## NCERT Solutions for Class 10 Maths

CBSE NCERT Solutions for Class 10 Maths Textbook is arranged through and pointwise manner so that you can easily grasp the concept behind the question. Here you can find NCERT Solutions for Class 10 Maths in PDF format that will help in framing own NCERT Class 10 Maths Solutions easily. You can also download these solutions and use whenever you need. Maths is one of the main subjects for Class 10th students. Maths NCERT Textbook will help in building fundamentals in the subject. You need to solve the exercises given between the chapters. If you're facing any problem while solving any question in the exercises then you can take help from this page. The answer of each chapter is provided in the list. You only need to select the required chapter from the list and start reading. ## Chapterwise NCERT Solutions for Class 10 Maths

#### Why NCERT Solutions for Class 10 Maths by Studyrankers?

These Maths Class 10 Solutions are prepared by our experts who are experienced and well qualified who have prepared step by step NCERT Class 10 Maths Solutions which will help you:
• In knowing the areas where one is lacking.
• We have touched all important points and detailed them so students can easily get them.
• NCERT Maths solutions also includes concept specific to the questions so you don't have to roam around the different sources to understand the question.
The Class 10th Maths textbook consists of total 15 chapters which can be divided into seven units. There are various questions provided between the chapter known as NCERT Solutions. These NCERT questions are important for the purpose of examinations and also help in developing your knowledge. We will start with number system and then move towards algebra. After which we will study coordinate geometry. We will also study concepts of trigonometry and mensuration. Lastly, we will study Statistics and Probability.

Chapter 1 - Real Numbers

There are total four exercises in the chapter. In the first exercise, there are four questions and most of them are based on Euclid's division lemma. The second exercise consists of HCF and LCM questions. The third exercise has three questions in which you prove numbers rational or irrational. The last exercise also has three questions based in which you have to expand fractions into decimals and write decimals in their fraction form.

Chapter 2 - Polynomials

The chapter has four exercises however the last exercise is optional. In the first exercise, you have to find zeroes of polynomials p(x). There are two questions in the second exercise. In the first, you have to verify the relationship between the zeroes and the coefficients while in the second you have to find a quadratic polynomial. The third exercise contains five questions in which you have to do division of polynomials and obtain zeroes of polynomials. The optional exercise has five questions in which you have to find zeroes of polynomials.

Chapter 3 - Pair of Linear Equations in Two Variables

There are seven exercises in which the last exercise is optional. In the first exercise, there are three world problems given. There are seven questions in the second exercise. The first question has two problems while in the second and third you have to compare the ratios of the pair of linear equations. In the fourth question, you have to find whether pairs of linear equations are consistent or inconsistent. The fifth question is a word problem and in the sixth question, we have to find another linear equation in two variables. In the last question, you have to draw the graphs of the equations. The third exercise has three questions. In the first, you have to solve the given pair of linear equations by the substitution method while in the second you need to find the value of ‘m'. The third question has six world problems. The fourth exercise has two questions. In the second question, you have to solve the pair of linear equations by the elimination method and the substitution method while the second question contains five world problems. The fifth exercise contains five questions in which you have to solve the pair of linear equations through various methods given. The sixth exercise has two questions. The last exercise is optional.

There are four exercises. The first has two questions, in the first you need to find check whether equations are quadratic equations or not while in the second you have to convert world problem into quadratic equations. In the second exercise, you need to find the roots of quadratic equations by factorization. The third exercise is also on finding the roots of quadratic equations. The fourth exercise has five questions based on finding roots.

Chapter 5 - Arithmetic Progressions

Four exercises are given in the whole chapter which is divided into various questions in which we have to find the term.

Chapter 6 - Triangles

There are six exercises including one optional having different set of questions based on the properties of triangles.

Chapter 7 - Coordinate Geometry

There are four exercises in the chapter. The questions are about finding the distance between the two points whose coordinates are given, finding the area of the triangle formed by three given points and finding the coordinates of the point which divides a line segment joining two given points in a given ratio.

Chapter 8 - Introduction to Trigonometry

There are four exercises consisting of various questions mainly on finding trigonometric ratios.

Chapter 9 - Some Applications of Trigonometry

There is only one exercise whose questions are based on the practical applications of trigonometry.

Chapter 10 - Circles

The chapter has two exercises. The first exercise has basic questions while in the second, there various questions in which you have to prove the given equations.

Chapter 11 - Constructions

In this chapter, you have to draw various constructions such as division of line segments, construction of Tangents to a Circle.

Chapter 12 - Areas related to Circles

Three exercises cover questions of the area of a circle and finding the areas of two special ‘parts’ of a circular region.

Chapter 13 - Surface Areas and Volumes

In this chapter, we will deal with the problems of finding areas and volumes of different solids such as cube, cuboid and cylinder.

Chapter 14 - Statistics

There are total four exercises in which you have to solve questions based on finding mean, median and mode from ungrouped data to that of grouped data. You will also have to solve questions related to cumulative frequency, the cumulative frequency distribution and how to draw cumulative frequency curves.

Chapter 15 - Probability

There are only two exercises in which one is optional. The questions is on finding the probability of getting a situation mostly on coins and dice.

#### Show that any positive odd integer is of the form 6q+1 or 6q+3 or 6q+5, where q is some integer.

Let a be any positive odd integer, we apply the division algorithm with a and b = 6.
Since 0≤r<6, the possible remainders are 0, 1, 2, 3, 4 and 5. i.e., a can be 6q or 6q + 1, or 6q + 2, or 6q + 3, or 6q +4, or 6q +5 where q is quotient.
However, since a is odd
∴a cannot be equal to 6q,6q+2,6q +4
∵All are divisible by 2
Therefore, any odd integer is of the form 6q+1 or 6q+ 3 or 6q+5.

#### What is circumference of a circle?

The total length of boundary of a circle is called circumference of a circle.
Circumference of a circle = 2πr; where 'r is radius of the circle.

#### What is an event in Probability?

The collection of some or all possible outcomes of a random experiment is called an event

#### What is an impossible event in Probability?

An event associated with random experiment is called an impossible event. If it never occurs when every experiment is performed.

Notes of Maths Class 10th

Important Questions for Class 10 Maths