NCERT Solutions Class 10 Mathematics 2025: Download Chapter-wise Solutions PDF

NCERT Solutions Class 10 Mathematics for all chapters is available here free download. Students can use the pdf links provided in this article to download the Class 10 NCERT Mathematics Chapter-by-Chapter solutions. Students studying for the board exam will find the Mathematics Class 10 NCERT Solutions pdf useful. The CBSE urges students in class 10 to utilise the NCERT textbook. The NCERT Mathematics book for class 10 was produced by expert instructors and intellectuals. Students may get entire solutions and answers from NCERT Solutions. The NCERT Mathematics answer for class 10 is based on the most up-to-date curriculum and syllabus. These solutions can be used as a reference when solving difficulties or as a source to clarify topics.

NCERT Solutions Class 10 Mathematics: Download Pdf

The NCERT Class 10 Book has 15 chapters, and you may get solutions to all of them here, delivered by a qualified Mathematics teacher. Students will benefit from doing these textbook activities as they prepare for the board test. Class 10 math is the most important topic, and you will need to put in a lot of practise time so that you can easily solve the math sums in higher classes. Real Numbers, Polynomials, Pairs of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions, Triangles, Some Applications of Trigonometry, Constructions, Surface Areas and Volumes, Statistics Probability are some of the topics covered in this NCERT Solutions for Class 10 Mathematics.

NCERT Solutions of Class 10 Mathematics Chapter 1: Real Numbers

In this NCERT Solutions for Class 10 Mathematics Chapter 1, Real Numbers, You will gain a thorough understanding of real and irrational numbers. The Division Lemma of Euclid is stated as follows: “Given positive integers a and b. The LCM and HCF of any two positive numbers are calculated using Euclid’s Division algorithm, which is based on this lemma. In this chapter, you can learn about irrational numbers, rational numbers, and decimal expansion with the help of this theorem. NCERT solutions for chapter 1 of Mathematics for class ten The subject of Real Numbers includes Euclid’s division lemma, the Fundamental Theorem of Arithmetic, the decimal representation of rational numbers, and proofs of the irrationality of √2, √3, √5, among other topics.

NCERT Solutions of Class 10 Mathematics Chapter 2: Polynomials

In this Class 10 Mathematics NCERT Solutions Chapter 2, you can learn about finding the number of zeroes in a graph, understanding the Geometrical Meaning of the Zeroes of a Polynomial, Relationship between Zeroes and Coefficients of a Polynomial, quadratic polynomial, concept of division algorithm, and more in this Class 10 Mathematics NCERT Solutions Chapter 2. There are four problems in total in these NCERT solutions for class 10 Mathematics chapter 2 Polynomials, including an optional practise. These answers are taken from the 10th Grade Mathematics Book Solution.

NCERT Solutions of Class 10 Mathematics 3rd chapter : Pair of Linear Equations in Two Variables

The concept of Pair of Linear Equations in Two Variables is explained in NCERT Solutions for Class 10 Mathematics Chapter 3. There are seven problems in these NCERT solutions for class 10 Mathematics chapter 3 Pair of Linear Equations in Two Variables. You can learn how to represent a situation algebraically and graphically, as well as how to solve a pair of linear equations using the Graphical Method, Elimination Method, Substitution, Cross-Multiplication Method, and other methods in this Class 10 Mathematics NCERT Chapter 3 – Pair of Linear Equations in Two Variables.

NCERT Solutions of Class 10 Mathematics Chapter 4: Quadratic Equations

NCERT Solutions for Class 10 Mathematics Chapter 4 will teach you how to write a quadratic equation in standard form. This NCERT answer for class 10 Mathematics chapter 4 Quadratic Equations includes four tasks. Students learn about quadratic equations as they relate to day-to-day activities in this chapter. Solutions of quadratic equations by factorization, relationship between discriminant and type of roots, completing the square method, use of quadratic formula, and other topics are covered in NCERT Chapter 4 – Quadratic Equations for Class 10 Mathematics.

NCERT Solutions of Class 10 Mathematics Chapter 5: Arithmetic Progressions

NCERT Solutions for Class 10 Mathematics Chapter 5 will introduce students to a new topic known as Arithmetic Progression (A.P.). The NCERT solutions for class 10 Mathematics chapter 5 Arithmetic Progressions covers topics such as the difference between an AP, representing a situation in the form of an AP, determining whether a series is AP, and the final exercise includes higher-level questions based on AP, so that students have a strong understanding of analytical and problem-solving skills. In Class 10 Mathematics NCERT Chapter 5 – Arithmetic Progressions, there are four topics that are based on the most recent NCERT Book syllabus.

NCERT Solutions of Class 10 Mathematics 6th Chapter: Triangles

In this NCERT solution for class 10 Mathematics chapter 6, students will be required to study those figures that have the same shapes but are not necessarily the same size. You will learn about the concept of a similar and congruent figure in this chapter. You will also learn about the criterion for two triangles being similar, as well as various theorems about triangle similarities. NCERT solutions for chapter 6 of Mathematics in class 10- Triangles includes topics such as triangle definitions, the ratio of the areas of two identical triangles, the right triangle, and matching angles, among others. Based on the newest NCERT Book syllabus, there are six topics in Class 10 Mathematics NCERT Chapter 6 – Triangles.

NCERT Solutions of Class 10 Mathematics Chapter 7: Coordinate Geometry

In this NCERT Solutions for class 10 Mathematics, chapter 7, students will learn how to find the distance between two places if the coordinates are supplied. You will also learn how to calculate the area of a triangle formed by three points and the coordinates of the point that divides a line segment connecting two points. NCERT solutions for chapter 7 of Mathematics in class ten Concepts of coordinate geometry, Area of a triangle, Distance formula, Graphs of Linear Equations, and other topics are covered in Coordinate Geometry. NCERT Chapter 7 – Coordinate Geometry in Class 10 Mathematics covers four topics.

NCERT Solutions of Class 10 Mathematics Chapter 8: Introduction to Trigonometry

In Class 10 Mathematics NCERT Chapter 8– Introduction to Trigonometry, there are four topics: trigonometric ratios of an acute angle, a right-angled triangle, Values of the trigonometric ratios 30, 45, and 60, relationships between the ratios, and complementary angle trigonometric ratios, and so on. In these NCERT solutions for class 10-Mathematics chapter 8 Introduction to Trigonometry, all solutions are thoroughly described in a step-by-step approach. 

NCERT Solutions of Class 10 Mathematics Chapter 9: Some Applications of Trigonometry

This NCERT solution for class 10 Mathematics chapter 9 Some Applications of Trigonometry only covers one topic. In this NCERT Chapter 9– Some Applications of Trigonometry for Class 10 Mathematics, you will learn about the applications of trigonometry, such as its usefulness in geography, navigation, finding the position of an island, line of sight, angle of elevation, angle of depression, and other topics as well. 

NCERT Solutions of Class 10 Mathematics Chapter 10: Circles

In your early classes, you learned about the circle, chord, segment, arc, and so forth. However, students will explore the various instances in which a circle and a line are supplied in a plane in this chapter of NCERT solutions for class 10 Mathematics chapter 10 Circles. This chapter covers two topics: the tangent at any point on a circle, and the lengths of tangents of the circle taken from an external point, among others. 

Important Theorems to remember:

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

NCERT Solutions of Class 10 Mathematics Chapter 11: Constructions

You will learn about construction in this lesson, and it will be of benefit you if you have learnt the concept of construction in previous classes. Division of a line segment in a specific ratio, Tangents to a circle from a point outside it, Construction of a triangle, and other topics are covered in this NCERT solutions for class 10 Mathematics, chapter 11- Constructions. This chapter is divided into two sections. The methods and techniques for constructing tangents to the circle are taught in detail in this chapter, with plenty of examples provided before each task. Before each exercise, the students are provided examples to help them comprehend the procedures and theorems.

NCERT Solutions of Class 10 Mathematics Chapter 10: Areas Related To Circles

You will learn about the concepts of perimeter and area of a circle in this NCERT solutions for class 10 Mathematics chapter 10 Areas Related to Circles. This chapter covers three different concepts. It covers topics such as the circumference of planar objects, including triangles, circles, and simple quadrilaterals, as well as the area of a circle, the area of sectors and segments of a circle, and the circumference of sectors and segments of a circle.

Important formulas for the students to note:

1. Circumference = 2πr
2. Area of the circle = πr2
3. Area of the sector of angle θ = (θ/360) × πr2
4. Length of an arc of a sector of angle θ = (θ/360) × 2 π r where r is the radius of the circle

NCERT Solutions of Class 10 Mathematics Chapter 13: Surface Areas and Volumes

This NCERT Solutions for class 10 Mathematics chapter 13 has five tasks. You can learn how to calculate the surface area of a cuboid, cone, sphere, cylinder, and hemisphere, among other things. You can learn about surface areas and volumes of combinations of any object from this NCERT solution for class 10-Mathematics chapter 13 Surface Areas and Volumes. Surface areas and volumes of cubes, cuboids, spheres, hemispheres, cones, and right circular cylinders are studied in this chapter. , for example, problems with solids that are not more than two separate solids. Other topics ask about the transformation of one shape into another. This chapter also covers how to calculate the volume, curved surface area, and total surface area of a cone’s frustum.

Important formulas for the students to note:

1. Diameter of sphere = 2r
2. Volume of Cylinder = π r2 h
3. Volume of cone = ⅓ π r2 h
4. Total surface area of cuboid = 2(lb + bah + he)
5. Volume of Cuboid = l × b × h

NCERT Solutions of Class 10 Mathematics Chapter 14: Statistics

In this NCERT Chapter, you will learn how to convert ungrouped data to grouped data numerically and how to calculate the Mean, Mode, and Median. Cumulative frequency, cumulative frequency distribution, draw cumulative frequency curves, Cumulative frequency graph, and other topics are covered in this NCERT solution for class 10 Mathematics chapter 14 Statistics.

NCERT Solutions of Class 10 Mathematics Chapter 15: Probability

In this last NCERT Solutions for Class 10 Mathematics chapter 15, you will learn about Probability, and you will understand the definition of probability at the beginning of the chapter. This chapter has two exercises. NCERT Solutions for chapter 15 of Mathematics for class 10 the idea of probability, simple tasks for determining the probability of an event, the distinction between experimental and theoretical probability, and other topics are covered in probability. Probability is also an extremely important chapter for students to concentrate on because it will be studied further and new subjects will be introduced in future lessons.

NCERT Solutions of Class 10 Mathematics All Chapters

All chapters of NCERT Mathematics Class 10 solutions are listed below. Students can get Class 10 Mathematics NCERT chapter-by-chapter solutions by clicking on the link for the appropriate chapter number.

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