## NCERT Solutions for Class 10 Maths| Based on updated Syllabus of CBSE

The NCERT solutions for Mathematics Textbook as prescribed by CBSE Schools is strictly based on latest pattern of Central Board of Secondary Education for the Board Exams 2020. Maths is one of the most important subject for Class 10 students. NCERT Textbook of Class 10 build the basic fundamental which will help you at higher levels. If you want to opt Science stream in upper classes then you must clear all the concept and doubts. Solving **NCERT Solutions for Class 10 Maths** will memorize all the important formulas and theories that are important for the examination. We are committed to provided most accurate and detailed answers of every NCERT questions. These ncert solutions are simple and prepared in a way so that you can easily grasp the concepts related to each question. If you are facing any type of problem then you can take help from here. You can use the links provided below to start reading you problematic chapter.

**List of all chapters of NCERT solutions for class 10 Maths**

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

**Benefits of NCERT Solutions for 10th Class Maths**

These NCERT Solutions are prepared by our expert Maths Faculty and accurate and detailed. These will be helpful in revising important formulas. We have added figures wherever necessary so that you can understand it easily. Through these solutions students can strengthen their problem-solving skills. Students can understand the problem easily and in less time.

The first chapter of Class 10 Maths is Real Number and the textbook ends with Probability. We have provided all the important details of each chapter below.

**Chapter 1 – Real Numbers**

There are four exercises in the chapter. This chapter starts with Euclid’s division lemma and Algorithm. A lemma is a proven statement used for proving another statement. An algorithm is a series of well defined steps which gives a procedure for solving a type of problem. For any two given positive integers ‘a’ and ‘b’ there exists unique whole numbers ‘q’ and ‘r’ such that a = bq + r, where 0 ≥ r < b Here, a = Dividend, b = Divisor q = Quotient, r = Remainder. This is Euclid’s division lemma. Euclid’s Division Algorithm is a technique to compute the HCF of two positive integers ‘a’ and ‘b’ (a > b). We will revise our previous concepts of rational and irrational numbers and their decimal expansion. We will study Fundamental Theorem of Arithmetic where every composite number can be expressed as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

**Chapter 2 – Polynomials**

Polynomial is an algebraic expression of the form p(x) = a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + …… + a_{n} x^{n}, in which the variables involved have only non-negative integral exponents, is called a polynomial in x of degree n. The highest power of the variable in a polynomial is called its degree. A polynomial of degree 1 is called a linear polynomial. A polynomial of degree 2 is called a quadratic polynomial. A polynomial of degree 3 is called a cubic polynomial. A real number ‘a’ is said to be a zero of the polynomial p (x), if p (a) = 0. In this chapter, there are total four exercises and most of the question is based on finding zero of the polynomial.

**Chapter 3 – Pair of Linear Equations in Two Variables**

An equation which can be put in the form ax + by + c = 0 where a, b and c are real numbers (a, b ≠ 0) is called a linear equation in two variables. This chapter has a total of seven exercises which have various problems related solving linear equations through algebraic method, graphical method, elimination and substitution method.

**Chapter 4 – Quadratic Equations**

An equation of the form ax^{2} + bx + c = 0, where a, b, c are real numbers, and a ≠ 0, is called a quadratic equation in the variable x. There are four exercises in this chapter. We will learn various methods of solving quadratic equation such as by factorisation method, completing the square, finding the nature of roots.

**Chapter 5 – Arithmetic Progressions**

An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term. The fixed number is called the common difference, which can be positive, negative or zero. The common difference of an A.P. can be obtained by subtracting any term from its following term. In this chapter, we have to find the nth terms and the sum of n consecutive terms.

**Chapter 6 – Triangles**

There are various questions given in this chapter in total six exercises on the basis of the properties of triangles. Here we will mainly discuss the congruency and similarity of plane figures. Two geometric figures are said to be congruent, if they have the same shape and the same size. Two geometric figures having the same shape (but not necessarily the same size) are called similar figures.Two congruent figures are always similar but two similar figures need not to be congruent.

**Chapter 7 – Coordinate Geometry**

Coordinate plane and coordinate of a point are the plane containing two mutually perpendicular lines X’OX and Y’OY intersecting each other at O is called coordinate plane. X’OX and Y’OY are called xaxis and y-axis respectively. There are four exercises in the chapter. In most of the questions, you have to finde the distance between the two points whose coordinates are provided and the area of a triangle formed by three given points.

**Chapter 8 – Introduction to Trigonometry**

The certain ratios involving the sides of a right triangle are called trigonometric ratios. We will learn about trigonometric ratios of specific angles such as are 0°, 30°, 45°, 60° and 90° and trigonometric identities. The value of sin A increases from 0 to 1, as A increases from 0° to 90°. The value of cos A decreases from 1 to 0, as A increases from 0° to 90°. The value of tan A increases from 0 to ∞ , as A increases from 0° to 90°.An equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angles involved.

**Chapter 9 – Some Applications of Trigonometry**

In this chapter, we are solving the problems related to heights and distances. A line drawn from the eye of the observer to the point in the object viewed by the observer is called the line of sight. The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal-level. The angle of depression of the point viewed is the angle formed by the line of sight with the horizontal level when the point being viewed is below the horizontal level.

**Chapter 10 – Circles**

A Circle is a closed shape with a certain set of points in a plane at a specific distance from the center of the circle. There are only two exercises. A tangent to a circle is a line that touches the circle at only one point. The tangent at any point of a circle is perpendicular to the radius, through the point of contact.

**Chapter 11 – Constructions**

In this chapter, we will see the division of line segment. To divide a line segment in a given ratio m : n, we divide this segment into (m + n) equal parts. Then we take m parts on one side and n on the other. The idea of dividing a line segment in any ratio is used in construction of a triangle similar to a given triangle, whose sides are in a given ratio with the corresponding sides of the given triangle.

**Chapter 12 – Areas Related to Circles**

In this chapter, we will learn to find areas of special parts of a circular region. The total distance (perimeter) around a circle is called its circumference. The plane surface enclosed in a circle is called its area. If ‘r’ be the radius of a circle, then Circumference of the circle = 2πr and Area of the circle = πr^{2}.

**Chapter 13 – Surface Areas and Volumes**

The chapter is about finding Surface Areas and Volumes of solid shapes. An object having definite shape and size is called a solid. Solids like a book, a tile, a match box, an almirah, a room, etc. are called cuboids. Solids like dice, ice-cubes, sugar-cubes, etc. are called cubes. Solids like jars, circular pillars, circular pipes, circular pencils, gas jars, road rollers, etc. are called cylinders. Solids like conical tents, ice-cream cones, funnels, etc. are called cones. Solids like cricket balls, footballs etc., are called spheres. When a cone is cut by a plane parallel to the base of the cone then the portion between the plane and the base is called the frustum of the cone.

**Chapter 14 – Statistics**

In this chapter, we are finding mean, median and mode which are measures of central tendency that is numerical representatives of the given data. Cumulative frequency of a class is the frequency obtained by adding the frequencies of all the classes preceding the given class.

**Chapter 15 – Probability**

Probability is measure of degree of certainty of occurrence of events. Event is the collection of some or all possible outcomes of a random experiment is called an event. Experiment means an operation which can produce some well-defined outcome. Random Experiment is an experiment which is repeated under identical condition do not produce the same outcome every time but the outcome in a trial is one of the several possible outcomes.It is measure of degree of certainty of occurrence of events. The questions are based on finding the probability of getting a situation mostly on coins and dice.