping that the data shared regarding Class 10 Maths NCERT Solutions Chapter 12 as far as our knowledge is concerned has been beneficial to an extent. In case of any additional information being required feel free to drop a comment and let us know. We will try to clarify your doubts as soon as possible.

Class 10 Maths NCERT Solutions Chapter 11: You will find solutions related to CBSE Class 10 Maths Chapter 11 Constructions. Furthermore, you will get an idea after referring to the NCERT Class 10 Maths Solutions Chapter 11 Exercises 11.1,11.2, 11.3, 11.4 prevailing on this page. Download the Maths Class 10 NCERT Chapter 11 Solutions PDF available free of cost and use whenever you want. All the solutions are prepared by our experts keeping in mind the standards and guidelines as per the Latest NCERT Textbooks.

Going through the Class 10 Maths NCERT Solutions for Constructions helps you get a better understanding of the concepts and the methods used for approach. Clarify your doubts in regards to important questions, Formulas with the notes present related to NCERT Class 10 Maths Solutions Chapter 11 Constructions. Avail the topis and subtopics listed under CBSE Class 10 Maths Chapter 11 Constructions to have an overview of what to prepare.

Topics and Subtopics listed under Constructions

Name of the Section	Name of the Topic
11	Constructions
11.1	Introduction
11.2	Division of a line segment
11.3	Construction of tangents to a circle
11.4	Summary

NCERT Class 10 Maths Solutions Chapter 11 – Constructions

We tried providing you the Class 10 Maths NCERT  Solutions Chapter 11 both in Hindi and English Mediums which can be of extreme help during your assignments and homework. Detailed solutions are given for Various Questions that come under Constructions. Working on these Exemplar Problems and notes can help you score good marks in your Board Examination. Practice more and more NCERT Maths Class 10 Solutions Chapter 11 Constructions and attempt the exam with confidence.

Class	10
Subject	Maths
Book	Mathematics
Chapter Number	11
Name of the Chapter	Constructions

Class 10 Maths NCERT Solutions Chapter 11 Constructions Ex 11.1

Class 10 Maths NCERT Solutions Chapter 11 Constructions Ex 11.2

Maths NCERT Solutions Class 10 Chapter 11 – Solved Exercises

The NCERT Solutions provided here helps the students of UP, MP and CBSE Boards as they are implementing NCERT Textbooks. In addition, we gave the NCERT Class 10 Maths Chapter 11 Solutions in both Hindi and English Medium so that you can pick anything of your choice. Revise and brush up the concepts of NCERT Class 10 Maths Chapter Constructions and score well. Division of line segment and construction of tangents to a circle falls under this chapter.

Total weightage from Chapter 11 Constructions is 4 Marks. You will get a 4 Mark Question from this chapter and Similar Triangles Concept is important and practice it well. Make sure to go through all the exercises of Class 10 Maths NCERT Solutions for Chapter 11 Constructions 11.1, 11.2, 11.3, 11.4 existing here as they can be of help.

Before going to the exam, brainstorm the important questions, notes, and formulas regarding Chapter 11 Constructions. As we have provided step by step solutions, complex fundamentals too become simple for you. Accelerate your exam preparation with the CBSE Class 10 Maths Constructions Solutions that are easy to understand.

Now that you have gone through the Class 10 Maths NCERT Solutions Chapter 11 we wish you got little idea on concepts to cover for your exam. If you need any further assistance regarding NCERT Class 10 Maths Chapter 11 Solutions drop us a comment and we will try to resolve your queries.