# NCERT Solutions for Class 10 Maths

## NCERT Solutions for Class 10 Maths PDF Updated for 2021-22 Session

**NCERT Solutions for Class 10 Maths** for all the exercises from Chapters 1 to 15 are provided here. These NCERT Solutions are curated by our expert faculty to help students in their board exam preparations. Students looking for the **NCERT Solutions of Class 10 Maths** can download all chapter-wise pdf to find a better approach to solve the problems.

The answers to the questions present in the NCERT books are undoubtedly the best study material a student can get hold of. These CBSE **NCERT Solutions for Class 10 Maths** 2021-22 will also help students to build a deeper understanding of concepts covered in Class 10 Maths textbook. Practising the textbook questions will help students analyze their level of preparation and the knowledge of concepts. The NCERT Solutions to these questions present in the books can help students to clear their doubts quickly.

NCERT Solutions Class 10 Maths ChaptersNCERT Solutions Class 10 Maths Chapter DetailsCBSE Class 10 Maths Exam Pattern 2020-2021CBSE Class 10 Chapter-wise Marks WeightageCBSE Question Paper Design

## NCERT Solutions Class 10 Maths Chapters

- Chapter 1 Real Numbers
- Chapter 2 Polynomials
- Chapter 3 Pair of Linear Equations in Two Variables
- Chapter 4 Quadratic Equations
- Chapter 5 Arithmetic Progressions
- 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 Areas Related to Circles
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability

### NCERT Solutions for Class 10 Maths Free PDF Download

The NCERT Solution of Class 10 Maths list comprises all the chapter-wise answers to the questions present in the **NCERT Book for Class 10 Maths** written in a very precise and lucid manner, maintaining the objective of textbooks. The students can refer to the NCERT Solutions for Class 10 as their additional references and study materials. Practising NCERT textbook exercises solutions will surely help the students in their preparation for the examination.

## NCERT Solutions Class 10 Maths Chapter Details and Exercises

### NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

In Chapter 1 of Class 10, students will explore real numbers and irrational numbers. The chapter starts with the Euclid’s Division Lemma which states that “Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0≤r<b”. The Euclid’s Division algorithm is based on this lemma and is used to calculate the HCF of two positive integers. Then, the Fundamental Theorem of Arithmetic is defined which is used to find the LCM and HCF of two positive integers. After that, the concept of an irrational number, a rational number and decimal expansion of rational numbers are explained with the help of theorem.

*Topics Covered in Class 10 Maths Chapter 1 Real Numbers:*

*Topics Covered in 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 irrationality of **√**2, **√**3, **√**5 Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

Class 10 Maths NCERT Solutions PDF Chapter 1 Exercises |
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☞NCERT Solutions Real Numbers Class 10 Exercise 1.1 – 5 Questions (4 Long Answers, 1 Short Answer) |

☞NCERT Solutions Real Numbers Class 10 Exercise 1.2 – 7 Questions (4 Long Answers, 3 Short Answers) |

☞NCERT Solutions Real Numbers Class 10 Exercise 1.3 – 3 Questions (3 Short Answers) |

☞NCERT Solutions Real Numbers Class 10 Exercise 1.4 – 3 Questions (3 Short Answers) |

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

- NCERT Real Numbers Class 10 Notes
- Real Numbers Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Real Numbers
- RD Sharma Solutions Real Numbers Class 10

### NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

In Polynomials, the chapter begins with the definition of degree of the polynomial, linear polynomial, quadratic polynomial and cubic polynomial. This chapter has a total of 4 exercises including an optional exercise. Exercise 2.1 includes the questions on finding the number of zeroes through a graph. It requires the understanding of Geometrical Meaning of the Zeroes of a Polynomial. Exercise 2.2 is based on the Relationship between Zeroes and Coefficients of a Polynomial where students have to find the zeros of a quadratic polynomial and in some of the questions they have to find the quadratic polynomial. In Exercise 2.3, the concept of division algorithm is defined and students will find the questions related to it. The optional exercise, 2.4 consists of the questions from all the concepts of Chapter 2.

**Topics Covered in Class 10 Maths Chapter 2 Polynomials:**

**Topics Covered in Class 10 Maths Chapter 2 Polynomials:**

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithms for polynomials with real coefficients.

Class 10 Maths NCERT Solutions PDF Chapter 2 Exercises |
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☞NCERT Solutions Polynomials Class 10 Exercise 2.1 – 1 Question (1 Short Answer) |

☞NCERT Solutions Polynomials Class 10 Exercise 2.2 – 2 Questions (2 Short Answers) |

☞NCERT Solutions Polynomials Class 10 Exercise 2.3 – 5 Questions (2 Short Answers, 3 Long Answers) |

☞NCERT Solutions Polynomials Class 10 Exercise 2.4 – 5 Questions (2 Short Answers, 3 Long Answers) |

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

- NCERT Polynomials Class 10 Notes
- Polynomials Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Polynomials
- RD Sharma Solutions Polynomials Class 10

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

This chapter explains the concept of Pair of Linear Equations in Two Variables. This chapter has a total of 7 exercises, and in these exercises, different methods of solving the pair of linear equations are described. Exercise 3.1 describes how to represent a situation algebraically and graphically. Exercise 3.2 explains the methods of solving the pair of the linear equation through Graphical Method. Exercises 3.3, 3.4, 3.5 and 3.6 describe the Algebraic Method, Elimination Method, Cross-Multiplication Method, Substitution Method, respectively. Exercise 3.7 is an optional exercise which contains all types of questions. Students must practise these exercises to master the method of solving the linear equations.

*Topics Covered in Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables:*

*Topics Covered in Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables:*

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for the number of solutions. The solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method. Simple situational problems. Simple problems on equations reducible to linear equations.

Class 10 Maths NCERT Solutions PDF Chapter 3 Exercises |
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☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.1 – 3 Questions (2 Short Answers, 1 Long Answer) |

☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.2 – 7 Questions (5 Short Answers, 2 Long Answers) |

☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.3 – 3 Questions (2 Short Answers, 1 Long Answer) |

☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.4 – 2 Questions (2 Long Answers) |

☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.5 – 4 Questions (4 Short Answers) |

☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.6 – 2 Questions (2 Long Answers) |

☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.7 – 8 Questions (1 Short Answer, 7 Long Answers) |

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

- NCERT Pair of Linear Equations in Two Variables Class 10 Notes
- Pair of Linear Equations in Two Variables Class 10 Important Questions,
- NCERT Exemplar Solutions Class 10 Pair of Linear Equations in Two Variables
- RD Sharma Solutions Pair of Linear Equations in Two Variables Class 10

### NCERT Solutions of Class 10 Maths Chapter 4 Quadratic Equations

In this chapter, students will get to know the standard form of writing a Quadratic Equation. The chapter goes on to explain the method of solving the quadratic equation through the factorization method and completing the square method. The chapter ends with the topic on finding the nature of roots which states that, a quadratic equation ax² + bx + c = 0 has

- Two distinct real roots, if b² – 4ac > 0
- Two equal roots, if b² – 4ac = 0
- No real roots, if b² – 4ac < 0

**Topics Covered in Class 10 Maths Chapter 4 Quadratic Equations:**

**Topics Covered in Class 10 Maths Chapter 4 Quadratic Equations:**

Standard form of a quadratic equation ax^{2} + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization; and by using the quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.

Class 10 Maths NCERT Solutions PDF Chapter 4 Exercises |
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☞NCERT Solutions Maths Quadratic Equations Class 10 Exercise 4.1 – 2 Questions (1 Short Answer, 1 Long Answer) |

☞NCERT Solutions Maths Quadratic Equations Class 10 Exercise 4.2 – 6 Questions (6 Short Answers) |

☞NCERT Solutions Maths Quadratic Equations Class 10 Exercise 4.3 – 11 Questions (8 Short Answers, 3 Long Answers) |

☞NCERT Solutions Maths Quadratic Equations Class 10 Exercise 4.4 – 5 Questions (2 Short Answers, 3 Long Answer) |

*Also access the following resources for NCERT Class 10 Chapter 4 Quadratic Equations at BYJU’S:*

- NCERT Quadratic Equations Class 10 Notes
- Quadratic Equations Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Quadratic Equations
- RD Sharma Solutions Quadratic Equations Class 10

### NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions

This chapter introduces students to a new topic that is Arithmetic Progression, i.e. AP. The chapter constitutes a total of 4 exercises. In Exercise 5.1, students will find the questions related to representing a situation in the form of AP, finding the first term and difference of an AP, finding out whether a series is AP or not. Exercise 5.2 includes the questions on finding out the nth term of an AP by using the following formula;

a_{n }= a + (n-1) d

The next exercise i.e., 5.3, contains the questions on finding the sum of first n terms of an AP. The last exercise includes higher-level questions based on AP to enhance students’ analytical and problem-solving skills.

**Topics Covered in Class 10 Maths Chapter 5 Arithmetic Progressions:**

**Topics Covered in Class 10 Maths Chapter 5 Arithmetic Progressions:**

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

Class 10 Maths NCERT Solutions PDF Chapter 5 Exercises |
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☞NCERT Solutions Class 10 Maths Arithmetic Progressions Exercise 5.1 – 4 questions (1 Short Answer, 3 Long Answers) |

☞NCERT Solutions Class 10 Maths Arithmetic Progressions Exercise 5.2 – 20 questions (10 Short Answers, 10 Long Answers) |

☞NCERT Solutions Class 10 Maths Arithmetic Progressions Exercise 5.3 – 20 Questions (7 Short Answer, 13 Long Answers) |

☞NCERT Solutions Class 10 Maths Arithmetic Progressions Exercise 5.4 – 5 Questions (5 Long Answers) |

*Also access the following resources for NCERT Class 10 Chapter 5 Arithmetic Progressions at BYJU’S:*

- NCERT Arithmetic Progressions Class 10 Notes
- Arithmetic Progressions Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Arithmetic Progressions
- RD Sharma Solutions Arithmetic Progressions Class 10

### NCERT Solutions for Class 10 Maths Chapter 6 Triangles

In Chapter 6 of Class 10 CBSE Maths, students will study those figures which have the same shape but not necessarily the same size. The chapter Triangles starts with the concept of a similar and congruent figure. It further explains the condition for the similarity of two triangles and theorems related to the similarity of triangles. After that, the areas of similar triangles have been explained with a theorem. At the end of this chapter, the Pythagoras Theorem and converse of Pythagoras Theorem is described.

*Topics Covered in Class 10 Maths Chapter 6 Triangles:*

*Topics Covered in Class 10 Maths Chapter 6 Triangles:*

Definitions, examples, counter-examples of similar triangles.

- (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.
- (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
- (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
- (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
- (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.
- (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.
- (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
- (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
- (Prove) In a triangle, if the square on one side is equal to the sum of the squares on the other two sides, the angle opposite to the first side is a right angle.

Class 10 Maths NCERT Solutions PDF Chapter 6 Exercises |
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☞Triangles Class 10 Exercise 6.1 – 3 Questions (3 Short Answers) |

☞Triangles Class 10 Exercise 6.2 – 10 Questions (9 Short Answers, 1 Long Answer) |

☞Triangles Class 10 Exercise 6.3 – 16 Questions (12 Short Answers, 4 Long Answers) |

☞Triangles Class 10 Exercise 6.4 – 9 Questions (7 Short Answers, 2 Long Answers) |

☞Triangles Class 10 Exercise 6.5 – 17 Questions (15 Short Answers, 2 Long Answers) |

☞Triangles Class 10 Exercise 6.6 – 10 Questions (5 Short Answers, 5 Long Answers) |

*Also access the following resources for NCERT Class 10 Chapter 6 Triangles at BYJU’S:*

- NCERT Triangles Class 10 Notes
- Triangles Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Triangles
- RD Sharma Solutions Triangles Class 10

### NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

In this chapter, students will learn how to find the distance between two points whose coordinates are given, and to find the area of the triangle formed by three given points. Along with this, students will also study how to find the coordinates of the point which divides a line segment joining two given points in a given ratio. For this purpose, students will get introduced to Distance Formula, Section Formula and Area of a Triangle in this chapter of Coordinate Geometry.

**Topics Covered in Class 10 Maths Chapter 7 Coordinate Geometry:**

**Topics Covered in Class 10 Maths Chapter 7 Coordinate Geometry:**

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

Class 10 Maths NCERT Solutions PDF Chapter 7 Exercises |
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☞Coordinate Geometry Class 10 Exercise 7.1 – 10 Questions (3 Short Answers, 7 Long Answer) |

☞Coordinate Geometry Class 10 Exercise 7.2 – 10 Questions (2 Short Answers, 8 Long Answer) |

☞Coordinate Geometry Class 10 Exercise 7.3 – 5 Questions (2 Short Answers, 3 Long Answer) |

☞Coordinate Geometry Class 10 Exercise 7.4 – 8 Questions (3 Short Answers, 5 Long Answer) |

*Also access the following resources for NCERT Class 10 Chapter 7 Coordinate Geometry at BYJU’S:*

- NCERT Coordinate Geometry Class 10 Notes
- Coordinate Geometry Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Coordinate Geometry
- RD Sharma Solutions Coordinate Geometry Class 10

### NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

This chapter will introduce students to Trigonometry. They will study some ratios of a right triangle with respect to its acute angles, called trigonometric ratios of the angles. The chapter also defines the trigonometric ratios for angles of 0^{0} and 90^{0}. Further, students will also know how to calculate trigonometric ratios for some specific angles and establish some identities involving these ratios, called trigonometric identities.

*Topics Covered in Class 10 Maths Chapter 8 Introduction to Trigonometry:*

*Topics Covered in Class 10 Maths Chapter 8 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 of the trigonometric ratios of 30^{o}, 45^{o} and 60^{o}. Relationships between the ratios. Proof and applications of the identity sin^{2}A + cos^{2}A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

Class 10 Maths NCERT Solutions PDF Chapter 8 Exercises |
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☞Introduction to Trigonometry Class 10 Exercise 8.1 – 11 Questions (8 Short Answers, 3 Long Answers) |

☞Introduction to Trigonometry Class 10 Exercise 8.2 – 4 Questions (2 Short Answers, 2 Long Answers) |

☞Introduction to Trigonometry Class 10 Exercise 8.3 – 7 Questions (5 Short Answers, 2 Long Answers) |

☞Introduction to Trigonometry Class 10 Exercise 8.4 – 5 Questions (3 Short Answers, 2 Long Answers) |

*Also access the following resources for NCERT Class 10 Chapter 8 Trigonometry at BYJU’S: *

- NCERT Introduction to Trigonometry Class 10 Notes
- Introduction to Trigonometry Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Introduction to Trigonometry
- RD Sharma Solutions Introduction to Trigonometry Class 10

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

This chapter is the continuation of the previous chapter as here the students will study the applications of trigonometry. It is used in geography, navigation, construction of maps, determining the position of an island in relation to the longitudes and latitudes. In this chapter, students will see how trigonometry is used for finding the heights and distances of various objects, without actually measuring them. They will get introduced to the term line of sight, angle of elevation, angle of depression.

**Topics Covered in Class 10 Maths Chapter 9 Some Applications of Trigonometry:**

**Topics Covered in Class 10 Maths Chapter 9 Some Applications of Trigonometry:**

Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30°, 45°, 60°.

Class 10 Maths NCERT Solutions PDF Chapter 9 Exercise |
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☞Some Applications of Trigonometry Class 10 Exercise 9.1 – 16 Questions (16 Long Answers) |

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*Also access the following resources for NCERT Class 10 Chapter 9 Some Applications of Trigonometry at BYJU’S: *

- NCERT Some Applications of Trigonometry Class 10 Notes
- Some Applications of Trigonometry Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Some Applications of Trigonometry
- RD Sharma Solutions Some Applications of Trigonometry Class 10

### NCERT Solutions for Class 10 Maths Chapter 10 Circles

In earlier classes, students have studied about a circle and various terms related to a circle such as a chord, segment, arc, etc. In this chapter, students will study the different situations that arise when a circle and a line are given in a plane. So, they will get thorough with the concept of Tangent to a Circle and Number of Tangents from a Point on a Circle.

*Topics Covered in Class 10 Maths Chapter 10 Circles:*

*Topics Covered in Class 10 Maths Chapter 10 Circles:*

Tangent to a circle at, point of contact.

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

Class 10 Maths NCERT Solutions PDF Chapter 10 Exercises |
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☞Circles Class 10 Exercise 10.1 – 4 Questions (2 Short Answer, 2 Long Answers) |

☞Circles Class 10 Exercise 10.2 – 13 Questions (2 Short Answers, 14 Long Answers) |

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

- NCERT Circles Class 10 Notes
- Circles Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Circles
- RD Sharma Solutions Circles Class 10

### NCERT Solutions for Class 10 Maths Chapter 11 Constructions

This chapter consists of a total of 2 exercises. Whatever students have learned about construction in earlier classes will also help them. In Exercise 11.1, students will study how to divide a line segment, whereas in Exercise 11.2 they will study the construction of tangents to a circle. Methods and steps for construction are explained and also some examples are additionally given to make it clearer to the students.

*Topics Covered in Class 10 Maths Chapter 11 Constructions:*

*Topics Covered in Class 10 Maths Chapter 11 Constructions:*

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

Class 10 Maths NCERT Solutions PDF Chapter 11 Exercises |
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☞Constructions Class 10 Exercise 11.1 – 7 Questions (7 Long Answers) |

☞Constructions Class 10 Exercise 11.2 – 7 Questions (7 Long Answers) |

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

- NCERT Constructions Class 10 Notes
- Constructions Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Constructions
- RD Sharma Solutions Constructions Class 10

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

This chapter begins with the concepts of perimeter and area of a circle. Using this concept, the chapter further explains how to find the area of sector and segment of a circular region. Moreover, students will get clarity on finding the areas of some combinations of plane figures involving circles or their parts.

**Topics Covered in Class 10 Maths Chapter 12 Areas Related to Circles:**

**Topics Covered in 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 the central angle of 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circles should be taken.)

Class 10 Maths NCERT Solutions PDF Chapter 12 Exercises |
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☞Areas Related to Circles Class 10 Exercise 12.1 – 5 Questions (5 Short Answers) |

☞Areas Related to Circles Class 10 Exercise 12.2 – 14 Questions (9 Short Answers, 5 Long Answers) |

☞Areas Related to Circles Class 10 Exercise 12.3 – 16 Questions (9 Short Answers, 7 Long Answers) |

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*Also access the following resources for NCERT Class 10 Chapter 12 Areas Related to Circles at BYJU’S: *

- NCERT Areas Related to Circles Class 10 Notes
- Areas Related to Circles Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Areas Related to Circles
- RD Sharma Solutions Areas Related to Circles Class 10

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

In Chapter 13, there are a total of 5 exercises. The first exercise consists of the questions based on finding the surface area of an object formed by combining any two of the basic solids, i.e cuboid, cone, cylinder, sphere and hemisphere. In Exercise, 13.2 questions are based on finding the volume of objects formed by combining any two of a cuboid, cone, cylinder, sphere and hemisphere. Exercise 13.3 deals with the questions in which a solid is converted from one shape to another. Exercise 13.4 is based on finding the volume, curved surface area and total surface area of a frustum of a cone. The last exercise is optional and has high-level questions based on all the topics of this chapter.

*Topics Covered in Class 10 Maths Chapter 13 Surface Areas and Volumes:*

*Topics Covered in Class 10 Maths Chapter 13 Surface Areas and Volumes:*

- 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.
- Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combinations of not more than two different solids are taken).

Class 10 Maths NCERT Solutions PDF Chapter 13 Exercises |
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☞Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 13.1 – 9 Questions (2 Short Answers, 7 Long Answers) |

☞Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 13.2 – 8 Questions (1 Short Answer, 7 Long Answers) |

☞Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 13.3 – 9 Questions (9 Long Answers) |

☞Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 13.4 – 5 Questions (5 Long Answers) |

☞Solutions of NCERT Maths Class 10 Surface Areas and Volumes Exercise 13.5 – 7 Questions (7 Long Answers) |

*Also access the following resources for NCERT Class 10 Chapter 13 Surface Areas and Volumes at BYJU’S: *

- NCERT Surface Areas and Volumes Class 10 Notes
- Surface Areas and Volumes Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Surface Areas and Volumes
- RD Sharma Solutions Surface Areas and Volumes Class 10

### NCERT Solutions for Class 10 Maths Chapter 14 Statistics

Here, students will learn the numerical representation of ungrouped data to grouped data and finding the Mean, Mode and Median. Also, the concept of cumulative frequency, cumulative frequency distribution and how to draw cumulative frequency curves will be explained.

*Topics Covered in Class 10 Maths Chapter 14 Statistics:*

*Topics Covered in Class 10 Maths Chapter 14 Statistics:*

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

Class 10 Maths NCERT Solutions PDF Chapter 14 Exercises |
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☞NCERT Solutions of Maths Class 10 Statistics Exercise 14.1 – 9 Questions (9 Long Answers) |

☞NCERT Solutions of Maths Class 10 Statistics Exercise 14.2 – 6 Questions (6 Long Answers) |

☞NCERT Solutions of Maths Class 10 Statistics Exercise 14.3 – 7 Questions (7 Long Answers) |

☞NCERT Solutions of Maths Class 10 Statistics Exercise 14.4 – 3 Questions (3 Long Answers) |

*Also access the following resources for NCERT Class 10 Chapter 14 Statistics at BYJU’S: *

- NCERT Statistics Class 10 Notes
- Statistics Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Statistics
- RD Sharma Solutions Statistics Class 10

### NCERT Solutions for Class 10 Maths 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 various examples given to explain it in an effective way. So, before going through the exercise problems students must solve the examples of CBSE Maths first.

*Topics Covered in Class 10 Maths Chapter 15 Probability:*

*Topics Covered in Class 10 Maths Chapter 15 Probability:*

The classical definition of probability. Simple problems on finding the probability of an event.

Class 10 Maths NCERT Solutions PDF Chapter 15 Exercises |
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☞NCERT Solutions of Maths Class 10 Probability Exercise 15.1 – 25 Questions (22 Short Answers, 3 Long Answers) |

☞NCERT Solutions of Maths Class 10 Probability Exercise 15.2 – 5 Questions (5 Short Answers) |

*Also access the following resources for NCERT Class 10 Chapter 15 Probability at BYJU’S: *

- NCERT Probability Class 10 Notes
- Probability Class 10 Important Questions
- NCERT Exemplar Solutions Class 10 Probability
- RD Sharma Solutions Probability Class 10

** NCERT Solutions for Class 10 Maths PDF** in

*English Medium as well as Hindi Medium (हिंदी मीडियम)*for the academic year 2021-22 are not only followed by CBSE but also UP Board, Uttarakhand board and all other boards following NCERT Textbooks.

## CBSE Class 10 Maths Exam Pattern 2020-2021

The Central Board of Secondary Education conducts the CBSE Class 10 Maths Exam for a total of 100 marks where 80 marks are allocated to the theory paper and 20 marks for internal assessment. By going through the CBSE Maths exam pattern 2020-2021 for Class 10, students can understand how the marks are awarded to every answer, based on the steps. The board releases the sample paper and marking scheme before the board exam each year so that students can get well versed with the exam pattern and question paper design. Students who are appearing for the exams must go through the Marking Scheme 2020-2021. According to the CBSE revised pattern, 25% of questions from theory paper are objective questions. While the number of questions has increased, marks per question have been reduced, converting maximum questions to objective types or very short answer type. Here, you can find the CBSE Class 10 Maths Exam pattern.

CBSE Class 10 Maths (Basic and Standard Paper) Marking Scheme | |||

Sections | No. of Questions | Marks per Question | Total Marks |

Section A | 20 Questions | 1 Mark | 20 |

Section B | 6 Questions | 2 Marks | 12 |

Section C | 8 Questions | 3 Marks | 24 |

Section D | 6 Questions | 4 Marks | 24 |

Total | 40 Questions | 80 |

*CBSE Class 10 Chapter-wise Marks Weightage*

Every year the board releases the sample paper and chapter-wise marks weightage before the board exam so that students get well versed with the exam pattern and question paper design. The marking scheme for the exam 2020-2021 is released by the CBSE on the official site. Here, you can find the CBSE Class 10 Chapter-wise marks weightage according to the previous year question papers.

Unit | Marks |

1. Number System | 06 |

2. Algebra | 20 |

3. Coordinate Geometry | 06 |

4. Geometry | 15 |

5. Trigonometry | 12 |

6. Mensuration | 10 |

7. Statistics | 11 |

Total Marks | 80 |

### Question Paper Design- Standard Maths and Basic Maths

#### MATHEMATICS – Standard Question Paper Design Class X (2020-2021)

**Time – 3 hours**

**Max. Marks – 80**

Sl. No. | Typology of Questions | Total Marks | Percentage weightage (approx.) |

1 | Remembering: Having memory of previously studied materials by terms, answers, basic concepts and recalling facts.Understanding: Show understanding of ideas by comparing, organizing, interpreting, translating, describing and stating main ideas | 43 | 54 |

2 | Applying: Solve problems to situations by applying the learnt facts, knowledge, rules and techniques in various ways. | 19 | 24 |

3 | Analysing: Examine the information into parts by recognizing the causes. Make inferences and find evidence to support generalizationsEvaluating: Present opinions by making judgments about the validity of ideas, information or quality of work based on a set of criteria.Creating: Combine information in a different way by grouping elements in a new pattern or creating alternative solutions | 18 | 22 |

Total | 80 | 100 |

Internal Assessment | 20 Marks |

Pen Paper Test and Multiple Assessment (5+5) | 10 Marks |

Portfolio | 05 Marks |

Lab Practical (Lab activities to be done from the prescribed books) | 05 Marks |

#### MATHEMATICS – Basic Question Paper Design Class X (2020-2021)

**Time – 3 hours**

**Max. Marks – 80**

Sl. No. | Typology of Questions | Total Marks | Percentage weightage (approx.) |

1 | Remembering: Having memory of previously studied materials by terms, answers, basic concepts and recalling facts.Understanding: Show understanding of ideas by comparing, organizing, interpreting, translating, describing and stating main ideas | 60 | 75 |

2 | Applying: Solve problems to situations by applying the learnt facts, knowledge, rules and techniques in various ways. | 12 | 15 |

3 | Analysing: Examine the information into parts by recognizing the causes. Make inferences and find evidence to support generalizationsEvaluating: Present opinions by making judgments about the validity of ideas, information or quality of work based on a set of criteria.Creating: Combine information in a different way by grouping elements in a new pattern or creating alternative solutions | 8 | 10 |

Total | 80 | 100 |

Internal Assessment | 20 Marks |

Pen Paper Test and Multiple Assessment (5+5) | 10 Marks |

Portfolio | 05 Marks |

Lab Practical (Lab activities to be done from the prescribed books) | 05 Marks |

### Benefits of NCERT Solutions Class 10 Maths:

The Class 10 NCERT Maths solutions given here in PDFs have several benefits which include:

- The solutions given here are very easy to understand.
- Solutions are provided in steps for better understanding.
- Diagrams are given to help the students in visualizing the solutions.
- All the questions from each chapter are covered.

Students are advised to prepare all the chapters covered in the solution modules, which will eventually help them to gain a deeper knowledge of concepts. For effective preparations, it is essential for students to understand all the steps provided in the solutions.

### How are CBSE Class 10 Maths Solutions of NCERT Helpful for Board Exams?

CBSE Class 10 Maths is an important subject for students. Here, we have provided complete assistance to students for its preparation. Class 10 is the first benchmark for any student that will reflect in the future records of achievement. CBSE always prescribes the NCERT books for board exam preparation.

Exam preparation is a rigorous process that requires an overall understanding of individual chapters. This process demands hard work towards studies and an effective approach to getting through the solutions. This significant role is played by Class 10 **Maths NCERT solutions** to equip students in the preparation of competitive entrance exams. NCERT books are best known for putting forth the concepts in a simple way for better understanding. NCERT Class 10 Books for Mathematics are written in the most lucid and clear manner that helps to break the complex problems in the most efficient way.

Keep visiting to get complete chapter-wise solutions in PDF for all the classes. Students can also find the NCERT Solutions for Class 10 Science, at BYJU’S. Students can download BYJU’S App to get a personalized learning experience and prepare for the exams more effectively.

## Frequently Asked Questions on **NCERT Solutions for Class 10 Maths**

### How to grasp the important concepts covered in the **NCERT Solutions for Class 10 Maths**?

Students who aspire to score good marks in the Class 10 exams are advised to download the NCERT Solutions from BYJU’S. The solutions are curated with utmost care by a set of faculty having vast experience in the respective subject. Each and every minute detail is explained in an interactive manner to make it easier for the students while learning. The step wise solutions are designed by keeping in mind the marks weightage allotted as per the CBSE guidelines.

### Will the **NCERT Solutions for Class 10 Maths** help me to solve the problems easily?

The Class 10 exam is one of the major turning points in the life of students. Mathematics is the subject which mainly contains numericals and understanding of concepts which helps to score more marks. Students are recommended to first understand the syllabus for the academic year and learn the concepts based on them for a better performance. Solving the textbook problems by referring to the solutions PDF will improve the logical thinking and analytical skills among students.

### Where will I get the **NCERT Solutions for Class 10 Maths** PDF?

Students can get the** NCERT Solutions for Class 10 Maths** PDF on BYJU’S. The solutions are prepared by the subject matter experts keeping in mind the understanding capacity of students. The main objective of creating solutions is to help students learn the complex concepts without any difficulty. Students can also cross check their answers while solving the textbook problems to get an idea about the other methods of answering the questions efficiently.

### Are the **NCERT Solutions for Class 10 Maths** useful for the students under the CBSE board?

Given below are some of the uses of the **NCERT Solutions for Class 10 Maths** –

1. It builds a strong foundation of fundamental concepts and improves confidence to face the board exams.

2. The method of solving complex problems can be learnt easily.

3. It is a perfect study material for the students to finish their assignments on time and to score more marks in the board exams.

### How to get an idea about the important concepts in the **NCERT Solutions for Class 10 Maths**?

Before the start of an academic year, students should download the CBSE syllabus and go through it for a clear idea about the concepts which are important for the exams. Students must solve the NCERT Textbook problems by choosing a correct study material which satisfies their needs. Practising the problems on a regular basis by referring to the **NCERT Solutions for Class 10 Maths** improves the problem solving abilities of students.

### Is the BYJU’S **NCERT Solutions for Class 10 Maths** important?

The **NCERT Solutions for Class 10 Maths** at BYJU’S are created in such a way that the students can grasp the concepts and clear their doubts instantly. The solutions contain comprehensive explanations to make the subject more interesting for the students. The PDF of solutions can be accessed by the students from BYJU’S and can be used to improve their conceptual knowledge.

### Is the **NCERT Solutions for Class 10 Maths** the best reference guide for the CBSE students?

Among the numerous study materials available in the market, students should select the right one based on their requirements. The **NCERT Solutions for Class 10 Maths** from BYJU’S is considered to be the best reference guide for the CBSE students. The solutions are available in both chapter wise and exercise wise format which can be downloaded and used by the students. The links of the PDF can be accessed by the students without any time constraints.