## NCERT Solutions for Class 10 Maths

NCERT Solutions for Class 10 Mathematics answers all the questions and answers from the NCERT Maths Class 10 textbook. CBSE NCERT Solutions for Class 10 Maths are really useful for students of CBSE class 10. Class 10th Students from CBSE board, UP board, Gujarat board, Bihar, Uttarakhand, Maharashtra board can take advantage of NCERT Solutions. Class 10 Mathematics is a very important subject not only in Class 10th but also in many competitive entrance exams. These 10th Class NCERT Solutions can also help you in cracking exams like JEE Main, JEE Advanced, NEET and more. Maths of Class 10 is quite complex. These maths solutions can help you score higher grades in exams and will make you an expert in Class 10 Mathematics.

CBSE NCERT Maths Solutions for Class 10 are very important and time-saving. From NCERT  Class 10th Mathematics Solutions, you will also get to know many tips and tricks of solving maths problems quickly. These maths solutions cover all the topics of CBSE Class 10th Maths like arithmetic progression, coordinate geometry, polynomials, quadratic equations, etc. You can download the PDF format of all the chapters of the academic year 2019-20 from the links below. CBSE NCERT Maths Solutions will solve all your maths questions and answers for class 10.

### NCERT Solutions for Class 10 Mathematics – Free Chapterwise PDF Download

You can download CBSE NCERT Solutions for Class 10 Maths of all the chapters from the links below. The following are the chapters covered under CBSE Class 10 Maths book. These solutions will solve all the 10th class math book answers.

Our experts at Toppr with more than 10+ years of experience have made these solutions for you. NCERT Solutions for Class 10 Mathematics by Toppr is preferred by more than 8 Million students refer especially from the 10th standard. We have made it very easy for students to download tenth standard maths solutions. NCERT solutions for class 10 maths is just one click away from your fingertips. You can also download free PDF of NCERT Solutions for Class 5, 6, 7, 8, 9, 10, 11, 12 from here. It is completely free.

You can also access CBSE Guide for Class 10 Maths

### Chapter 1 – Real Numbers

NCERT Solutions for Class 10 Mathematics covers Real Numbers as first chapter with four exercises. There are different types of numbers in Class 10 Mathematics. One of them is a real number. Real numbers are basically those that can be placed on a number line. If any number cannot be placed on the number line then it is an imaginary number. Examples of real numbers are a rational number, an irrational number, algebraic, fractions, complex, and even square roots are real nums.

#### Exercise 1.1, 1.2, 1.3, and 1.4

10th Class NCERT Solutions for Maths covers important topics of maths like rational and irrational in which you will get to learn about properties of whole and natural and also properties of integers. In the next exercise, you will learn about Euclid’s division algorithm by Mathematician Euclid. Euclid’s division can be applied in integer division too and can be used in many problems. We have solved more than 30 problems in this chapter, you can download NCERT Solutions for real nums from the link above.

### Chapter 2 – Polynomials

In the 2nd chapter of NCERT CBSE Class 10 book, you will learn about Polynomials. Polynomial is an equation or expression that has four or more than four algebraic terms. These algebraic terms can have different variables, powers, exponent, and degree. Similarly, equation with one term is monomial, with two-term are binomial, with three-term are trinomial. There are four exercises in this chapter.

#### Exercise 2.1 and 2.2

In exercise 2.1 you will learn about the zeros of polynomials p(x). The next exercise is about finding quadratic polynomials and verifying the relationship between the coefficients and zeros.

#### Exercise 2.3 and 2.4

In exercise 2.3, the value of the Polynomial and division algorithm is the topic. Finally, in the last exercise 2.4, you will be finding the zeros of polynomials. We have solved more than 20 problems in this chapter. Download NCERT Solutions for class 10 maths chapter 2 from the link above.

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

This is the third chapter of NCERT CBSE Class 10 Maths. Class 10 Mathematics textbook has seven exercises for this chapter. Topics covered under this chapter are graphical and algebraic methods to solve linear eqns, cross-multiplication method, and elimination method.

#### Exercise 3.1, 3.2, and 3.3

In exercise 3.1 you will get to solve seven questions. There are 3 problems in exercise 3.2. The third one has three questions to solve.

#### Exercise 3.4, 3.5, 3.6, and 3.7

Exercise 3.4 has only two questions related to linear equations. In fifth, you will have five questions related to a pair of linear equations. And only 2 questions in exercise 3.6. Exercise 3.7 is elective.

### Chapter 4 – Quadratic Equations

NCERT Solutions for Class 10 Mathematics covers Quadratic Equations as the fourth chapter. These expressions are those which start with the power of 2. These eqns have 3 terms in it, with the descending order of power from 2 to 0 (2,1,0). The solutions to the quadratic equation are more than 1. And these solutions are called roots of a quadratic equation. In four exercises of quadratic eqns, you will learn how to find the roots using different methods.

#### Exercise 4.1

In exercise 4.1 you will only have two questions in which you will be introduced to quadratic eqns. You will get to know how to understand if the equation is a quadratic equation or not.

#### Exercise 4.2, 4.3, and 4.4

In the other three exercises from 4.2 to 4.4, you will be finding roots of quadratic equations. Some important topics you will come across are the nature of roots, completing the square, applications of quadratic equations and factorization.

### Chapter 5 – Arithmetic Progressions

Arithmetic progression, in Class 10 Mathematics, is also known as an arithmetic sequence. It is a sequence of natural numbers that give us a constant number when the consecutive numbers are subtracted from each other.  In NCERT Solutions for Class 10 Maths chapter 5, you will learn about Arithmetic progression. It is one of the types of progression which also has a lot of real-life applications.

#### Exercise 5.1, 5.2, 5.3, and 5.4

From the four exercises of this chapter, you will learn how to understand sequence, patterns, between two constants. There are two types of an arithmetic sequence, finite arithmetic sequence and nth term of an arithmetic progression. We have solved more than 50 problems in the NCERT Solutions of Arithmetic progression.

### Chapter 6 – Triangles

In Chapter 6 of NCERT Solutions for Class 10 Maths, you will learn about Triangle. Triangle is a shape in geometry or polygon which has three vertices and edges. Hence, the name is Tri-angle. Tri means three. There are different types of triangles, right-angled triangle, scalene triangle, isosceles triangle, equilateral triangle. Triangle has most applications in Trigonometry.  This is the sixth chapter in CBSE Class 10 maths book.

#### Exercise 6.1, 6.2, 6.3, 6.4, 6.5, and 6.6

In this chapter, there are 6 exercises. You will learn around nine theorems in this chapter including Pythagoras theorem which will be also very helpful in further classes and higher exams. There are six exercises in this chapter.

### Chapter 7 – Coordinate Geometry

NCERT Solutions for Class 10 Maths covers Coordinate Geometry as 7th chapter. Coordinate Geometry is a part of geometry in which you will get to learn about the axis, coordinates, slopes, origins, etc. A plane in which position of points on a plane is defined by an ordered pair of numbers is called coordinates. Coordinate Geometry is a very important part of Class 10 CBSE Maths.

#### Exercise 7.1, 7.2, 7.3, and 7.4

NCERT Solutions of Class 10 Mathematics Chapter 5 Coordinate geometry covers four exercises that cover concepts of section formula, distance formula and more from CBSE Class 10 Mathematics books. Coordinate geometry falls between algebra and geometry and hence sometimes we also call it analytic geometry. There are four exercises in this chapter. Problems you will face will be something like finding the distance between two points whose coordinates are given. Download solutions for this chapter from the link above.

### Chapter 8 – Introduction to Trigonometry

Trigonometry is another important topic in CBSE Class 10 Mathematics. NCERT Solutions’ trigonometry covers more than 40 questions. It will help you understand the method used to solve trigonometry problems.

#### Exercise 8.1, 8.2, 8.3, and 8.4

Once again there are four exercises in this chapter. NCERT Solutions of Class 10 covers concepts of Trigonometric ratios and Trigonometric Identities. Download NCERT Solutions for Trigonometry from the links above.

### Chapter 9 – Some Applications of Trigonometry

Applications of Trigonometry is the 9th chapter of NCERT CBSE Class 10 Maths. Trigonometry has a lot of applications in real life and engineering as well.

#### Exercise 9.1

There is only one exercise in this chapter. It is one of the important chapters of CBSE Class 10 Mathematics in which you will learn to find the height and distance of different objects. Applications of Trigonometry contains more than 20 problems solved. Get NCERT Solutions for Applications of Trigonometry from the links above.

### Chapter 10 – Circles

Circle is a round shape in Maths which has a centre, radius, and diameter. All points of a circle are at an equal distance from the centre. Radius of the circle is half of the diameter. Circles chapter covers the tangents of a circle, an arc of a circle, and theorems related to a circle.

#### Exercise 10.1, 10.2, 10.3, and 10.4

According to CBSE Class 10 Maths book, there are four exercises in this chapter. NCERT Solutions of chapter 10 maths covers more than 20 problems.  You can download it from the links above.

### Chapter 11 – Constructions

You can download NCERT Solutions for CBSE Class 10 Maths Chapter 11 from the link above. This chapter is important and it will help you to understand how to draw tangents to the circle.

#### Exercise 11.1 and 11.2

There are two exercises in this chapter. Some more topics you will learn are tangent constructions and division of line segments. This is something advanced or higher level of what you learned in class 9 maths. In Class 10 you will also have to prove and give a mathematical explanation behind the construction. There are two exercises in this chapter which covers the division of line segments and construction of tangents.

### Chapter 12 – Areas Related to Circles

#### Exercise 12.1, 12.2, and 12.3

In this chapter, there are 3 exercises and you will learn the concept of area and perimeter of a circle, areas of sector and segment of a circle, area of the simple plane and different figures like rectangle, parallelogram, square and circle. You will also learn about how to find the area of a circle, semi-circle, and perimeter related to the arc of the circles. We have covered more than 30 questions in the NCERT Solutions of Class 10 Maths. You can download it from the link above.

### Chapter 13 – Surface Areas and Volumes

Cube, Cylinder, Cone and more different shapes!

#### Exercise 13.1, 13.2, 13.3, 13.4, and 13.5

There are 5 exercises in this chapter. Measuring surface areas and volumes of so many shapes can be confusing. Download NCERT Solutions for Class 10 Maths Chapter 13 – Surface areas and volumes from the links above. We have more than 60 problems solved in this chapter.

### Chapter 14 – Statistics

Statistics in Class 10 Maths deals with the analysis and presentation of data using charts and graphs. Using sample data we calculate the average, make predictions, and more. There are 4 exercises in this chapter.

#### Exercise 14.1, 14.2, 14.3, and 14.4

Statistics is an important concept that is used mostly in Business Mathematics. Our experts at Toppr have solved more than 50 problems in Statistics. Get NCERT Solutions for Class 10 Maths Chapter 14 from the links above.

### Chapter 15 – Probability

Probabilty is the last chapter in NCERT Solutions for Class 10 Maths. Probability in mathematics is a calculation of likeliness of specific event will happen or not. It helps us understand the odds or chances of anything. Dice is the best example when it comes to probability. In mathematics, we get the result of probability in 0 or 1. Probability is a chapter that has a lot of real-life applications.

#### Exercise 15.1 and 15.2

There are two exercises in this chapter. NCERT Solutions for Probability has more than 30 problems solved. Download Probability NCERT Solutions from the links above.

Download all the NCERT Solutions for CBSE Class 10 here. Also, you can get NCERT books for all classes and subjects from here.

### Download Toppr – The Best Learning App for  Class 5 to Class 12

Once you signup on Toppr you get free access to NCERT textbook solutions, sample papers, previous 10 years of question papers, and a lot of free resources. These solutions are most important for CBSE students. NCERT textbooks are the key to score higher in the CBSE exam. Toppr’s NCERT Solutions help you save your time and energy. You can solve all the answers from the NCERT books and then verify your answers from solutions of Toppr.

Some of the best features of the Toppr app are Online Classes, Mock tests, Adaptive Practice, and Live Doubts.  Our experts at Toppr solves your doubt even at 3 am-midnight

Solved Questions For You:

Question.1. Which of the following experiments have equally likely outcomes? Explain.
(i) A driver attempts to start a car. The car starts or does not start.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.
(iv) A baby is born. It is a boy or a girl

i) Equally likely outcome because either the car starts or does not. There can be no other possibility.

ii) Equally likely outcome because either the goes through the basket or it does not. There can be no other possibility.

iii) Equally likely outcome because in a true or false type of question, either the answer is correct or wrong. There can be only 2 possibilities or no other possibility.

iv) Equally likely outcome because either the child born is a girl or a boy. There can be no other possibility.

Question.2. Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

Answer: When a coin is tossed, there is an equally likely outcome of getting either a head or a tail, so tossing a coin is a fair way of deciding.

Question.3. Which of the following cannot be the probability of an event?

1. $$\frac{2}{3}$$
2. −1.5
3. 15%
4. 0.7

−1.5 cannot be a probability of an event as the probability of an event always lies between 0 and 1.

Question.4. A die is thrown once. Find the probability of getting a number which
(i) a prime number; (ii) a number lying between  and

Sample space = {1,2,3,4,5,6}

i) P (Prime number) = $$\frac{Number of prime numbers}{Sample space}$$​

P (Prime number) = $$\frac{3}{6}$$ = $$​\frac{1}{2}$$

ii) P (Number between 2and 6 = $$\frac{3}{6}$$ = $$​\frac{1}{2}$$

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