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NCERT Solutions for Class 10 Maths - Download Free PDF

NCERT Solutions for Class 10 Maths - Download Free PDF

Edited By Irshad Anwar | Updated on May 20, 2024 01:40 PM IST
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NCERT Solutions for Class 10 Maths are updated for the 2024–25 session, and all chapter solutions are provided here. These NCERT solutions guide students to crack board exams and make learning easier. NCERT Class 10 maths contains a total of 15 chapters, and all of them are important to study. It is necessary to solve all the exercises, including the additional exercises, to get a good score. The questions and answers given in the Class 10 maths NCERT solutions will help you understand each question in detail. By solving the entire exercise for the chapter and practicing the previous 5 years' questions, you can easily score well in the board exam. Practice and know how to answer the questions in a step-wise manner with the help of NCERT Solutions for class 10.

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

Class 10 Maths NCERT Solutions include important chapters such as geometry and trignometry. Find the class 10th chapter wise listing to help navigate the website. You can click on the chapter you wish to study below. Also, in order to study other subjects or even higher classes, you can take help from NCERT solutions that are answered using a step-by-step approach so that you do not miss any step while answering the problems in the examinations. If a student is good at maths, then, only a few additional things will be left to study. Students should practice problems from NCERT exercise, such as ex 7.1 class 10, ex 7.2 class 10, ex 9.1 class 10, ex 14.1 class 10 and others, to get a grasp of the concepts. Class 10 Maths solutions are provided in PDF format so that students can download the solutions to read offline at any time.

NCERT Solutions For Class 10 Maths - Chapter Wise

Here students can find class 10 maths all chapter name and NCERT solutions. Practice chapter-wise NCERT solutions for a comprehensive and in-depth understanding of the concepts.

NCERT Solutions for Class 10 Maths Chapter Details, Exercises, and Important Topics

Chapter 1 Real Numbers

In class 10 maths NCERT solutions Chapter 1, you are going to learn about Euclid’s Division Lemma and this concept is used to find the HCF, LCM, the relation between HCF and LCM and the fundamental theorem of arithmetic. Euclid’s Division Lemma will also be required if you want to prove that the given number is rational or irrational and the given rational number is terminating or non terminating repeating. There are many real-life examples of LCM and HCF mentioned in the NCERT class 10 maths solutions. There are a total of 4 exercises with a total of 48 questions in this chapter. Students can fine these exercises as well as NCERT Maths solutions class 10 in this page.

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Real Numbers Class 10 Maths NCERT Book Chapter 1 Topics

  • Euclid's division algorithm
  • Prime factorization
  • Highest common factor
  • Prime factorization
  • Prime & composite numbers
  • Rational & irrational numbers

Chapter 1 Exercises

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Chapter 2 Polynomials

The class 10 maths NCERT solutions Chapter 2 starts with an explanation of polynomials, referring to the previous classes and then explains the geometrical interpretation of the zeroes of the polynomial. Then it gives the relation between zeros and the coefficient of a given polynomial and also explains how to carry out the polynomial divisions. You have to be good in the 9 maths chapter on polynomials to beat this one. In NCERT solutions class 10 maths chapter 2 polynomials, step-by-step explanation is given in the answers of all 4 exercises, including the optional exercise.

Polynomials Class 10 Maths NCERT Book Chapter 2 Topics

  • The degree of a polynomial
  • Number of zeroes in a quadratic polynomial
  • The sum & product of quadratic polynomial
  • Division algorithm
  • The number of zeroes in a cubic polynomial

Chapter 2 Exercises

Chapter 3 Pair of Linear Equations in Two Variables

There are many real-life examples that can be formulated in linear equations in two variables. Let's take an example to understand: If a person buys some pens and pencils at a total of 41 Rs and the price of a pen and a pencil are 5 Rs and 4 Rs respectively. Then the statement can be represented as 5x + 4y=41Many such problems are mentioned in the class 10 NCERT maths solutions. The NCERT maths class 10 solution Chapter 3 covers various algebraic methods to solve a given pair of linear equations and a geometrical way of solving the pair of linear equations.

Pair Of Linear Equations In Two Variables Class 10 Maths Chapter 3 Topics

  • Solving a linear equation with two variables.
  • Representation of linear equation in a graph.
  • Solutions of linear equations using the graph.
  • Algebraic interpretation of linear equations.
  • Formation of linear equations using statements.

Chapter 3 Exercises

Chapter 4 Quadratic Equations

We get a quadratic equation if a quadratic polynomial is equated to zero with the condition that the coefficient of the variable with power two is not equal to zero. The main content of the class 10 maths NCERT solutions Chapter 4 includes the various methods of solving the quadratic equations and how to determine the consistency of quadratic equations from the value of discriminants. Every year around 8 to 10 marks questions come from this chapter only. In solutions of NCERT for class 10 maths chapter 4 quadratic equation, all the 4 exercises consisting of 46 questions are covered.

Quadratic Equations Class 10 Maths Chapter 4 Topics

  • Representation of situation in a quadratic equation.
  • Checking if an equation is quadratic or not.
  • Solving a quadratic equation using factorization/ roots of quadratic solutions.
  • The solution of the quadratic equation using completing the square method.
  • Solving a quadratic equation using the Sridharacharya formula.
  • Product of roots in a quadratic equation.
  • Sum of roots in a quadratic equation.

Chapter 4 Exercises

Chapter 5 Arithmetic Progressions

Any number series having the same difference between two immediate terms is called arithmetic progression. For example- 2, 5, 8, 11 is an arithmetic progression as the difference everywhere is 3. Every year around questions of 8 to 10 marks come from this chapter only. In this particular chapter, you will learn to solve questions related to nth /last term and questions related to the sum of an arithmetic progression. Also, some questions are based on the usage of both the concepts together. There are some real-life situations mentioned in the NCERT maths class 10 solutions. Studying a chapter by correlating to real-life examples will be interesting. In NCERT solutions class 10 maths chapter 5 arithmetic progression, we are covering all the 4 exercises including an optional exercise.

Chapter 5 Exercises

Chapter 6 Triangles

A closed shape made using three straight lines is known as geometry. The NCERT Class 10 Chapter 6 starts with an explanation of the difference between the congruent figures and similar figures. In this particular chapter, we will learn the similarity of triangles, criteria for similarity, area of triangles and understanding of Pythagoras theorem using the similarity of triangles. There are many interesting examples that can be solved using the similarity of triangles. In the solutions of this particular chapter, you will get solutions to all the 6 exercises including optional exercise consisting of 90 questions. All of the exercise including ex 6.3 class 10 are listed below.

Triangles Class 10 Maths Chapter 6 - Topics

  • Similarity of triangles
  • Theorems based on similar triangles
  • Areas of similar triangles
  • Theorems related to Trapezium
  • Pythagoras theorem

Chapter 6 Exercises

Chapter 7 Coordinate Geometry

This is one of the NCERT maths class 10 solutions chapters that you will use in almost all the areas of your higher studies, whether it is science, commerce or the arts. In class 10 maths, this chapter holds some specific concepts and questions and if you do them well, then things will become easy for you in the examination. The class 10 maths NCERT solutions chapter 7 coordinate geometry include the distance formulae, section formulae and the concept of finding the area of triangles if the coordinate of the vertex is given. The NCERT solutions for Class 10 Maths Chapter 7 to all the 4 exercises, including an optional exercise consisting of a total of 45 questions, are explained in a step-by-step manner. Students can practice these exercises, i.e. exercise 7.1 class 10 and exercise 7.2 class 10, which all are listed below.

Chapter 7 Exercises

Chapter 8 Introduction to Trigonometry

The chapter has originated from the right angle triangle. The properties, formulas, and ratios of trigonometry can be derived using length, breadth, and height of the right-angle triangle. In this chapter, there are a total of 4 exercises and questions of these exercises are mainly based on finding trigonometric ratios of the sides of a right-angled triangle. The class 10 NCERT maths solutions of this chapter cover important concepts to find trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles and trigonometric identities.

Chapter 8 Exercises

Chapter 9 Some Applications of Trigonometry

This chapter is just an extension of the concepts used in Chapter 8. This is the application based chapter which tells us the usage of trigonometry in real life. "Trigonometry" unit holds 12 marks out of 80 marks in the CBSE final maths paper and we can expect one question of 3 or 4 marks from this chapter. In NCERT solutions class 10, Chapter 9, we will learn how trigonometry is helpful in finding the distance and height of different objects without actually measuring them. This chapter has only 1 exercise for which answers are in the solutions of NCERT for class 10 maths chapter 9 some applications of trigonometry. students can practice all exercises, including exercise 9.1 class 10, to get deeper understanding of the concepts.

Chapter 9 Exercises

Chapter 10 Circles

A circle is nothing but a closed figure with a collection of points in a plane that are at a specific distance (radius) from a fixed point (centre). This chapter is an important part of geometry, along with triangles. This chapter in class 10 maths is an extension of class 9 maths chapter circles. In this chapter, we will discuss tangent to a circle and number of tangents from a point on the circle. The chapter holds good weight in the board examinations. Every year, approximately 10 to 12 marks come from this chapter only. The solution of NCERT class 10 maths covers all 2 exercises, consisting of overall total of 26 questions.

Chapter 10 Exercises

Chapter 11 Constructions

The NCERT solutions for Class 10 Maths Chapter 11 deal with the problem constructions. It is also known as a geometrical drawing, which deals with constructing geometric figures using some specific geometric tools. It is a part of the geometry unit and geometry holds 15 marks in the final CBSE exams and construction is a scoring topic for students. In this chapter, there is a total of 2 exercises with 14 questions. In the first exercise, we will learn how to divide a line segment and in the second exercise, we will learn the construction of tangents to a circle.

Chapter 11 Exercises

Chapter 12 Areas Related to Circles

In this maths problem solving class 10 chapter, we will deal with areas related to circles. This chapter is a part of the Mensuration unit, which holds 10 marks in the CBSE Class 10 final exam. In this chapter, there are 3 exercises with 35 questions in them. In this chapter, we will learn the perimeter and area of a circle, areas of sector and segments of a circle, and the areas of combinations of plane figures. In NCERT solutions for class 10 math, chapter 12, areas related to circles, detailed solutions to each question are given.

Circles Class 10 NCERT Topics

  • Tangent to a Circle
  • Radius and Tangent Relation
  • Tangent From External Point to the Circle

Chapter 12 Exercises

Chapter 13 Surface Areas and Volumes

We have already done some part of the mensuration in 9th grade math. In class 10 math NCERT solutions Chapter 13, we will discuss how to find surface areas and volumes of combinations that are formed by two or more of the basic solids such as cone, cuboid, cylinder, sphere, and hemisphere. Apart from all these shapes, a new shape, frustum, will be introduced here in this particular chapter. In this chapter, there are a total of 5 exercises with 38 questions in them. In all the exercises, we will deal with questions on finding surface areas and volumes of solids.

Chapter 13 Exercises

Chapter 14 Statistics

In the previous class, we learned about data representation and have solved many calculations based questions on that. Statistics is also somehow related to data handling. In NCERT solutions for Class 10 Maths Chapter 14, the questions will be based on data and we will discuss how to find the measures of central tendency namely, mean, mode and median, from the ungrouped data to the grouped data. In this chapter, there are a total of 4 exercises with 25 questions. In NCERT Class 10 Maths Chapter 14 Statistics, you will also learn about the concept of cumulative frequency, its distribution and how to draw cumulative frequency curves. Students can practice exercise such as exercise 14.1 class 10 that are listed below to get an in-depth understanding of concepts.

Chapter 14 Exercises

Chapter 15 Probability

Probability is one of the newest concepts you will learn here in 10th grade mathematics. In the previous class, you have learned about empirical probabilities or experimental probabilities, of events that are based on the results of actual experiments. In this NCERT class 10 maths, we will discuss the theoretical probability (also called classical probability) of an event, and solve simple questions based on this concept. In NCERT solutions for class 10 math, chapter 15 probability, two exercises, including optional exercise consisting of overall of 68 questions, are covered.

Chapter 15 Exercises

Benefits of Class 10 Maths NCERT Solutions

  • NCERT solutions class 10 maths will help you in the completion of homework as well as for better scores in the board examinations.
  • Using these solutions, you can observe and learn the steps to solving some typical kind of questions.
  • The class 10 NCERT maths solutions will help you create a strong base of mathematics and will help you face competitive examinations in the future.
  • Along with maths, you can also learn the NCERT solution for class 10 science.

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Frequently Asked Question (FAQs)

1. What are the important topics of NCERT Class 10 Maths?

All the topics of class 10 maths book are important. In the Class 10 Mathematics NCERT book there are 15 chapters. These chapters are from Algebra, Geometry, Trigonometry, Statistics, and Probability. All the topics of NCERT Class 10 Mathematics are important for the CBSE board exam as the syllabus of the CBSE board is based on the NCERT Syllabus. To get a good score students can practice 10th maths solution, NCERT exemplar questions for Class 10, and also the previous year papers for the board exam.

2. Is Class 10 Mathematics useful for higher studies?

Yes, definitely 10th maths solutions is useful for higher studies in the field of Mathematics, Science and Engineering. In Class 11 NCERT Mathematics the higher version of Arithmatic progression, Trigonometry , Statistics, Probability, Coordinate Geometry and Quadratic equations are studied. students can practice CBSE class 10 maths solutions to get in-depth understanding of the concepts.

3. Are NCERT Solutions for CBSE class 10 maths beneficial for CBSE board students?

The CBSE class 10 maths solutions have several benefits, including:

  1. Establishing a solid understanding of basic principles and boosting exam readiness.
  2. Facilitating the learning of methods to solve challenging problems.
  3. Providing a comprehensive study resource for completing assignments efficiently and enhancing exam performance.

Therefore, practice all class 10th chapters to score well in the exam. Students can find 10th maths solutions above in this article.

4. Why should I use class 10th maths NCERT solutions

Maths class 10 NCERT solutions provide step-by-step explanations for each question and exercise in the textbook. These class 10th maths ncert solutions help you grasp the concepts, methods, and techniques required to solve mathematical problems. Using these solutions can enhance your understanding and boost your confidence in the subject.

5. What are the chapters covered in maths class 10 ncert solutions?

Here, students can find all class 10 maths all chapter name that are covered in NCERT maths solutions class 10.

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

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Get answers from students and experts

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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