# NCERT Solutions

# Ncert Solutions For Class 10 Maths

**NCERT Class 10 Maths Solutions - Free PDF Download**

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##### NCERT Solutions for Class 10 Maths Download PDF files for free

NCERT Class 10 Maths Solutions can be very stressing and nerve racking for the students who are attempting in it because it is their first time appearing in the Board exams. The key to get success In Maths is to practice continuously or so they say but with a large syllabus like this, it becomes harder to cover everything. To solve this problem, our experts have come with NCERT 10 Maths Solution that not only focus on the important topics but also prepare you for the board exams by informing about the things like the patterns of the papers, the types of questions etc. with our Class 10 Maths NCERT Solutions, you will find the Maths easy and fun.

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###### Chapter 1 – Real Numbers

In Chapter 1 of 10th Class, students explore real numbers and irrational numbers. The chapter begins with Euclid's division lemma. Euclid's division algorithm is based on this lemma and is used to calculate the HCF of two positive integers. Then, the basic principle of arithmetic is defined, which can be used to find the LCM and HCF of two positive integers. Thereafter, the concept of irrational number, rational number, and decimal expansion of rational numbers is explained with the help of the theory.

###### Chapter 2 – Polynomials

In polynomials, the chapter begins with the definition of polynomial, linear polynomial, square polynomial, and cubic polynomial. This chapter contains a total of 4 exercises, including an optional exercise. Exercise 2.1 contains questions about finding the number of zeros by a graph. This requires understanding the geometric meaning of the zeroes of the polynomial. Exercise 2.2 is based on the relationship between the zero and the coefficient of the polynomial, where students have to find the square polynomial of zero, and in some questions they need to find the square polynomial. In Exercise 2.3, the concept of the segmentation algorithm is defined and the students come up with questions. There are questions from all the concepts of Alternative Exercises, 2.4 Chapter 2.

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

This chapter describes the concept of paired equations in two variables. This chapter has a total of 7 exercises, and in these exercises, various methods of solving a pair of linear equations are described. Exercise 3.1 describes how to represent a situation algebraically and linearly. Exercise 3.2 describes how to solve a pair of linear equations by graphical method. Exercise 3.3, 3.4, 3.5, and 3.6 describe the algebraic method, the elimination method, the cross-multiplication method, and the material method, respectively. Exercise 3.7 is an optional exercise that includes all kinds of questions. Students must practice these exercises to learn the method of solving linear equations.

###### Chapter 4 – Quadratic Equations

In this lesson, students learn the standard form of writing square equations. The chapter describes the method of solving the square equation by the factor method and completing the square method.

###### Chapter 5 – Arithmetic Progressions

This chapter introduces students to a new topic called arithmetic progress. This chapter has a total of 4 exercises. In Exercise 5.1, students get questions such as referencing a location as an AP, finding the first word of the AP and finding the difference, knowing that the series is AP. Exercise 5.2 There are questions about finding the NT term of AP using the following formula;

###### Chapter 6 – Triangles

In Chapter 6 of 10th CBSE Mathematics, students study the same size figures, but not necessarily the same size. The chapter begins with the concept of uniform and equal shapes. This further illustrates the situation of the theorems related to the equality of the two triangles and the similarity of the triangles. After that, the regions of similar triangles are described with a theorem. At the end of this chapter, the Pythagorean theorem and the Pythagorean theorem are explained.

###### Chapter 7 – Coordinate Geometry

In this lesson, students will learn how to find the distance between two given coordinates and find the area of the triangle formed by the given three points. In addition, students will also learn how to find the coordinates of a point dividing a line segment that connects two given points in a given ratio. For this purpose, students are introduced to the distance formula, section formula, and area of a triangle in this chapter.

###### Chapter 8 – Introduction to Trigonometry

This chapter introduces students to trigonometry. They study some proportions of the right triangle with respect to their acute angles, called angular trigonometric ratios. The chapter also defines trigonometric ratios for the angles 00 and 900. Next, students will also learn how to calculate trigonometric ratios for certain angles, and some of the identities with these ratios are called trigonometric identities.

###### Chapter 9 – Some Applications of Trigonometry

This chapter is a continuation of the previous chapter because here students study the applications of trigonometry. It is used in the creation of geography, navigation, and maps, which determine the location of an island relative to longitudes and latitudes. In this lesson, students will see how trigonometry is used to find the heights and distances of different objects without actually measuring them. They introduce focus period, angle of height, angle of depression.

###### Chapter 10 – Circles

In previous classes, students studied the different positions of a circle and the cord, segment, and arc. In this chapter, students study the plane, the circle, and the various conditions presented in a line. . So, they get by the concept of the number of tangents and the number of tangents to a circle.

###### Chapter 11 – Constructions

This chapter covers all 2 exercises. They also help students learn everything about construction in former classrooms. In Exercise 11.1, students study how to divide a line, while in Exercise 11.2 they study the structure of tangents in a circle. The construction techniques and steps are explained and at the same time some examples are given to make it more clear to the students.

###### Chapter 12 – Areas Related to Circles

This chapter begins with the concepts of the circumference and area of the circle. Using this concept, the chapter further explains how to find the area and section of a sphere. In addition, students will be able to find areas of certain combinations of aircraft figures with circles or their parts.

###### Chapter 13 – Surface Areas and Volumes

In Chapter 13, there are 5 exercises in total. The first exercise involves questions based on finding the surface area of the object formed by combining the two cubes, cones, cylinders, spheres, and hemispheres of the original solid. In Exercise 13.2 questions are based on finding the quantity of objects formed by combining the cuboid, cone, cylinder, sphere and any two of the hemispheres. Exercise 13.3 deals with the questions of converting solids from one shape to another. 13.4 Exercise The volume of the curved surface area depends on finding the surface area and the total surface area of the cone. The last exercise is optional and has a high level of questions based on all the topics in this chapter.

###### Chapter 14 – Statistics

Here students learn group data to find numerical representations of arbitrary data and to find the mean, mode and median. Also, the concept of cumulative frequency frequency, cumulative frequency frequency distribution and cumulative frequency frequency curves is explained.

###### Chapter 15 – Probability

The last chapter deals with probability. The chapter begins with a theoretical view of probability. Next, the chapter describes the difference between experimental probability and theoretical probability. Various examples are given to illustrate this effectively. Therefore, students must first solve examples of CBSE maths before they encounter exercise problems.