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Class 10 Maths Notes, Solved Exercises Solutions, MCQ’s

Now, you are a matric student of part two and you have an idea how a question paper will be and how will you prepare for it. Let’s discuss some important tips for preparing exams of mathematics subject. My first tip is: you should buy a rough register for doing the practice of mathematics solutions because the more practice you do, the more math will be easy for you. Let’s move forward to further tips. You should prepare chapters in a way that the arrangement of chapters is in the textbook. As a result, if you do any topic, you have all the idea of what is done in a question because everything will be gone through from you. And it will be easy to prepare it from our math notes for class 10.

Furthermore, talking about the exercises of a chapter, you must prepare from the start of the chapter. And understand all the topic and formulas, and by applying that formulas or methods you will have to practice their example questions. Finally, move forward to the exercises. Practice every question of an exercise one by one and if you see a question has many similar parts then you can skip some of them and practice only those parts they are unique or a little bit tough for you. You can do all the exercise in this manner. I recommend you should do questions yourself and if you find any difficulty simply skim the solution from our math notes for class 10.

If you find this page or website helpful, do share with your friends and family. Try to spread love to your loving ones. And if you are a teacher, you should recommend this site to your class students to help them to get maximum marks in exams and share this site with your colleagues.

This Post Has 92 Comments

nice app for matric part 2 students and it is very hellp ful for me

aoa please upload notes of urdu and ps of tenth matric part 2

Fail hi Hona hai iski kya jarurat

Brother try again and again until u succeed

Aoa plesa 10th ky math ky solution snd kr dy

Solution required chapter 2

Assalam u Alaikum Please bta den k ye notes download kese kren

Bro ap ne jo bhi ex download krni h us pe click kr do or next page pe apko notes nazr aayen gy ap ne un notes k right corner main ik arrow ka icon click krna h or next page pe apko download ka icon nzr aa jae ga ↓

TOO MUCH HELPFULL!

Where is 13.3

Thanks “free ilm” for all. Your website is very helpfull for me. thanks again.You are doing good work.

Its really good for students

Sir please. mathschapter 13 ki exercise 13.3 bhi upload kr dn…..

ok, we’ll add (correct) it

I want full math book download.

Please add 13.3

Sir g free ilm website ki mobile mein book kaise hote ha plz ;; ?Sir g your website free Ilm is very important for students Thank you very much

pahly exercise open karain jo chahye. then scroll down kar ky right corner py aik pop-out show hoga , us py click karain us ky baad new page open hoga pdf ka. wahan download ka option hai right upper corner py (down arrow)

Too much helpful but 13.3 missing

Mathematics intru trigonometry che 7 send kr den

Sir there’s a mistake in ex 7.4 last questions plz correct it

Already present in notes download it

I recommend you to make a math quiz (sort of test game) after every chapter

yes you right

karachi k liye hai ye??

Nice app for matric part 2

Very good ❤️ 👌 mind

this so productive for me, like i have been preparing every thing from here as there were no notes given to us in lockdown excellent websites. really helpful, also i was expecting paast board exams but still it is a great web.

Amazing bht chy solutions hai es mey

good job but 10 class mathe exersise questions are not same to book

thanks for your hard work keep it up

Assalam o Alaikum Notes download kiss trh huthy

11th math k notes????

nice website its very helpful for me

good job but 10 class mathe exercises questions are not same to book I think Notes for matric

They are according to book

Thank you so much dor such a helpful notes

13.3??? Plz upload soon..

I am such a nalaik bacha in maths but make it much easy for me

Amazing work Mashallah ❤️❤️

Dear sir AA nice website its very helpful for me, but you can tell lecture site so nice

Nice thanks bro

Very good website but their are some mistakes You may resolve these mistake

Nyc website 😊 very helpful for students🤗👍

Is very easy

Helping website. It has helped people.. But there are some mistake in 9th and 10th notes. I have not checked 11th and 12th so I cant say any thing about it. Please fix your mistakes so students can get better understanding. Because of these mistake students will lose their marks and which will be very bad for them and their future. I hope you will fix these mistakes. Inshallah you will coperate with me. Thank you very much.

We are fixing these mistakes.

Brother first go and improve your English

dude he was just trying to help you guys get better notes he didnt say anything bad about the author

dumb people nowadays 😑😑🙄

Method is very easy but alot of mistakes

It is not helpful for me.

Becuase it cannot be open

Very nice this notes helps to study well because purchase the notes rate is very high I am happy for the. Thank you 💕

!how to download ?

it is very helpfull for me

shame on your self this app is trying to help you and you are downgrading them just shame on you

Is it possible to upload Karachi board math new book solved in pdf????

Masshallah. Is may boht mistake ha

Ap ko kasey pta!?

Insan hai ghalte to hoti hai You have mind so correct the mistake

Mir poor baoard azad kashmir class 10th

Please upload pairing scheme 2023 of all subjects

it’s a very helpful page for students, keep up the good work👍

This help me alot Many of the I understood from here But there’s exercise (13.3) missing I request you to add it

JazakAllah..These notes are much helpful…and are solving even minute difficuties✨

These notes are very helpful..

Ni’ce app

Thank you so much

wonderful app hai kafi solution mil rahai hain

Thanks for your help ☺️

Thanks So much … Help For Math

Nice simple method adopted to communicate.

Sir! please also upload all definitions of all chapters of mathematics class 9 and 10 both.,,,,Thanks

Leave a Reply Cancel reply

  • NCERT Solutions for Class 10 Mathematics Free PDF Download

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. 

  • Chapter 1 – Real Numbers
  • Chapter 2 – Polynomials

Chapter 3 – Pair of Linear Equations in Two Variables

Chapter 4 – quadratic equations, chapter 5 – arithmetic progressions, chapter 6 – triangles, chapter 7 – coordinate geometry, chapter 8 – introduction to trigonometry, chapter 9 – some applications of trigonometry.

  • Chapter 10 – Circles

Chapter 11 – Constructions

  • Chapter 12 – Areas Related to Circles

Chapter 13 – Surface Areas and Volumes

Chapter 14 – statistics, chapter 15 – probability.

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.

Download NCERT Solutions for all subjects here.

Download NCERT 10th Class Solutions

You can also access CBSE Guide for Class 10 Maths

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NCERT Syllabus 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

  • Exercise 1.1
  • Exercise 1.2
  • Exercise 1.3
  • Exercise 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
  • Exercise 2.2
  • Exercise 2.3
  • Exercise 2.4

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.

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 
  • Exercise 3.2
  • Exercise 3.3
  • Exercise 3.4
  • Exercise 3.5
  • Exercise 3.6
  • Exercise 3.7

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.

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

  • Exercise 4.2
  • Exercise 4.3
  • Exercise 4.4

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 .

NCERT Solutions for Class 10 Subject-wise

  • Class 10 Mathematics
  • Class 10 Science – Physics, Biology, Chemistry
  • Class 10 Social Science – History 
  • Class 10 Geography
  •  Class 10 Economics
  • Class 10 Political Science
  • Class 10 General Knowledge
  • Class 10 Hindi
  • Class 10 English

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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. (iii) A trial is made to answer a true-false question. The answer is right or wrong. (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?

  • \(\frac{2}{3}\)

−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  2  and  6

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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NCERT Solutions for Class 10

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Class 10 - Maths

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Updated according to new NCERT - 2023-24 NCERT Books.

NCERT Solutions of all chapters of Class 10 Maths are provided with videos. All exercise questions, examples and optional exercise questions have been solved with video of each and every question.

Topics of each chapter include 

  • Chapter 1 Real Numbers - Euclid's Division Lemma, Finding HCF using Euclid's Division Algorithm, Fundamental Theorem of Arithmetic (Prime Factorisation), Finding HCF, LCM using Prime Factorization, Proving numbers irrational, Decimal Expansion of numbers
  • Chapter 2 Polynomials - Geometrical Meaning of Zeroes of Polynomial, Relationship between Zeroes & Coefficients of Polynomial, Division Algorithm.
  • Chapter 3 Pair of Linear Equations in Two Variables - Forming equations, Solving by graph, Checking consistency - Consistent or Inconsistent, Equations intersect at point or are parallel or coincident, infinitely many solutions, no solution, unique solution, Elimination, Substitution, Cross-multiplication method, 
  • Chapter 4 Quadratic Equations - Roots of quadratic equation by factorization (splitting the middle term), completing the square, quadratic formula, nature of roots D = b 2 - 4ac
  • Chapter 5 Arithmetic Progressions(AP) - What is AP, common difference (d), n th term of AP, Sum of n terms of A.P. (S n ) - both formulas
  • Chapter 6 Triangles - What is Similarity, Different types of Similarity - AA, AAA, SAS, SSS, Area of similar triangles, Pythagoras theorem
  • Chapter 7 Coordinate Geometry - Abscissa, Ordinate, Distance formula, Collinear Points, Types of quadrilateral/triangle formed, Finding Equidistant point, Finding ratio by section formula, Using properties of parallelogram with Section Formula, Finding Area of Triangle when vertices are given, Proving 3 points collinear using Area of Triangle Formula
  • Chapter 8 Introduction to Trigonometry - What is sin , cos, tan, cot, sec, cosec, Value of trigonometric ratios at 0°, 30°, 45°, 60° & 90°, sin (90 – θ) = cos θ , tan (90 – θ) = cot θ , sec (90 – θ) = cosec θ, sin 2 x + cos 2 x = 1 , sec 2 x = 1 + tan 2 x , cosec 2 x = 1 + cot 2 x. And how to remember all this
  • Chapter 9 Some Applications of Trigonometry - Finding height and distances, knowing what is angle of depression, angle of elevation
  • Chapter 10 Circles - Tangent to circle, Number of tangents from a point of the circle, Length of tangent.
  • Chapter 11 Constructions  - Using the concepts we have studied before, first we learn how to divide a line segment in a particular ratio, then we study how to draw a triangle similar to the triangle (where Scale Factor is greater than 1, and less than 1) and then we learn how to create a tangent to the circle from a point outside it. Justification of all the constructions is also explained.
  • Chapter 12 Areas Related to Circles - Finding Perimeter and area of circle, Length of arc of sector, Area of sector, Area of segment, Area of semicircle and doing some questions where all these concepts are used
  • Chapter 13 Surface Areas and Volumes - Surface area & volume of combination of solids - cone, cube, cuboid, cylinder, sphere, hemisphere, Conversion of one shape to another, Volume & Surface Area of frustum of cone.
  • Chapter 14 Statistics - Finding mean - Normal method, assumed mean method, step deviation method.  Finding median - for more than, less than using median class and cumulative frequency, Finding Mode, Drawing More than - less than ogive.
  • Chapter 15 Probability - Finding Probability of cases where 2 dies are thrown, or when using cards , Probability of complementary events.

In each chapter, there are two division - Serial Order Wise, and Concept Wise.

If you want to look for a specific question or example of the NCERT Book, click on any link below Serial Order Wise. 

If you want to study the chapter for the first time, or revise - Click on Concept Wise . Concept Wise the Teachoo's (टीचू) way of doing the chapter. First the concept is explained, and then the questions are explained, from easy to difficult.

When you click on a topic link or an exercise link, the first question will open. For other questions, there is a list with arrows which has all the questions. Click on any question or topic from that arrowed list to open it.

Click on any chapter below to find solutions to all questions.

Chapter 1 Class 10 Real Numbers

Chapter 2 class 10 polynomials, chapter 3 class 10 pair of linear equations in two variables, chapter 4 class 10 quadratic equations, chapter 5 class 10 arithmetic progressions, chapter 6 class 10 triangles, chapter 7 class 10 coordinate geometry, chapter 8 class 10 introduction to trignometry, chapter 9 class 10 some applications of trigonometry, chapter 10 class 10 circles, constructions, chapter 11 class 10 areas related to circles, chapter 12 class 10 surface areas and volumes, chapter 13 class 10 statistics, chapter 14 class 10 probability, important questions for exam - class 10, solutions of sample papers for class 10 boards.

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  • NCERT Solutions for Class 10 Maths
  • NCERT Solutions

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

NCERT Solutions for Class 10 Maths serve as a valuable resource for students navigating the complexities of mathematics at the 10th-grade level. These solutions are specifically designed to complement the NCERT class 10 Maths book , offering clear explanations and step-by-step solutions to problems. The aim is to make mathematical concepts more accessible and understandable for students. The Class 10 Maths NCERT solutions cover a wide range of topics, including algebra, geometry, trigonometry, statistics, and more. Students can rely on these solutions to reinforce their understanding of fundamental mathematical principles and enhance problem-solving skills. One notable advantage of NCERT Solutions Class 10 Maths is their alignment with the curriculum prescribed by the Central Board of Secondary Education (CBSE) . This ensures that students are well-prepared for their board exams, as the solutions closely follow the CBSE class 10th maths guidelines and exam patterns.

NCERT Solutions for Class 10 Maths - Chapter 1 to 15 with Exercises image

Class 10 Maths syllabus aims at helping the students build a strong base of these topics by giving them the basic knowledge about them, making them understand theorems and concepts and testing them enough in the form of exercise and examples in the textbook. The exercises in the NCERT textbook   are designed for the students to use their skills and learnings of each topic to the maximum. Before each exercise, the students are also given enough examples to refer to and understand the questions with the help of the step by step explanations provided in the textbooks.

👉 Please check here for   Crash Course for Class 10 CBSE

NCERT Solutions for Class 10 Maths | Chapter-Wise List

Given below are the chapter-wise NCERT Solutions for Class 10 Maths . These solutions are provided by the Maths experts at Vedantu in a detailed manner. You can use it as your 10th maths guide . Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

NCERT Solutions for Class 10 Maths provided here covers all the chapters and Exercises of Class 10 Maths. These solutions are prepared by expert teachers who are having years of experience in teaching Maths for Class 10 students. Class 10 Maths NCERT Solutions are explained in step by step manner and available in PDF format. Students can now download the class 10 Maths NCERT solutions PDFs for an uninterrupted learning experience.

The Class 10 Maths NCERT Solution PDFs cover all the Exercises from Chapters 1 - 15 present in the NCERT books. These Class 10 Maths solutions are written according to the CBSE exam guidelines to increase the students understanding of the subject and help them to score well. The NCERT solutions for class 10 Mathematics PDFs will not only prepare the students for final exams but will also help to understand the concept better as a 10th Maths guide . Science and Maths are two important subjects of class 10 and if you are looking for reliable and accurate NCERT Solutions for Class 10 Science you will find that on Vedantu.

Detailed Overview of Class 10 Maths NCERT Solutions

Ncert solutions for class 10 maths pdf updated for 2023-24 session.

NCERT Maths solution pdfs for Class 10 is a very reliable and accurate source of information. The study material contains an exhaustive explanation to all the questions. These answers are written clearly and step by step to maximise retention. While going through these solutions, students will find themselves understanding the concept better. Practising regularly is a prerequisite if students want to score well in mathematics. NCERT solutions Class 10th act as a perfect guide for you. You can consult the class 10th maths guide to brush up on your memory or help you if you get stuck somewhere.

The solutions provided by Vedantu are formulated and designed by professionals who have years of experience in the field of teaching. The answers are given in simple language for the students to understand the concept better. Vedantu aims at providing solutions for each question which is easy for students of different calibre to understand. All the syllabus and solutions are updated in accordance with the changes to the NCERT textbook or the syllabus guidelines given by the CBSE. Vedantu is the leading online platform providing answers for all the solutions for each and every subject and class. Helping students understand a subject and enjoy learning new things is what Vedantu strives for. Hence, the comfort and ease of the students are foremost when developing solutions for the questions. The solutions come in handy if the students get stuck or need to understand what they are doing wrong. It is a good way for the students to analyse their answers and performance and also get more practice by referring to the extra questions in the solutions pdf. 

NCERT Solutions for Class 10 Maths Chapter 1 - Real Numbers

There are 4 Exercises present in this chapter. Students will learn about real numbers and irrational numbers in the 1st chapter of Class 10 Maths. CBSE Class 10 Maths Chapter 1 explains Euclid’s Division Lemma, HCF, LCM, Divisibility of integers, rational number, irrational number and decimal expansion of rational numbers with the help of theorem.

Euclid’s Division Lemma states that “Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤r <b”. This gives the base for the division algorithm which is used to take out the HCF for two positive integers. The Fundamental Theorem of Arithmetic is also explained in this chapter. It explains how the LCM and HCF for two positive integers can be derived.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 1 of CBSE Class 10 Maths Solutions –

Chapter 1: Important Questions

Chapter 1: Important Formulas

Chapter 1: Revision Notes

Chapter 1: NCERT Exemplar Solutions

Chapter 1: RD Sharma Solutions

NCERT Solution for Class 10 Mathematics Chapter 2 - Polynomials

There are a total of 4 Exercises including an optional Exercise in the 2nd chapter of class 10 Maths. The first Exercise is about finding zeros of polynomials p(x). In the second Exercise, the students need to find a quadratic polynomial. The second Exercise is based on the relationship between 0’s and coefficients of a polynomial. The third Exercise has questions on the division of polynomials. The last Exercise covers questions from all the concepts of Class 10 Maths Chapter 2.

The students should also know the steps to derive the Division Algorithm for polynomials. It can be asked in the exam as it is an important concept in the chapter that has been explained.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 2 of CBSE Class 10 Maths Solutions –

Chapter 2: Important Questions

Chapter 2: Important Formulas

Chapter 2: Revision Notes

Chapter 2: NCERT Exemplar Solutions

Chapter 2: RD Sharma Solutions

NCERT Solutions for Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables

The third chapter of class 10 maths is about the linear equations in two variables. It describes what a linear equation in two variables is and how to solve the problems of linear equations in two variables. In the first Exercise (Ex 3.1), representing a problem or situation algebraically and graphically is taught. The second Exercise, i.e, Ex 3.2, depicts the methods of solving linear equations by graphical method. The next four Exercises, Ex 3.3, 3.4, 3.5 and 3.6 explain the different types of methods of solving the pairs of linear equations. The methods explained here are algebraic method, cross-multiplication method, elimination method and substitution method. Exercise 3.7 is a mixed bag. It contains questions from all the Exercises.

Important Formulas:

The general form for a pair of linear equations in two variables, x and y, is

$a_1 x + b_1 y + c_1 = 0$ and $a_2 x + b_2 y + c_2 = 0$

Where, $a_1, b_1, c_1, a_2, b_2, c_2$ - real numbers 

Here $a_1^2 + b_1^2 \neq 0$ and $a_2^2 + b_2^2 \neq 0$ 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 3 of CBSE Class 10 Maths Solutions –

Chapter 3: Important Questions

Chapter 3: Important Formulas

Chapter 3: Revision Notes

Chapter 3: NCERT Exemplar Solutions

Chapter 3: RD Sharma Solutions  

NCERT Solutions for Class 10 Maths Chapter 4 - Quadratic Equations

Chapter 4 of Class 10 Maths NCERT book PDF solution is all about quadratic equations. This chapter explains what a quadratic equation is and the methods of solving quadratic equations. It also explains the factorization method of solving quadratic equations and the square method. The chapter gives the details of relationships between discriminants and the nature of roots. Also, the problems of real-life have been solved as examples in this chapter.

Important formulas for the students to keep in mind:

If b 2 - 4ac > 0, then the answer obtained should be two distinct real roots. 

If b 2 - 4ac = 0, then the roots of the equation ax 2 + bx + c = 0 should be -b/2a

It can be said in this case then that the equation ax 2 + bx + c = 0 has two equal roots.

If b 2 – 4ac < 0, then there is no real number whose square is b 2 – 4ac. Hence, there are no real roots for the given quadratic equation in this case.

b 2 – 4ac is called the discriminant of this quadratic equation since, b 2 – 4ac determines whether the quadratic equation ax 2 + bx + c = 0 has real roots or not

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 4 of CBSE Class 10 Maths Solutions –

Chapter 4: Important Questions

Chapter 4: Important Formulas

Chapter 4: Revision Notes

Chapter 4: NCERT Exemplar Solutions

Chapter 4: RD Sharma Solutions

NCERT Solutions for Class 10 Mathematics Chapter 5 - Arithmetic Progressions

This chapter introduces a new topic to the students - Arithmetic Progression, commonly called AP. Students will learn what is AP, the derivation of the nth term, finding the sum of first n terms of the AP and solving the real-life problems using AP in this chapter. The first Exercise of the chapter teaches how to represent a problem or situation in the form of AP, how to find the first term and difference of the AP and to find whether the given series is AP or not. The next Exercise, Ex 5.2 explains how to find the nth term of the AP using the formula. The third Exercise describes how to find the sum of the first n terms of AP and contains questions related to the topic. The last and fourth exercises have questions related to the topics taught in the chapter.

Important formulas that come in handy while solving questions from the exercises in the textbook are:

Finding the nth term of a progression- n th term = a + (n-1) d

2. Sum of the first n terms in sequence- S n = n/2 [2a + (n-1)d]

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 5 of CBSE Class 10 Maths Solutions –

Chapter 5: Important Questions

Chapter 5: Revision Notes

Chapter 5: NCERT Exemplar Solutions

Chapter 5: RD Sharma Solutions

NCERT Solutions for Class 10 Maths Chapter 6 - Triangles

Chapter 6 of class 10 gives details about the triangles. The chapter gives details about the figures with the same shape but different sizes. It explains the similarity of the triangles, theorems associated with the similarity of triangles and the concept of congruent triangles. Further, theorems related to areas of triangles, the Pythagoras theorem and the converse of Pythagoras theorem is explained.

Important theorems that students should know thoroughly while preparing for the exam include:

Theorem 1: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Theorem 2: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Theorem 3: If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.

Theorem 4: If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.

Theorem 5: If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

Theorem 6: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Theorem 7: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

Theorem 8: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Theorem 9: In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

All the exercises throughout the chapter test how well the students have understood these theorems and if they are able to apply them and get answers to the questions. If the students have enough practice of the questions from the exercise, then understanding the theorems will be relatively easy for them as well.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 6 of CBSE Class 10 Maths Solutions –

Chapter 6: Important Questions

Chapter 6: Revision Notes

Chapter 6: NCERT Exemplar Solutions

Triangles : RD Sharma Solutions

NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry

Class 10 Maths Chapter 7 explains coordinate geometry, the maths of locating a given point with the help of an ordered pair of numbers. The coordinate or cartesian geometry helps to find the distance between two points whose coordinates are given. The concept of finding the area of a triangle formed by three given points. Also, the ways of finding the coordinates of the point which divides a line segment joining two given points in a given ratio are explained in the chapter. The students will learn distance formula, section formula and area of triangles in this chapter of NCERT Solutions.

1. Distance Formula - $P Q=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

2. Section Formula - $m_1: m_2=\left(\dfrac{m_1 x_2+m_2 x_1}{m_1+m_2}, \dfrac{m_1 y_2+m_2 y_1}{m_1+m_2}\right)$

2. Area of Triangle $ = \dfrac{1}{2}\left[x_1\left(y_2 - y_3\right) + x_2\left(y_3 - y_1\right) + x_3\left(y_1 - y_2\right)\right]$

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 7 of CBSE Class 10 Maths Solutions –

Chapter 7: Important Questions

Chapter 7: Revision Notes

Chapter 7: NCERT Exemplar Solutions

Coordinate Geometry Solutions : RD Sharma Solutions

NCERT Solutions for Class 10 Maths Chapter 8 - Introduction to Trigonometry

Chapter 8 of NCERT Solutions introduces trigonometry to the students. Trigonometry is the study of the ratio of right triangles with respect to the acute angles, which are known as trigonometric ratios of the angles. Also, the trigonometric ratios for angles 0∘ and 90∘. Students will also learn to calculate trigonometric ratios for the given angles and also a few trigonometric identities.

The chapter gives a basic introduction to trigonometry that comes in handy for the students in Class 11 and 12 as well. They are taught the introductory formulas of trigonometry so that they have a strong grip over the basics that will help them in higher classes and the future. In addition to the formulas, the relationship between the ratios and angles is also explained in the chapter. 

1. $\sin \theta = \dfrac{\text{Side opposite to angle}}{\text{Hypotenuse}} = \dfrac{\text { Perpendicular }}{\text { Hypotenuse }} = P/H$

2. $\cos \theta = \dfrac{\text { Adjacent side to angle } \theta}{\text { Hypotenuse }} = \dfrac{\text { Base }}{\text { Hypotenuse }} = B/H$

3. $\tan \theta = \dfrac{\text {Side opposite to angle }\theta}{\text {Adjacent side to angle }\theta} = P/B$

4. $\sec \theta = \dfrac{1}{\cos \theta}$

5. $\cot \theta = \dfrac{1}{\tan \theta}$

6. $\text{cosec} \theta = \dfrac{1}{\sin \theta}$

7. $\tan \theta = \dfrac{{Sin} \theta}{{Cos} \theta}$

Trigonometric ratios that are important for complementary angles are:

sin (90° – A) = cos A,

cos (90° – A) = sin A,

tan (90° – A) = cot A,

cot (90° – A) = tan A,

sec (90° – A) = cosec A,

cosec (90° – A) = sec A

sin 2 A + cos 2 A = 1,

sec 2 A – tan 2 A = 1 for 0° ≤ A < 90°,

cosec 2 A = 1 + cot 2 A for 0° < A ≤ 90°

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 8 of CBSE Class 10 Maths Solutions –

Chapter 8: Important Questions

Chapter 8: Revision Notes

Chapter 8: NCERT Exemplar Solutions

NCERT Solutions for Class 10 Maths Chapter 9 - Some Applications of Trigonometry

Chapter 9 is the continuation of chapter 8 where the students will learn about the application of trigonometry which they learnt in the previous chapter. This chapter helps to understand how trigonometry is applied to our everyday life to find out the height and distance of various objects. They will also learn how trigonometry is applied and used in navigation, construction and determining the position of any piece of land based on the total latitude and longitudes.

Topics Covered in Class 10 Maths Chapter 9 - Some Applications of Trigonometry:

In Class 10 Maths Chapter 9, we delve into "Some Applications of Trigonometry" with a focus on "Heights and Distances." This involves exploring angles of elevation and depression, specifically at 30°, 45°, and 60°.

Let's understand a few key points:

Line of Sight: This is the line drawn from your eye to the point you're looking at.

Angle of Elevation: When the point you're viewing is above your eye level, like when you tilt your head up.

Angle of Depression: When the point you're viewing is below your eye level, like when you lower your head.

To apply these concepts practically to solve problems related to heights and distances, consider three key factors:

The distance from the observer (DE) to the base of the object (minar).

The angle of elevation (∠BAC) from the observer to the top of the object.

The height of the observer (AE).

Assuming you know these three conditions, you can determine the height of the object (minar). In the figure, we observe that CD equals CB plus BD. Here, BD is equivalent to AE, which represents the height of the observer.

To find BC, we utilize trigonometric ratios involving ∠BAC or ∠A in triangle ABC. Since BC is the opposite side concerning the known ∠A, our options are narrowed down to using either tan A or cot A, as these ratios involve AB and BC.

Therefore, we can use tan A = BC/AB or cot A = AB/BC to find BC. Adding AE to BC yields the height of the minar.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 9 of CBSE Class 10 Maths Solutions –

Chapter 9: Important Questions

Chapter 9: Revision Notes

Chapter 9: NCERT Exemplar Solutions

NCERT Solutions for Class 10 Mathematics Chapter 10 - Circles

Chapter 10 for class 10 maths, NCERT Solutions continues the details of Circles studies in previous classes. In this chapter, students will be introduced to the concept of tangents and the number of tangents from a point on a circle. 

Important Theorems –

Theorem 1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Theorem 2: The lengths of tangents drawn from an external point to a circle are equal.

Tangents to a circle from a certain point have three situations:

1. There is no tangent to a circle passing through a point lying inside the circle.

2. There is one and only one tangent to a circle passing through a point lying on the circle.

3. There are exactly two tangents to a circle through a point lying outside the circle.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 10 of CBSE Class 10 Maths Solutions –

Chapter 10: Important Questions

Chapter 10: Revision Notes

Chapter 10: NCERT Exemplar Solutions

NCERT Solutions for Class 10 Mathematics Chapter 11 - Constructions

Chapter 11 is one of the interesting chapters. This chapter is all about constructing various geometric figures. The students will learn to divide a line segment, and how to draw tangents to a circle. The methods of construction are well explained in the chapter to clear the concepts.

Methods and steps for the construction of the tangents to the circle are explained in the chapter with enough examples before each exercise. Examples before each exercise are given so that understanding the methods and theorems becomes easier for the students.

In Class 10 Maths Chapter 11 on Constructions, We Learn about Three Main Topics:

1. Division of a Line Segment: This is about splitting a line into two parts, but not just any parts. We learn to do this in a specific ratio. Imagine you have a line, and you want to divide it in a certain way. This is what we're talking about here.

2. Tangent to a Circle: Ever wondered how to draw a line that just touches a circle from the outside? That's what we dive into here. It's like drawing a line that gently rests against the circle from a point outside it.

3. Constructing a Similar Triangle: Here, we explore how to create a triangle that looks just like another triangle but maybe in a different size. We use something called a scale factor to guide us in making the new triangle the right size compared to the original one.

Important Points:

Construction 11.1: To divide a line segment in a given ratio.

This is about splitting a line in a specific ratio. Think of it as cutting a line into pieces, but we're being very precise about how long each piece is.

Construction 11.2: To construct a triangle similar to a given triangle as per the given scale factor.

Imagine you have a triangle, and you want to make another one that looks just like it but maybe bigger or smaller. That's what we're learning to do in this construction, using something called a scale factor.

Construction 11.3: To construct the tangents to a circle from a point outside it.

Drawing a line that gently touches a circle from the outside might sound tricky, but with this construction, we figure out just how to do that. It's like drawing the perfect tangent line to the circle.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 11 of CBSE Class 10 Maths Solutions –

Chapter 11: Important Questions

Chapter 11: Revision Notes

Chapter 11: NCERT Exemplar Solutions

NCERT Solutions Class 10 Maths Chapter 12 - Areas Related to Circles

As the name suggests, the chapter is about the perimeter and area of a circle. The concepts of finding the area of a sector and segment of a circle are clarified here. This chapter further explains how to find the area of the figures that contains a circle or part of a circle.

Important formulas from within the chapter for the students to practice–

Circumference = 2πr

Area of the circle = πr 2

Area of the sector of angle θ = (θ/360) × πr 2

Length of an arc of a sector of angle θ = (θ/360) × 2 π r where r is the radius of the circle

  Along with this, students can also download additional study materials provided by Vedantu, for Chapter 12 of CBSE Class 10 Maths Solutions –

Chapter 12: Important Questions

Chapter 12: Revision Notes

Areas Related to Circles: NCERT Exemplar Solutions

NCERT Solutions for Class 10 Maths Chapter 13 - Surface Areas and Volumes

Chapter 13 of Class 10 Maths NCERT book PDF solution is about the surface areas and volumes of different objects and shapes. In the five Exercises of this chapter, find the surface area of any object which is made up of two or more different solid shapes. The solid shapes include cuboid, cone, sphere, hemisphere and cylinder. Then, there are questions on finding the volume of the objects that are again made up of two different solid shapes. Also, there are questions that ask about the conversion from one shape to another. This chapter further explains how to find the volume, curved surface area and total surface area of a frustum of a cone.

Important formulas used for calculating surface areas and volumes of different objects

TSA of new solid = CSA of one hemisphere + CSA of cylinder + CSA of other hemispheres

Diameter of sphere = 2r

The surface area of sphere = 4 π r 2

The volume of Sphere = 4/3 π r 3

The curved surface area of Cylinder = 2 πrh

Area of two circular bases = 2 πr 2

The total surface area of Cylinder = Circumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr 2

Volume of Cylinder = π r 2 h

Slant height of cone = l = √(r 2 + h 2 )

Curved surface area of cone = πrl

Total surface area of cone = πr (l + r)

Volume of cone = ⅓ π r 2 h

Perimeter of cuboid = 4(l + b +h)

Length of the longest diagonal of a cuboid = √(l 2 + b 2 + h 2 )

Total surface area of cuboid = 2(l×b + b×h + l×h)

Volume of Cuboid = l × b × h

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 13 of CBSE Class 10 Maths Solutions –

Chapter 13: Important Questions

Chapter 13: Revision Notes

Surface Areas and Volumes: NCERT Exemplar Solutions

NCERT Solutions for Class 10 Maths Chapter 14 - Statistics

This is another interesting chapter where the students learn about the numerical representation of data, grouped or ungrouped. They further learn about finding the mean, median and mode of the given data. In the next exercise, they will learn about the cumulative frequency distribution and draw cumulative frequency curves.

The mean of the grouped data can be found by 3 methods.

1. Direct Method: $\overline{{x}}=\dfrac{\sum_{i=1}^n f_i x_i}{\sum_{i=1}^n f_i}$, where $\sum f_i x_i$ is the sum of observations from value $i=1$ to $n$ And $\sum f_i$ is the number of observations from value $i=1$ to $n$

2. Assumed mean method: $\overline{{x}}=a+\dfrac{\sum_{i=1}^n f_i d_i}{\sum_{i=1}^n f_i}$

3. Step deviation method $: \overline{{x}}=a+\dfrac{\sum_{i=1}^n f_i u_i}{\sum_{i=1}^n f_i} \times h$

4. Mode: $=l+\dfrac{f_1-f_0}{2 f_1-f_0-f_2} \times h$

5. Median: $=l+\dfrac{\dfrac{n}{2}-c f}{f} \times h$

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 14 of CBSE Class 10 Maths Solutions –

Chapter 14: Important Questions

Chapter 14: Revision Notes

NCERT Solutions for Class 10 Maths Chapter 15 - Probability

Chapter 15 or the last chapter of NCERT Solutions for Class 10 Maths teaches probability. It elaborates and explains the difference between experimental probability and theoretical probability.  The chapter is full of examples to clarify the concept of probability to the learners.

Probability is also an extremely important chapter for the students to focus on as this chapter is further discussed and new topics are introduced in the classes ahead. It is important that the students get a strong grip on the basics of the chapter in class 10 so that keeping up with the formulas and new topics introduced in higher classes is easier. If the students understand well and practice enough it is also an easy chapter to score good marks in.

The chance of something happening, let's call it event E, is called its probability, written as P(E). 

\[ P(A) = \dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

We figure this out by assuming that all the possible outcomes are equally likely.

If an event is guaranteed to happen, we say it has a probability of 1. If it's impossible, then its probability is 0.

The probability of any event E is a number between 0 and 1. If it's a sure thing, it's close to 1; if it's impossible, it's close to 0.

When an event has only one possible outcome, it's called an elementary event. When we add up the probabilities of all the elementary events in an experiment, the total is always 1.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 15 of CBSE Class 10 Maths Solutions –

Chapter 15: Important Questions

Chapter 15: Revision Notes

Finding accurate answers online is a difficult task but Vedantu’s NCERT class 10 Maths SolutionsPDF is a reliable source. Students can download the PDF easily and start going through the chapters. You will find clear categorisation and step by step solutions of all the questions with a clear conclusion. This will help you to understand how you can write answers in your exams to help you score well.

CBSE Class 10 Maths Exam Pattern for 2023-24

The Central Board of Secondary Education conducts CBSE Class 10 Board exams every year. The exam is of 100 marks where 80 marks are for theory whereas 20 marks are given for internal assessment. To understand the marking scheme in a better way, you should understand the exam pattern clearly. To score well in the exam, you should know how much mark is awarded for each question and each step of the question. Every year, just before the board exams, the board releases sample papers and marking schemes so that all the doubts of the students are cleared. According to the revised pattern of CBSE, 25% of the theory questions are going to be objective. The number of questions is increased and the marks per question are reduced. This marking scheme will be helpful to the students as the maximum number of questions will become objective or very short answer type as the marks per question has been reduced.

CBSE focuses on the all-around development of Class 10 students to prepare them for their further education. To perform well in Class 10 then becomes fairly important. So students are advised to go through the NCERT solution for Class 10 PDF regularly. CBSE marking scheme is stepwise so you have scored accordingly. Therefore students should write each step clearly and give a proper conclusion at the end of the answer. The unit wise marks weightage of the mathematics paper is as follows:

The paper has four sections. There are a total of 30 questions for 80 marks.

CBSE Class 10 Maths Chapter-Wise Marks Weightage 

Internal assessment for cbse class 10 maths, cbse class 10 maths question paper design 2023-24, cbse class 10th new plan 2023.

The following are some major changes that are planned to be introduced in the new CBSE Exam Pattern:

Question papers will be designed to assess students' problem-solving and analytical skills.

The paper design will be revised to include more short answer-type questions, like those ranging from 1 to 5 points.

Some vocational course exams might be held in February, and final board exams will be completed in March within 15 days.

Following the early completion of boards, the results are likely to be announced earlier than the existing structure's schedule.

Topics Covered in Class 10 Chapter Wise

1. Real Numbers 

Real Numbers

Euclid’s Division Lemma

Fundamental Theorem of Arithmetic

Irrational Numbers

Rational Numbers

2. Polynomials 

Zeros of a polynomial. 

Relationship between zeroes 

Coefficients of quadratic polynomials only.

3. Pair of Linear Equations in Two Variables

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. 

Algebraic conditions for number of solutions. 

Solution of a pair of linear equations in two variables algebraically – by substitution and by elimination. 

Simple situational problems. 

Simple problems on equations reducible to linear equations.

4. Quadratic Equations

Standard form of a quadratic equation ax 2 + bx + c = 0, (a ≠ 0). 

Solutions of quadratic equations (only real roots) by factorization, and by using the quadratic formulas. 

Relationship between discriminant and nature of roots. 

Situational problems based on quadratic equations.

5. Arithmetic Progression

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

6. Triangles 

Concept of a similar and congruent figure

Theorems related to the similarity of triangles

Areas of similar triangles

Pythagoras Theorem and converse of Pythagoras Theorem

7. Coordinate Geometry

Concepts of coordinate geometry.

Graphs of linear equations. 

Distance formula. 

Section formula.

8. Introduction to Trigonometry

Trigonometric ratios of an acute angle of a right-angled triangle. 

Proof of their existence. 

Values of the trigonometric ratios. 

Relationships between the ratios.

9. Some Applications of Trigonometry

Angle of elevation. 

Angle of Depression.

Simple problems on heights and distances.

10. Circles

Various terms related to a circle such as a chord, segment.

Important Theorems

Tangent to a Circle.

Number of Tangents from a Point on a Circle.

11. Constructions

Dividing a line segment.

Construction of tangents to a circle.

12. Areas Related to Circles

Calculate the area of a circle

Area of sectors and segments of a circle. 

Problems based on areas and perimeter.

Circumference of the above plane figures.

13. Surface Areas and Volumes

Surface areas and volumes of combinations of any two figures like cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

Problems that involve converting one type of metallic solid into another and other mixed problems. 

14. Statistics

Mean, median and mode of grouped data. 

Mean by Direct Method and Assumed Mean Method only.

15. Probability

Classical definition of probability. 

Simple problems on finding the probability of an event.

Benefits of NCERT Solution for Class 10 Maths: Your 10th Maths Guide

NCERT 10 Maths solutions PDF created at Vedantu is one of the most sought after study materials online. Vedantu’s online learning ecosystem has everything the students need. Students go through the PDF and gain an in-depth understanding of the topics which prepares them for their final exams and also for their further studies. Some key features of the Class 10 NCERT Maths solution PDF are:

Step by step calculation of every question to improve understanding of the topic.

An exhaustive explanation of the problems to encourage concept-based learning.

Up to date with the improvements made in the syllabus.

Categorised chapter wise to improve ease of use.

Great for revision and brushing up before examinations.

Additional questions to help you track your progress.

Follow an exam pattern to help you score well in the examinations.

Great for revision as the whole syllabus is consolidated in one solution PDF that makes it easier for the students to refer to before the exam.

Solutions are provided in a simple easy to understand language. 

Extra solved questions are also provided so that students can refer to them while practising extra questions

Modified to any changes made in the syllabus or exam pattern by the CBSE board.

They are available to download for free on the Vedantu website. The students can download them at any point they feel necessary and start focussing on their preparation with the help of the solutions pdf.

How will CBSE Class 10 Maths Solutions Help You To Score High Marks in Board Exams?

Maths is an important as well as difficult subject to crack. To score high marks in maths board exams, you need to have a clear picture of the concepts taught in grade 10. If you can grasp the concepts and topics of class 10 maths, you can definitely score very high marks in the board exams. But this is not easy. You need to do constant practise along with understanding the topics and the concepts behind them. To make the work smarter for you, NCERT Solutions are provided. Here, a detailed description of all the topics is provided by the highly qualified experts of Vedantu. They put all their experience in the pdf of NCERT Solutions for Class 10 Maths . So, if you want to score high marks in board exams do refer to our pdfs which will make your scoring high.

The solutions PDF can help you at any point for wherever you are getting stuck in the syllabus. It has extra practice questions for you to assess your performance once you have understood the concepts clearly. The concepts are explained in such an easy manner that the students can understand them quickly. Maths is a subject that requires thorough practice besides the understanding of the concept. The PDF gives easy to understand explanations and enough practise questions for the students to follow. It is their complete guide for how to prepare for exams well and score good marks in the board exams. The solutions pdf have enough extra questions for you to understand the kinds of questions to expect in the exam as well. The sample papers provided online can also be practised. This 10th Maths Guide will give you a chance to assess your knowledge of all the topics and also how you would attempt the actual exam.

Why Refer NCERT Maths Class 10 Solutions PDF for Board Exams?

The Class 10 NCERT Maths solutions PDF for boad exam have several benefits, such as: 

NCERT Maths Class 10 PDF is a free PDF available online, providing students with easy access to study materials.

The exam pattern emphasizes application-based learning, testing concepts taught in textbooks.

Students need to be well-versed in formulas, theorems, identities, and diagrams for exams, making preparation seem challenging.

Vedantu’s NCERT solution for Class 10 , assisting students in their exam preparations. 

The PDF is organized into chapters, facilitating efficient use as a reference study material.

NCERT Solutions for Class 10 PDF helps manage time during exam preparations by providing quick access to specific chapters for problem-solving.

Chapters are focused on based on their marks weightage, and solutions are presented in an easy-to-understand language.

The solutions PDF becomes a go-to book for revision, allowing students to practice and score well in exams.

Solutions are designed by experienced teachers who understand exam expectations, providing insights into correct answer formulation.

The NCERT textbook is the main resource recommended by the CBSE for Class 10 Maths exam preparation.

Students are advised to thoroughly practice each question and example from the textbook for exam readiness along with 10th Maths Guide. 

Board exam question papers are usually formed from the NCERT textbooks , establishing the textbook's importance.

Vedantu’s solutions PDF aligns with the NCERT book , ensuring accuracy and relevance.

The solutions PDF is updated in accordance with changes in the textbook or CBSE requirements.

After studying from NCERT textbooks , students can refer to the solutions PDF for extra help and practice.

The solutions PDF provides answers to exercise questions, aiding students when they face challenges.

The NCERT textbook serves as the primary resource for students to commence their exam preparation.

Examples in the textbook offer insights into question paper expectations, guiding students on answer formulation.

Vedantu’s NCERT Solutions for Class 10 Maths, aligned with the NCERT textbook, stand as a valuable and accessible tool for students to ace their exams with a clear understanding of concepts and effective problem-solving skills.

  

Important Tips for Scoring Well in the Board Exams

Class 10 is an important class in most students’ school lives and is the first class where the students have to appear for a board exam. The class may seem daunting but if the students have been thorough with their studies for the whole academic year then it will not be difficult for them to score good marks at all. To achieve a good score it is necessary that the students keep the following tips and suggestions in mind for the whole year and especially while preparing for the exams.

1. Regular Revision is Key:

Consistency in revising and practicing daily lessons is crucial.

Regular practice ensures a better understanding and prevents topics from becoming overwhelming during exams.

2. Practice Extensively:

Practice all examples and exercises in the NCERT book.

Utilize solutions PDF for self-assessment and focus on areas with incorrect answers.

Refer to Vedantu's solutions for additional practice and clarity.

3. Concept Clarity Matters:

Seek teacher assistance for any doubts promptly.

Utilize Vedantu's Solutions PDF for easy-to-understand explanations.

Ensure a clear understanding of all concepts well in advance of exams.

4. Understand Syllabus and Paper Pattern:

Familiarize yourself with the syllabus, topic weights, and exam pattern.

This knowledge aids in efficient exam preparation.

5. Effective Time Management:

Create a timetable considering topic weights and personal strengths/weaknesses.

Set daily and weekly goals for focused and motivated study sessions.

Include breaks for effective learning and retention.

6. Identify Strengths and Weaknesses:

Allocate equal time to all topics; practice weaker areas more.

Ensure confidence in every topic by thorough practice.

7. Note-taking for Consolidation:

Write down theorems and formulas for consolidation and quick revision.

Notes act as a reference point and aid in better memorization.

8. Class 10 Maths Resources:

Master with our detailed class 10th Maths Guide.

Practice sample papers and previous years' question papers.

Understand the question patterns to prepare effectively.

Vedantu's website offers sample papers for practice.

9. Prioritize Rest and Preparation:

Ensure a good night's sleep and a healthy meal before the exam.

Gather necessary materials the night before to avoid last-minute stress.

10. Exam Simulation for Time Management:

Practice answering sample papers under timed conditions.

Assess and improve time management skills to attempt all questions.

11. Presenting Answers Effectively:

Answer questions in the order presented in the paper.

Highlight final answers and relevant formulas for clarity.

Avoid leaving any questions unattempted; partial answers can secure marks.

Following the above-mentioned tips and being sincere in your preparation will help you score good marks in the exams. Having a strong base in Maths in Class 10 is definitely beneficial for classes ahead and in the future. This will help you have an edge over others even in competitive exams. Most competitive exams have maths sections and the questions generally asked pertain to what you may have learnt in school. Having a good grip over the formulas and the topics will definitely help you perform well in these exams as well.

CBSE Class 10 Maths Study Materials

Conclusion .

Vedantu's NCERT Solutions for Class 10 Mathematics offer a comprehensive and user-friendly resource for students. The solutions align seamlessly with the Class 10 Maths book PDF in an accessible format, enhancing understanding and aiding effective exam preparation. The structured approach ensures clarity on complex topics, making it an invaluable tool for students seeking mastery in mathematics. The availability of the NCERT Class 10 Maths book PDF further facilitates easy access and study. With the convenience of a FREE downloadable PDF, it caters to diverse learning styles. Vedantu's Class 10 NCERT Maths Solutions helps students navigate the challenges of their mathematics curriculum.

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FAQs on NCERT Solutions for Class 10 Maths

1. How will NCERT Solutions for Class 10 Maths help me in learning?

NCERT Solutions for class 10 Maths is prepared for overall learning of a student. It explains all the concepts of class 10 CBSE. It also provides the solutions of all the NCERT textbook questions. Also, it has questions for practice. So, you can learn the concepts, solve NCERT textbook questions and also practice extra questions provided hence learning the all of maths class 10 CBSE.

2. How can I cover the whole syllabus of Class 10 Maths on time?

To cover the whole syllabus of class 10 Maths on time, you can refer to NCERT Solutions for class 10 from Vedantu. Compiled by a group of experts, these solutions will prove a true guide to you. Whether it's about covering the syllabus or scoring high marks, Vedantu’s NCERT Solutions always comes handy. So, download the solutions today and enjoy studying!

3. Can I get NCERT Solutions for Class 10 Maths for free?

Yes, you can download NCERT Solutions for class 10 Maths for completely free of cost from Vedantu’s official website. The solutions are prepared by the experts of Vedantu after a lot of research and these are as per the latest guidelines of CBSE. You can download it hassle free from the official website of Vedantu at free of cost.

4. If I am stuck on any concept or numerical problem, will NCERT Solutions for Class 10 Maths help me?

Yes, definitely. NCERT Solutions for class 10 Maths are designed in such a way that it will help you in concept clearance and then practice. In Mathematics, concept clearance is very much required as the questions will be based on concepts only and you have to solve it logically. So, refer to NCERT Solutions for class 10 Maths and enjoy learning.

5. Is NCERT Solutions for Class 10 Maths enough for scoring high in exams?

Scoring high in exams depends on how well you are aware of the concepts and how well you can imply that on numerical and logical problems. NCERT Solutions will help you in clearing your concepts well and building a strong foundation. So, if your concepts are clear, and you practice well, NCERT Solutions are enough to score high marks in the exam.

6. Where will I get the NCERT Solutions for Class 10 Maths PDF?

Solutions for Class 10 Maths is one of the best ways for you to prepare for your board exam. The solutions are present on Vedantu’s website (vedantu.com) free of cost. Vedantu’s NCERT solutions are available in PDF format so that you can download them and use them to study online. Students can download these from Vedantu mobile app as well. All the solutions are explained in an easy format along with the concepts. With these solutions in your hand, you won’t have to worry about finishing your NCERT syllabus .

7. How to master in Class 10 Maths CBSE?

In order to master your Class 10 CBSE , you need to focus on finishing your NCERT syllabus. This involves solving all the questions and the examples. To help you with this, Vedantu offers NCERT Solutions for Class 10 Maths in PDF format . You can use these as a guide for finishing the NCERT exercises. All the solutions are provided in a step-by-step format for your benefit. It is the easiest way for you to score well in your exams.

8. Where can I download CBSE Class 10 NCERT Mathematics PDF Solutions?

CBSE Class 10 NCERT Mathematics PDF solutions are nothing short of a blessing for the students. Vedantu offers PDFs of thoroughly written solutions where all the questions from NCERT exercises are explained in detail. Follow these steps to download them:

Visit the page of ‘ NCERT Solutions for Class 10 Maths ’ on the official website of Vedantu (vedantu.com).

Find the exercise for which you want a solution and click on the ‘Download PDF’ link.

The solutions will be downloaded into your system. You’ll also receive a message/ mail with a direct download button of your preferred solution.

9. What are the concepts explained in the solutions of NCERT Class 10 Maths Textbook?

The Vedantu’s solutions of NCERT Class 10 Maths textbook can help all the students of Class 10th with helpful tips and tricks for solving math problems. These tricks are provided at the end of all chapters. There are 15 chapters in total that students have to study for the Class 10 exam. All the chapters are explained in a detailed manner by the subject matter experts. You can download the NCERT Class 10 Maths PDF solutions from Vedantu (vedantu.com) and learn all the chapters from the syllabus.

10. How can I save these Class 10 NCERT Maths Solutions for reference?

Vedantu’s Class 10 NCERT Maths Solutions is the easiest way for you to prepare for your Class 10 exams. These solutions PDF cover the concepts as well as solutions to exercises. If you want to save them for reference, you will have to download their PDF files. There is a separate PDF file for each exercise that you can save on your mobile phone or computer for future reference. If you want, you can print these files for easy access.

NCERT SOLUTIONS FOR CLASS 10

Cbse class 10 study materials.

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NCERT Solutions for Class 10 Maths

Chapterwise cbse ncert solutions for class 10 maths updated for 2023-24 session.

NCERT Solutions for Class 10 Maths

Chapter Wise NCERT Solutions for Class 10 Maths

  • Chapter 1- Real Numbers
  • Chapter 2- Polynomials
  • Chapter 3- Pair of Linear Equations in Two Variables
  • Chapter 4- Quadratic Equations
  • Chapter 5- Arithmetic Progressions
  • Chapter 6- Triangles
  • Chapter 7- Coordinate Geometry
  • Chapter 8- Introduction to Trigonometry
  • Chapter 9- Some Applications of Trigonometry
  • Chapter 10- Circles
  • Constructions  (Not in Syllabus)
  • Chapter 11- Areas Related to Circles
  • Chapter 12- Surface Areas and Volumes
  • Chapter 13- Statistics
  • Chapter 14- Probability

NCERT Solutions for Class 10 Maths Exercise wise with Stepwise Solutions

Ncert solutions for class 10 maths chapter 1 real numbers.

Real Numbers Mindmap

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

Ncert solutions for class 10 maths chapter 3 pair of linear equations in two variables, ncert solutions for class 10 maths chapter 4 quadratic equations, ncert solutions for class 10 maths chapter 5 arithmetic progressions, ncert solutions for class 10 maths chapter 6 triangles, ncert solutions for class 10 maths chapter 7 coordinate geometry, ncert solutions for class 10 maths chapter 8 introduction to trigonometry, ncert solutions for class 10 maths chapter 9 some applications of trigonometry, ncert solutions for class 10 maths chapter 10 circles, ncert solutions for class 10 maths chapter 11 constructions, ncert solutions for class 10 maths chapter 12 areas related to circles, ncert solutions for class 10 maths chapter 13 surface areas and volumes, ncert solutions for class 10 maths chapter 14 statistics, ncert solutions for class 10 maths chapter 15 probability, weightage of marks unit wise for cbse class 10 maths.

Questions wise Marking Scheme for Mathematics Class 10

Why you should solve Class 10 Maths NCERT Solutions

Why ncert solutions for class 10 maths by studyrankers.

  • 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.

Related Readings

  • MCQ Questions for Class 10 Maths
  • Revision Notes for Class 10 Maths
  • NCERT Solutions for Class 10
  • Important Questions for Class 10 Maths

Frequently Asked Questions on Class 10 Geography NCERT Solutions

Where to find class 10 maths ncert solutions, what is circumference of a circle, what is an event in probability, how many chapters are there in class 10 ncert maths textbook, contact form.

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10th Class Math Notes | Solved Key Book

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Are you searching for 10th class math notes for all exercises? You are on the right page. Here we have uploaded solved questions of the 10th class math in PDF format. These solution notes are equally beneficial in all Punjab boards. Including Faisalabad Board, Lahore Board, Gujranwala Board, Sahiwal Board, Rawalpindi Board, Sargodha Board, Multan Board, and DG khan Board. Click below on the desired Chapter to get its Notes.

Chapter 1 - Quadratic Equation

Exercise 1.2

Exercise 1.3

Chapter 2 - Theory of Quadratic Equation

Exercise 2.2

Exercise 2.3

Exercise 2.4

Exercise 2.5

Exercise 2.6

Exercise 2.7

Chapter 3 - Variations

Exercise 3.2

Exercise 3.3

Exercise 3.4

Exercise 3.5

Exercise 3.6

Chapter 4 - Partial Fractions

Exercise 4.2

Exercise 4.3

Chapter 5 - Set & Functions

Exercise 5.2

Exercise 5.3

Exercise 5.4

Chapter 6 - Basic Statistics

Exercise 6.2

Chapter 7 - Introduction to Trigonometry

Exercise 7.2

Exercise 7.3

Exercise 7.4

Chapter 8 to 10 SQs and MCQs

Chapter 11 to 13 sqs and mcqs, how to prepare from 10th class math solution notes.

Now, you are a student of the 10th class and you have an idea of how a question paper might be and how will you prepare for that paper. Let us discuss some essential suggestions for preparing for the exams in math subjects. Our first suggestion is: you have to buy a rough register for doing the practice of math solutions, because the more practice you do, the more math will become easy for you.

Let us move toward the next suggestion. You should prepare chapters according to the arrangement of chapters is in the mathematics textbook. As a result, if you practice any topic, you have all the ideas of what is done in a question now it’s easy and clear for you to understand. And it will be much easier to prepare it from our 10 class math notes of all exercises.

10th Class Math Exercise wise Solution Notes

Furthermore, when you start the practice of a chapter, you must do it from the start of the chapter. And comprehend all the topics and formulations of related exercises, and by applying those formulas you do practice their example questions as well.

Also, when it comes to exercises in a chapter, do not wait until the end of the chapter to prepare them. Learn all the topics and formulas, and apply them to their example questions by examining their formulas and methods. In the end, let’s do the exercises. Practice the questions in the exercise one by one, if you see that two or more of the questions are similar. But it is tough for you to answer the other parts, try to focus only on the parts that are unique or that are challenging for you.

Finally, circulate forward to the exercises of the chapter of maths class 10 notes. Practice every question of an exercise completely. You can do all the exercises in this manner. I recommend that you should practice each question yourself and if you find any difficulty simply check out our provided 10th class maths solution pdf in Urdu and English medium.

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Even though the authors tried their best. Sometimes errors happen unavoidably. It would be appreciated, however, if any suggestions were made for further improvement. Please leave a comment if you have any questions. You can expect a quick response to your question. In order to help your friends do well in the 10th class exam, we hope that you’ll let them know about our hard work. Please leave a comment if you have any questions. We will certainly answer it. Sharing is caring, so please spread the word.

Related Articles

Ch 1 – quadratic equation – exercise 1.2, ch 3 – variations – exercise 3.2, ch 2 – theory of quadratic equation – exercise 2.6, ch 5 – set & functions – exercise 5.4, 15 comments.

Please Add 10th Class Math (Science Group) Urdu Medium All Definitions

wow great notes😱😱😱

SIR THANKS FOR SUCH A GOOD NOTES

Help full material Thanks soo much

Thank u for. Good notes

Thanks for your words of appreciation.

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Give a full book solution pdf

sir bht achy notes hain. main aur b websites sy dekha hy pr kisi pr sary notes available ni

Shukria sir,

best notes of math. thanks

good notes sir

thanks for your appreciation:)

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NCERT Solutions for Class 10 Maths for 2024 Board Exams | Free PDF Download

Our professional faculty has curated these NCERT Solutions to aid students in their term-by-term exam preparation. Students looking for NCERT Solutions for Class 10 Maths can download complete chapter-by-chapter to help them solve questions more effectively. 

All the solutions of the NCERT books are without a doubt the best study material available for the students. These CBSE NCERT solutions for Class 10 Maths  will also help the students in developing a more in-depth grasp of subjects presented in the textbook. Practicing the questions from the textbook will assist pupils in assessing their degree of preparation and subject comprehension. This solved exercise has very helpful for your exam.

NCERT Solutions Class 10 Maths  All Chapters:

Practice Comprehensively with Oswaal360 CBSE Online Courses for Class 10 Board Exams 2024

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Are You a Teacher? Apply for  FREE CBSE Class 10 Specimen Sample Books For Teachers  from our end.

CBSE Previous Year Solved Papers Class 10

The NCERT Solutions for Class 10 Maths list contains all of the chapter-wise solutions to the NCERT Book for Class 10 Maths problems, given clearly and transparently while preserving the textbook's purpose. The NCERT Solutions for 10th Class  can be used as extra references and study tools by students. Practicing NCERT textbook exercise answers would undoubtedly aid students' test preparation.

These assist students in comprehending or solving the sorts of problems that a paper setter asks in the board examinations for  CBSE   Class 10 Maths . Furthermore, offering solutions to all areas relating to circles assists students in effectively preparing for the board examinations.

The subject matter experts make sure that the errors in the  NCERT  textbooks are resolved according to the  NCERT  rules and syllabus. 

The solutions to the  NCERT -based questions for all the chapters   of Class 10 Maths  are accessible at  Oswaal CBSE Class 10 Maths . These solutions will assist students in acing their board examinations by preparing for the examinations ahead of time. Students may clarify all of their conceptual questions or doubts with the assistance of the notes provided in Maths NCERT Solutions for Class 10 of all the chapters. Experts have created these NCERT Solutions based on the most recent update to the  CBSE  Syllabus to help students in Class 10 prepare well for their term-wise examinations.

Chapter Details and Exercises of Class 10 Maths NCERT Solutions:

The NCERT Solutions Chapter 1 Real Number for Class 10 Maths:

math solved exercises class 10

Students in grade 10 will investigate real and irrational numbers in Chapter 1. The chapter begins with Euclid's Division Lemma, which asserts that "given two positive numbers a and b, there are two distinct integers q and r fulfilling

a= bq + r, 0 ≤ r < b."

Based on this lemma, Euclid's Division technique is used to determine the HCF of two positive numbers. The Fundamental Theorem of Arithmetic, which is utilized to compute the LCM and HCF of two positive integers, is then defined. The idea of an irrational number, a rational number, and the decimal expansion of rational numbers are then described using a theorem.

Real Numbers:

A quantity that may be stated as a limitless decimal expansion in mathematics is a real number. Unlike natural numbers 1, 2, 3... derived from counting, real numbers are utilized to measure constantly altering quantities such as size and time. Real numbers are represented by R.

Real numbers are classified into two types, i.e., rational and irrational numbers . 

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Rational number:

A number may be expressed as the quotient p/q of two integers, with q ≠ 0. In addition to fractions, the set of rational numbers includes all integers. Each can be described as a quotient with the integer as the numerator and one as the denominator. Rational numbers are represented by Q.

Rational numbers are divided into two subparts, i.e., non-integer rational numbers and rational integer numbers.

Integer rational numbers are those rational numbers made up of integers, whereas non-integer rational numbers do not contain integers.

This class of rational numbers, i.e., integers, is further classified into two groups, i.e., negative and whole numbers. Thus, whole numbers are the numbers that are the combination of natural numbers along with 0.

Irrational numbers

Those types of real numbers, which are not rational, are referred to as irrational numbers. Irrational numbers, in other words, cannot be stated as the ratio of two integers. When the length ratio of two-line segments is an irrational number, the line segments are said to be incommensurable, which means that they have no "measure" in common. That is, no length ("the measure"), no matter how small, can be employed to convey the lengths of both given segments as integer multiples of itself. 

Chapter 1 Real Numbers:

The Fundamental Theorem of Arithmetic claims made after analysing previous work and showing and inspiring with examples. The representation of rational numbers in decimal terms in terms of terminating/non-terminating recurring decimals.

Important Steps to Take

To get the HCF of two positive numbers, say c and d, with c > d, apply the following steps:

Step 1:  Apply the division lemma of Euclid to c and d. So, we look for whole numbers, q and r, such that c = dq + r, 0≤ r< d.

Step 2:  If r = 0, the HCF of c and d equals d. We apply the division lemma to d and r if r = 0.

Step 3:  Repeat the process until the remaining equals zero. At this point, the divisor will be the desired HCF. This approach works because HCF (c, d) = HCF (d, r), where HCF (c, d) represents the HCF of c and d, respectively.

NCERT Solutions for 10th Grade Maths Chapter 1 Exercises:

Also available at  CBSE Class 10 Books  contains the following materials for NCERT Class 10 Chapter 1 Real Numbers :

  • Notes for NCERT Real Numbers Class 10
  • Important Real Numbers Class 10 Questions
  • Class 10 NCERT Exemplar Solution of Chapter Real Numbers

Chapter 2 Polynomials –NCERT Solutions for Class 10 Maths:

The chapter Polynomials opens with a definition of the degree of a polynomial, a linear polynomial, a quadratic polynomial, and a cubic polynomial. This chapter has four exercises, one of which is optional. Exercise 2.1 covers questions about determining the number of zeroes in a graph. It necessitates a grasp of the Polynomial's Zeroes Geometrical Meaning. Exercise 2.2 is based on the Zeroes and Coefficients of a Polynomial's relationship. In some of the problems, students must discover the zeros of a quadratic polynomial and the quadratic polynomial. The idea of the division algorithm is described in Exercise 2.3, and students will find questions connected to it. The optional Exercise, 2.4, contains questions from all of Chapter 2's topics.

Polynomials

Polynomials are sums of k⋅xⁿ terms, where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. A polynomial is an expression in mathematics that consists of indeterminates (also known as variables) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. x 2 -4x + 7 is an example of a polynomial with a single indeterminate x. In three variables, consider x 3 + 2xyz + 2yz + 1. Polynomials may be found in many fields of mathematics and science.

Zeros of Polynomial

A polynomial's zeros are all the x-values that make the polynomial equal zero. They are fascinating to us for various reasons, one of which is that they reveal the x-intercepts of the polynomial graph. These are closely related to the polynomial factors.

Topics that are covered in Chapter 2: Polynomials for Class 10 Maths

The topics of the relationship between zeroes, coefficients of quadratic polynomials, and zeroes of a polynomial are covered in Chapter 2, i.e., Polynomials for Class 10 Maths.

Steps to Take

We begin by arranging the dividend and divisor words in decreasing order of their degrees. Remember that putting the terms in this sequence is referred to as "writing polynomials in standard form."

Step 1:  To get the first term of the quotient, divide the dividend's highest degree term by the divisor's highest degree term. Then proceed with the dividing procedure.

Step 2:  To get the second term of the quotient, divide the highest degree term of the new dividend by the divisor's highest degree term. Carry out the dividing procedure once again.

Step 3:  The remainder degree is now smaller than the divisor's degree. As a result, we cannot continue to divide.

We can see that Dividend = Divisor × Quotient + Remainder once more. We're using an approach similar to Euclid's division algorithm, which you learned about in Chapter 1.

There are two polynomials p(x) and g(x) with g(x) ≠ 0, we may evaluate polynomials h(x) and m(x) such that p(x) = g(x) × h(x) + m(x), where m(x) = 0 or degree of m(x) < degree of g (x).

This is known as the Polynomial Division Algorithm .

NCERT Solutions for Class 10 Maths Chapter 2 Exercises:

Our CBSE Class 10 books also has the following resources for NCERT Class 10 Chapter 2 Polynomials :

  • Notes for NCERT Polynomials Class 10
  • Important Polynomials Class 10 Questions
  • Class 10 NCERT Exemplar Solutions for Chapter Polynomials

Class 10 Maths NCERT Solutions of Chapter 3: Pair of Linear Equations in Two Variables

The concept or idea of a "Pair of Linear Equations in Two Variables" is explained in this chapter. This chapter has seven problems, each of which describes a different approach to solving the pair of linear equations. Exercise 3.1 describes how to algebraically and visually depict a scenario. Exercise 3.2 illustrates how to solve the pair of linear equations using the graphical method. The Algebraic, Elimination, Cross-Multiplication Method, and Substitution Methods are described in Exercises 3.3, 3.4, 3.5, and 3.6. Exercise 3.7 is an optional exercise with a variety of questions. Students must practice these activities to grasp the process of solving linear equations.

Linear equation in two variables

It is defined as an equation which is in the form dx+ny+l, where d, n, and l are absolute values, and d and n are not equal to zero. It is known as the linear equation in two variables.

Topics that are covered in Chapter 3: Pair of Linear Equations in two variables for Class 10 Maths:

Several solutions have algebraic conditions: a pair of two-variable linear equations, their graphical solutions, and their consistency and inconsistency. A pair of linear equations' algebraic solutions in two variables using substitution and elimination. Simple situational and equation problems can be reduced to linear equations. 

Formulas of Importance

The general form of the pair of linear equations in two variables, i.e., x and y are f 1 x + g 1 y + h 1 = 0 and f 2 x + g 2 y + h 2 = 0, where f 1 , g 1 , h 1 , f 2 , g 2 , h 2 are all real integers and f 12 + g 12 ≠ 0, f 22 + g 22 ≠ 0

Class 10 Maths Chapter 3 NCERT Solutions Exercises

Our CBSE Class 10 books also has the following resources for NCERT Class 10 Chapter 3 Pair of Linear Equations in Two Variables:

  • Notes for NCERT Class 10 Pair of Linear Equations in Two Variables
  • Class 10 Maths Important Questions, Pair of Linear Equations in Two Variables
  • Class 10 NCERT Exemplar Solutions Pair of Linear Equations in Two Variables

NCERT Solutions for Grade 10 Maths Chapter 4 Quadratic Equations:  

Students will learn the traditional manner of formulating a Quadratic Equation in this chapter. The chapter then explains how to solve a quadratic problem using the factorization approach and complete the square method. The chapter concludes with determining the nature of roots, which asserts that a quadratic equation ax² + bx + c = 0 has two separate real roots if b² – 4ac > 0 and two equal roots if b² – 4ac = 0.

If b² – 4ac < 0, there are no genuine roots.

Chapter 4 Quadratic Equations of Class 10 Maths:

The standard form of a quadratic equation is ax 2 + bx + c = 0 (a ≠ 0). Factorization and the quadratic formula solve quadratic equations (only real roots). The relationship between the discriminant and the nature of the roots. Situational questions based on quadratic equations that are relevant to everyday activities (problems on equations reducible to quadratic equations are excluded)

math solved exercises class 10

As a result, the roots of ax 2 + bx + c = 0 are both -b/2a.

As a result, in this example, the quadratic equation ax 2 + bx + c = 0 has two equal real roots.

There is no real integer whose square is b 2 – 4ac if b 2 – 4ac = 0. As a result, there are no true roots for the given quadratic equation in this example. 

Because b 2 – 4ac decides whether or not the quadratic equation ax 2 + bx + c = 0 has real roots, it is the discriminant of this quadratic equation.

As a result, the quadratic equation ax 2 + bx + c = 0 has

  • If b 2 – 4ac > 0, there are two different real roots.
  • If b2 – 4ac = 0, there are two equal real roots.

NCERT Solutions for Grade 10 Maths Chapter 4 Exercises

Also available in Our CBSE Class 10 books with the following materials for NCERT Class 10 Chapter 4 Quadratic Equations:

  • Notes on Quadratic Equations for Class 10 NCERT
  • Important Quadratic Equations Class 10 Questions
  • Class 10 Quadratic Equations NCERT Exemplar Solutions

Chapter 5 Arithmetic Progressions NCERT Solutions for Class 10 Maths

This chapter introduces students to Arithmetic Progression, abbreviated as AP. There are four exercises in this chapter. Students will discover questions in Exercise 5.1 about describing a scenario in the form of AP, evaluating the first term and difference of an AP, and determining if a series is AP or not. Exercise 5.2 offers questions about calculating the nth term of an AP using the following formula:

a n = a + (n-1) d

The next Exercise, 5.3, offers questions on calculating the sum of the first n terms of an AP.

The last Exercise contains AP-based higher-level problems to help students improve their analytical and problem-solving abilities.

Class 10 Maths Chapter 5 Arithmetic Progressions:

Why do you want to learn about Arithmetic Progression? The nth term and the sum of the first n terms of A.P. are deduced and used to solve difficulties in everyday life.

(Applications based on an A.P.'s sum to n words are not permitted.)

If the terms of AP are a 1 , a 2 , a 3 , a 4 , a 5 , a 6 ... and d is the common difference between each term, then the sequence is an a+d, a+2d, a+3d, a+4d, a+5d,...., n th term..., where an is the first term. The nth term for mathematical progression is now;

a + (n-1) d = n th term

Arithmetic Progression's first n terms' sum;

S n = n/2 [2a + (n-1) d]

NCERT Solutions for Class 10 Maths Chapter 5 Exercises:

Our CBSE Class 10 books also has the following materials for NCERT Class 10 Chapter 5 Arithmetic Progressions:

  • Class 10 NCERT Arithmetic Progressions Notes
  • Important Arithmetic Progressions Class 10 Questions
  • Class 10 NCERT Exemplar Solutions Progressions in Arithmetic

Chapter 6 Triangles : NCERT Solutions for Class 10 Maths

Students in 10th Grade CBSE Maths will study figures with the same shape but not necessarily the same size in Chapter 6. Triangles begin with the notion of a comparable and harmonious form. It goes on to describe the criteria for the similarity of two triangles as well as theorems about triangle similarity. Following that, the areas of identical triangles were defined using a theorem. The Pythagoras Theorem and its converse are discussed at the conclusion of this chapter.

Class 10 Maths Chapter 6 Triangles: Definitions, examples, and counter examples of related triangles

  • (Demonstrate) If a line is drawn parallel to one side of a triangle and intersects the other two sides at separate locations, the other two sides are split in the same ratio.
  • (Motivate) A line is parallel to the third side if it splits two sides of a triangle in the same ratio.
  • (Motivate) If the corresponding angles in two triangles are identical, their corresponding sides are proportionate, and the triangles are comparable.
  • (Motivate) If two triangles' corresponding sides are proportionate, their complementary angles are equal, and the two triangles are identical.
  • (Motivate) If a triangle's one angle equals one angle of another triangle and the sides that include these angles are proportionate, the two triangles are comparable.
  • (Inspire) When a perpendicular is drawn from the vertex of a right triangle's right angle to the hypotenuse, thus the triangles which are on either side of the perpendicular are identical to the complete triangle and each other.
  • (Inspire) The ratio of the two identical triangle's areas is equal to the ratio of their corresponding side squares.
  • (Prove) The square on the hypotenuse of a right triangle equals the sum of the squares on the other two sides.
  • (Motivate) If the square on one side of a triangle equals the sum of the squares on the other two sides, the right angle is the angle opposite the first side.

Theorems of Importance

Theorem 6.1:  At one side of a triangle, a parallel line is drawn, which intersects the other two sides in distinct spots; the remaining two sides are split in the same ratio.

Theorem 6.2:  A line is parallel to the third side if it divides any of the two sides of a triangle in the same ratio.

Theorem 6.3:  If the corresponding angles in two triangles are identical, their corresponding sides are in the same ratio (or percentage), and the two triangles are comparable. 

Theorem 6.4:  If the sides of one triangle in two triangles are proportional to (i.e., in the same ratio as) the sides of the other triangle, then their corresponding angles are equal, and thus the two triangles are comparable.

Theorem 6.5:  If one angle of one triangle equals one angle of another triangle, and the sides containing these angles are proportionate, the two triangles are identical.

Theorem 6.6:  The ratio of the two comparable triangle areas is equal to the square of the ratio of their corresponding sides, according to Theorem 6.6.

Theorem 6.7 states that if a perpendicular is drawn from the vertex of a right triangle's right angle to the hypotenuse, triangles on both sides of the perpendicular are comparable to the complete triangle.

Theorem 6.8:  The square of the hypotenuse of a right triangle is equal to the sum of the other two sides square.

Theorem 6.9:  When the square of one side of a triangle equals the summation of the squares of the other two sides, the angle opposite the first side is right.

NCERT Solutions for Class 10 Maths Chapter 6 Exercises

Our CBSE Class 10 books also has the following materials for NCERT Class 10 Chapter 6 Triangles:

  • Triangles Class 10 NCERT Notes
  • Important Triangles Class 10 Questions
  • Class 10 NCERT Exemplar Solutions Triangles

Chapter 7 Coordinate Geometry: NCERT Solutions for Class 10 Maths

Students will learn how to calculate or evaluate the distance between two locations whose coordinates are supplied and the area of a triangle formed by three specified points in this chapter. Students will also learn how to identify the coordinates of the point that splits a line segment connecting two specified points in a specific ratio. Students will study the Distance Formula, Section Formula, and Area of a Triangle in this chapter of Coordinate Geometry. 

Coordinate Geometry

The geometrical study by using coordinate points is known as coordinate geometry (or analytic geometry). It is possible to estimate the distance between two points, divide lines in an m:n ratio, identify the midpoint of a line, calculate the area of a triangle in the Cartesian plane, and so on using coordinate geometry.

Class 10 Maths Chapter 7 Coordinate Geometry:

math solved exercises class 10

Lines (In two dimensions)

Concepts of coordinate geometry and graphs of linear equations are reviewed.

Distance calculation formula

The formula for Sections (internal division)

Important formula

Distance Formula

math solved exercises class 10

NCERT Solutions for Class 10 Maths Chapter 7 Exercises

Our CBSE Class 10 Books also has the following materials for NCERT Class 10 Chapter 7 Coordinate Geometry:

  • Notes for NCERT Coordinate Geometry Class 10
  • Important Coordinate Geometry Class 10 Questions
  • Class 10 NCERT Exemplar Solutions Coordinate Geometry Solutions

Chapter 8 Introduction to Trigonometry: NCERT Solutions for Class 10 Maths

Trigonometry will be introduced to pupils in this chapter. They will investigate trigonometric ratios of angles, ratios of a right triangle to its sharp angles. The chapter also defines trigonometric ratios for angles ranging from 00 to 900. Students will also understand how to compute trigonometric ratios for specific angles and create trigonometric identities employing these ratios.

Chapter 8 of Class 10 Maths: Trigonometry Overview

Trigonometric ratios of a right-angled triangle's acute angle Evidence of their existence (well defined). Trigonometric ratio values of 300, 450, and 600. Relationships among the ratios

IDENTITIES TRIGONOMETRIC

Application and proof of the identity sin 2 A + cos 2 A = 1. Only simple identities will be provided.

Important formulas

Trigonometry Maths Formulas for Class 10 address three key functions for a right-angle triangle: Sine, Cosine, and Tangent. Assume that a right-angled triangle ABC is right-angled at point B and has ∠θ.             

Trigonometry Table

Trigonometric Ratios of Complementary Angles

  • sin (90° – A) = cos A
  • cos (90° – A) = sin A,
  • tan (90° – A) = cot A,
  • cot (90° – A) = tan A,
  • sec (90° – A) = cosec A,
  • cosec (90° – A) = sec A
  • sin 2 A + cos 2  A = 1,
  • sec 2 A – tan 2  A = 1 for 0° ≤ A < 90°,
  • cosec 2 A = 1 + cot 2  A for 0° < A ≤ 90°

NCERT Solutions pdf for Class 10 Maths Chapter 8 Exercises

Our CBSE Class 10 books also has the following materials for NCERT Class 10 Chapter 8 Trigonometry:

  • Notes for NCERT Class 10 Introduction to Trigonometry
  • Important Trigonometry Questions from Class 10
  • Class 10 NCERT Exemplar Introduction to Trigonometry Solutions 

NCERT Solutions for Class 10 Maths Chapter 9 Trigonometry Applications

This chapter builds on the previous one by teaching students about trigonometry applications. It is used in geography, navigation, map production, and calculating an island's location in reference to longitudes and latitudes. Students will learn how to utilize trigonometry to find the heights and distances of various objects without having to measure them. They will learn about line of sight, angle of elevation, and angle of depression.

Chapter 9 of Class 10 Maths covers the following topics: Some Trigonometry Applications

HEIGHTS AND DISTANCES-Angle of Elevation and Angle of Depression

math solved exercises class 10

Simple height and distance issues. A problem should have no more than two right triangles. Elevation/depression angles should not exceed 30 degrees, 45 degrees, and 60 degrees.

Important Notes –

  • The line of sight is the line drawn from an observer's eye to a point in the thing being observed.
  • The angle created by the line of sight with the horizontal when the item being viewed is above the horizontal level, like when we elevate our head to look at it, is named the angle of elevation of the point observed.
  • The angle of depression of a point on an item being observed is the angle created by the line of sight with the horizontal when the point is below the horizontal level, like when we lower our heads to look at the point being viewed.

You would need to be aware of the following: 

  • The distance DE between the student's feet and the foot of the minar
  • The angle of elevation, BAC, of the minar's top
  • The student's AE height.

Assuming the three requirements mentioned above are met, how can we calculate the minar's height? 

CD = CB + BD in the diagram. In this case, BD = AE, which is the student's height.

To calculate BC, we shall utilize trigonometric ratios of BAC or A.

The side BC in ABC is the opposite side in regard to the known A because these ratios include AB and BC, our search narrows to tan A or cot A.

As a result, tan A = BC/AB or cot A = AB/BC, which, when solved, gives us BC.

The height of the minar may be calculated by adding AE to BC.

NCERT Solutions pdf for Class 10 Maths Chapter 9 Exercises

With our CBSE Class 10 books, you may also find the following materials for NCERT Class 10 Chapter 9 Some Applications of Trigonometry:

  • Notes for NCERT Some Applications of Trigonometry Class 10
  • Some Trigonometry Applications Class 10 Important Questions
  • Class 10 NCERT Exemplar Solutions Some Trigonometry Applications

Chapter 10 Circles –NCERT Solutions for Class 10 Maths  

Students have previously learned about a circle and different circle-related terminology such as a chord, segment, arc, etc. Students will investigate the many circumstances when a circle and a line are presented in a plane in this chapter. As a result, they will get thoroughly acquainted with the concepts of Tangent to a Circle and Number of Tangents from a Point on a Circle.

Class 10 Math Topics Chapter 10 Circles:  

Point of contact tangent to a circle

  • Establish that the Tangent at any point on a circle is perpendicular to the radius via the point of contact.
  • (Prove) Tangents drawn from an exterior point to a circle have identical lengths.

Theorems of Importance –

  • The Tangent at any point on a circle is perpendicular to the radius through the point of contact, according to Theorem 10.1.
  • The lengths of tangents taken from an exterior point to a circle are identical, according to Theorem 10.2.

Number of Tangents from a Circle Point

Case 1:  There is no tangent to a circle that passes through a point located within the circle.

Case 2:  There is only one Tangent to a circle that passes through a point on the circle.

Case 3:  There are two tangents to a circle that intersects at a place outside the circle.

NCERT Solutions pdf for Class 10 Maths Chapter 10 Exercises

Our CBSE Class 10 books also has the following materials for NCERT Class 10 Chapter 10 Circles:

  • Class 10 Important Questions for Circles
  • Notes of NCERT Class 10 for Circles
  • Circles NCERT Exemplar Solutions Class 10

Chapter 11 Constructions: NCERT Solutions Class 10 Maths

There are two exercises in this chapter. Whatever learners learned about building in previous sessions will also be helpful. Students will learn how to split a line segment in Exercise 11.1 and create tangents to a circle in Exercise 11.2. Methods and processes for building are discussed, and some examples are provided to help students understand.

Class 10 Math Topics Chapter 11 Constructions:

  • Line segment division in a particular ratio (internally).
  • Tangents to a circle from points outside of it.

Important Notes – 

11.1: To split a line segment in a specific ratio.

11.2: Build a triangle identical to a given triangle using the specified scale factor.

11.3: To build the tangents to a circle from a location outside it.

NCERT Solutions pdf for Class 10 Maths Chapter 11 Exercises

Our CBSE Class 10 books also has the following materials for NCERT Class 10 Chapter 11 Constructions:

  • Notes for NCERT Constructions Class 10
  • Important Constructions Class 10 Questions
  • NCERT Exemplar Solutions Constructions Class 10

NCERT Solutions for Class 10 Maths Chapter 12 Circle Areas

This chapter begins with the notions of circle perimeter and area. The chapter goes on to describe how to find the area of a sector and segment of a circular region using this notion. Furthermore, students will gain confidence in calculating the areas of various plane figure combinations involving circles or their portions.

Topics Covered in Class 10 Maths Chapter 12 Circle:  

Motivate the area of a circle, the area of a circle's sections and segments. As mentioned earlier, area and perimeter/circumference problems are based on the plane. (When computing the area of a circle segment, issues should be limited to central angles of 60° and 90° only. Plane figures with triangles, basic quadrilaterals, and circles should be used.)

Circumference of the circle: A circle's perimeter is the linear distance travelled around the circle. The perimeter of a circle is known by a unique name, Circumference. The circumference multiplied by the diameter is given by the formula 2πr.

Area of circle: The circle area is πr 2 , where r is the circle's radius and π = 22/7 or 3.14 (maybe used interchangeably for problem-solving purposes). Thus, an area of the circle is nothing but is the ratio of a circle's circumference to its diameter.  

A Circle's Segment

A circular segment is a section of a circle "separated" from the portion of the circle by a secant or chord.  

A circle's sector

A circle sector is the portion of a circle bounded by an arc and two radii. The smaller region is referred to as the minor sector, while the larger area is the major sector.

A Sector's Angle

The angle of a sector is defined as the angle formed by the sector's two radii.

The Angle of a Sector

A sector's angle is defined as the angle created by the sector's two radii.

                                 L= (θ/360°) × 2πr

Where θ is the sector angle and r is the circle's radius.

Students may also utilize this NCERT Exemplar to complete even the most challenging problems and prepare for examinations. However, sample papers and previous year's question papers are quite helpful in understanding the sorts of questions a paper setter asked in the examination from this chapter 12 and the marking system. 

This chapter covers the Areas related to the Circles subjects listed below:  

  • Areas related to Circles
  • Segment and Sector of a circle
  • Areas of a combination of a plane figure.

Students will learn to calculate various circle areas and combinations of plane figure areas, in Chapter 12.  

Students in the tenth grade are also given online study tools, including notes, example books, NCERT answers, and question papers, to help them prepare for the board examinations.

This chapter may take some time to complete, and students must pay close attention. The NCERT Exemplar for Class 10 Maths is provided here to assist students in solving chapter concerns and obtaining proper answers to complex questions.

Important Formulas –

  • Circumference = 2πr
  • Area of the circle = πr 2
  • Area of the sector of angle θ = (θ/360) × π r 2
  • Length of an arc of a sector of angle θ = (θ/360) × 2 π r, where r is the radius of the circle

NCERT Solutions pdf for Class 10 Maths Chapter 12 Exercises

Exercise 12.1 includes five solved questions. Four of them are short answer type questions , and the remaining one is the MCQ   type.

This exercise is primarily concerned with the perimeter and area of a circle. In this lesson, students learn how to determine the circumference and area using formulae and apply what they've learned to real-world problems. Solutions give an overview of the chapter's essential themes and assist students in becoming familiar with these concepts.

In this exercise 12.1 of Chapter 12 , students are given the solutions to many questions to perform well in their first term examinations.

The solutions to the  NCERT -based questions of  Chapter 12 for Class 10 Maths, Areas Related to Circles , is an essential study resource for Class 10 students. These assist students in comprehending or solving the sorts of problems that a paper setter asked in the first term examinations of  CBSE   Class 10 Maths . Furthermore, offering solutions to all areas relating to circles assists students in effectively preparing for the board examinations.

The subject matter experts make sure that the errors in the  NCERT  textbooks are resolved according to the  NCERT  rules and syllabus.

The solutions to the Exercise 12.1   NCERT -based questions of  Chapter 12 for Grade 10 Maths  are accessible at our Oswaal books. These solutions will assist students in acing their first term examinations by preparing for the examinations ahead of time.

Students may clarify all of their conceptual questions or doubts with the assistance of the notes of Maths NCERT Solutions for Class 10 of this chapter which we provide. Experts have created these NCERT Solutions based on the most recent update to the  CBSE  syllabus for 2022-23 to help students in Class 10 prepare well for their term-wise examinations

Our CBSE Class 10 books also has the following resources for NCERT Class 10 Chapter 12 Areas Related to Circles:

  • Notes on Circles in Class 10 NCERT
  • Notes on Circles for Class 10 NCERT Important questions
  • NCERT Exemplar Solutions Class 10 Areas Related to Circles

Chapter 13 Surface Areas and Volumes - NCERT Solutions for Class 10 Maths

There are five exercises in Chapter 13. The first Exercise consists of questions on calculating the surface area of an object made by merging any two fundamental solids, namely a cuboid, cone, cylinder, sphere, and hemisphere. 13.2 questions in Exercise are focused on determining the volume of objects generated by joining any two of a cuboid, cone, cylinder, sphere, or hemispheres. Exercise 13.3 has questions on converting a solid from one shape to another. Exercise 13.4 involves calculating the volume, curved surface area, and total surface area of a cone's frustum.

Chapter 13 Surface Areas and Volumes in Class 10 Maths:

  • Surface areas and volumes of any two of the following combinations: cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.
  • Difficulties involving the transformation of one type of metallic solid into another and other mixed problems (Problems involving the combination of no more than two different solids are considered.)
  • Total SA of new solid = CSA of one hemisphere + CSA of cylinder + CSA of another hemisphere
  • Diameter of sphere = 2r
  • The surface area of the sphere = 4 π r 2
  • The volume of Sphere = 4/3 π r 3
  • The curved surface area of the Cylinder = 2 πrh
  • Area of two circular bases = 2 πr 2
  • The total surface area of Cylinder = Circumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr2
  • Volume of Cylinder = π r 2 h
  • Slant height of cone = l = √ (r2 + h2)
  • Curved surface area of cone = πrl
  • Total surface area of cone = πr (l + r)
  • Volume of cone = ⅓ π r 2 h
  • Perimeter of cuboid = 4(l + b +h)
  • Length of the longest diagonal of a cuboid = √ (l 2 + b 2 + h 2 )
  • Total surface area of cuboid = 2(l×b + b×h + l×h)
  • Volume of Cuboid = l × b × h

NCERT Solutions pdf for Class 10 Maths Chapter 13 Exercises

Our CBSE Class 10 Books also has the following resources for NCERT Class 10 Chapter 13 Surface Areas and Volumes:

  • Notes for NCERT Class 10 Surface Areas and Volumes
  • Class 10 Important Questions on Surface Areas and Volumes
  • Surface Areas and Volumes in NCERT Exemplar Solutions Class 10

NCERT Solutions for Class 10 Maths Chapter 14 Statistics

Students will learn how to convert ungrouped data to grouped data and how to calculate the Mean, Mode, and Median. In addition, the notion of cumulative frequency, cumulative frequency distribution, and how to design cumulative frequency curves will be discussed.

Class 10 Maths Chapter 14 Statistics:

Grouped data mean, median, and mode (bimodal situation to be avoided). Only the Direct Method and the Assumed Mean Method are used to calculate the mean.

The mean of the grouped data  can be found by 3 methods

 1. Direct Method:

math solved exercises class 10

4. The mode of grouped data: 

math solved exercises class 10

5. The median for a grouped data:

math solved exercises class 10

NCERT Solutions PDF for Class 10 Maths Chapter 14 Exercises

Our CBSE Class 10 books also has the following materials for NCERT Class 10 Chapter 14 Statistics:

  • Notes for NCERT Statistics Class 10
  • Important Statistics Class 10 Questions
  • Statistics NCERT Exemplar Solutions Class 10

Class 10 Maths NCERT Solutions Chapter 15 Probability  

The final chapter is about Probability. The chapter begins with a theoretical look at probability. Following that, the chapter discusses the distinction between experimental and theoretical probability. There are several instances provided to illustrate it effectively. So, before proceeding with the practice questions, students must first complete the CBSE Maths examples. 

Chapter 15 Probability NCERT Class 10 Maths:  The classical definition of probability. Simple issues involve determining the likelihood of an event.

  • The theoretical probability (also called classical probability) of an event E, written as P(E), is defined as
  • The probability of an actual occurrence (or sure event) is 1.
  • The probability of an impossible event is nil.
  • The probability of an occurrence E is expressed as a number P(E) such that 0 ≤ P (E) ≤ 1
  • An important event is one that has only one outcome. The total of all the probability of an experiment's elementary occurrences is 1.

NCERT Solutions pdf for Class 10 Maths Chapter 15 Exercises  

Our CBSE Class 10 books also has the following resources for NCERT Class 10 Chapter 15 Probability:

  • Notes for NCERT Probability Class 10
  • Important Probability Class 10 Questions
  • Class 10 Probability NCERT Exemplar Solutions

NCERT Solutions for Class 10 Maths PDF in English Medium and Hindi Medium (for the academic year 2022-23 are used not only by CBSE but also by UP Board, Uttarakhand Board, and all other boards that use NCERT Textbooks.

Advantages of NCERT Solutions Class 10 Math:

The Class 10 NCERT Math Solutions in PDF format provided here offer various advantages, including:

  • The answers provided here are simple to grasp.
  • For ease of comprehension, solutions are presented in phases.
  • Diagrams are provided to assist students in visualizing solutions.
  • Each chapter's questions are answered.

Students are urged to prepare all of the chapters covered in the solution modules, as this will help them obtain a deeper understanding of the subjects. Students must comprehend all of the processes outlined in the solutions to make good preparations.

How Can CBSE Class 10 Maths Solutions from NCERT Help with Term Exams?

Math in CBSE Class 10 is an essential topic for students. We have offered full preparatory support to students here. Class 10 is the initial criterion for each student that will be reflected in subsequent accomplishment records. CBSE consistently recommends NCERT books for term-by-term test preparation.

Exam preparation is a time-consuming procedure that necessitates a thorough comprehension of individual chapters. This technique necessitates diligent study and a systematic approach to completing the solutions. NCERT 10 Class Maths Solutions play an essential part in preparing students for competitive admission tests. NCERT books are well-known for presenting topics in an easy-to-understand format. NCERT Class 10 Mathematics Books are written most understandably and straightforwardly, allowing complicated problems to be broken down effectively.

Continue to visit to obtain complete chapter-by-chapter NCERT Solutions for Class 10 Maths PDF free download for all courses. NCERT Solutions for Class 10 Science may also be found at class 10 . Students at class 10 benefit from a customized learning experience that helps them prepare for tests more successfully.

NCERT  Solutions assist students in solidifying their knowledge of the mathematics concept.

Diagrams are used to answer questions, making learning more dynamic and thorough.

The language used in  NCERT  Solutions is simple and easy to grasp.

Students benefit from a step-by-step approach to problem-solving.

Allows learners to work through challenging problems in their own time.

NCERT  Solutions for various courses and disciplines are also available for students to use. Well-experienced professors of class 10 books create these answers to offer clarity on essential ideas and problem-solving abilities.

Students can also obtain a firm grasp of critical topics by referring to additional study resources available at  CBSE class 10 books .

The NCERT Solutions for Class 10 Maths are essential in shaping a kid's future since the grades that student achieves on the board test ultimately form the student's potential. The examinations for Classes 10 CBSE board are the first public examinations that all students must attempt. The CBSE board exams assess the candidate's practical and theoretical knowledge. As a result, students must comprehend the principles, and connecting them to real-world applications will help them develop solid practical knowledge.

Our subject specialists develop the Class 10 NCERT Solutions to give a one-stop solution for all Maths queries. These Solutions for Class 10 NCERT provide an ideal platform for understanding all of the Maths ideas in the syllabus for students hoping to achieve in the CBSE Classes 10 Board Exam. The NCERT Solutions of solved examples and the exercise questions are explained with illustrated graphs and well-labelled diagrams that make learning effortless. It helps students create a strong conceptual point, which is crucial in the later phases of competing in competitive tests. The solutions to the  NCERT -based questions  for class 10 are easily accessible.

Solutions for Class 10 Maths NCERT include all the exercise problems from the NCERT Maths textbook. Our highly trained subject specialists have developed these Math answers to assist students in their test preparation. These answers will guide students in acquiring a higher grasp of the ideas taught in the Class 10 Maths curriculum. Students may assess their preparation and knowledge of statements by practicing NCERT Class 10 Maths textbook problems.

These assist students in comprehending or solving the sorts of problems that a paper setter asks in the first term examinations of  CBSE   Class 10 Maths . The subject matter experts make sure that the errors in the  NCERT  textbooks are resolved according to the  NCERT  rules and syllabus. The solutions to the  NCERT -based questions  for Grade 10 Maths  are accessible through class 10 books .  These solutions will assist students in acing their board examinations by preparing them ahead of time. Students may clarify all of their conceptual questions or doubts with the assistance of the notes of Maths  NCERT  Solutions for Class 10 of different chapters. Experts have created these NCERT Solutions based on the most recent update to the  CBSE  Syllabus to help students in Class 10 prepare well for their board examinations.

Students should complete Class 10 Maths NCERT Solutions after finishing the curriculum since it gives many problems from each unit to practice. Use these solutions to clarify any confusion, if anyone gets stuck when answering the issues, and supplementary references and study resources. All Math solutions are written unambiguously and prominently, considering the goal of textbooks. Students are urged to download and practice these solutions regularly to get a commendable rank in the Board exams. Students must comprehend all the processes outlined in the answers for successful preparation.

If you wish to strengthen your fundamental knowledge in several disciplines, the NCERT book is a fantastic place to start. It includes several diagrams, flowcharts, tables, and illustrations to supplement the various themes and concepts. It is a fantastic beginning point for people who wish to study a certain subject because it is designed to improve the fundamental understanding of pupils who read it. We think that after reading this, you will be grateful that we got your back, but this is not only for a subject.

The CBSE Class 10 math curriculum seeks to create learner knowledge and evaluation of basic concepts such as algebra, geometry, surface areas, volumes, statistics, and probability. The key to success in mathematics is practice. It is difficult to score well in this topic only by reading and memorizing the formulae; consequently, students are urged to practice them on a regular basis in order to obtain a good place in the board examinations. We provide class 10 Revision Notes for Mathematics so that students may quickly prepare all of the concepts included in the class 10 maths syllabus in a much better and more effective manner.

Maths Solutions for Class 10 include solutions to all of the questions and problems in the textbook. Real Numbers, Quadratic Equations, Triangles, Introduction to Trigonometry, Some Applications of Trigonometry, Area Related to Circles, Circles, Surface Areas and Volumes, and other topics are covered in Maths Solutions for Class 10. A team of subject specialists has developed Maths Solutions for Class 10, and the format follows the CBSE guidelines. It outlines each solution step by step so that students can comprehend it quickly, and marks are assigned to each step so that students may learn the answer writing skill from an exam standpoint.

We have supplied NCERT Class 10th Solutions to assist students in understanding the content, completing their assignments, and preparing for exams. With these answers, students will significantly improve their knowledge and problem-solving abilities. These solutions were developed under the supervision of professional educators and mentors while keeping the most recent NCERT curriculum in mind to provide you with up-to-date material. The questions and solutions are explained step-by-step in depth so that you can better comprehend them. Each subject presents solutions with brief details to give you the necessary context.

CBSE Question Bank Class 10

Frequently Asked Questions about NCERT Class 10 Maths Solutions

How can one understand the key ideas taught in the NCERT Solutions for Class 10 Maths?

Ans . Students who want to do well in their Class 10 examinations should get the NCERT Solutions for class 10 maths books . A group of teachers with extensive knowledge in the particular area curates the solutions with great care. Every minute topic is discussed engagingly to make studying easy for the pupils. The step-by-step answers are created using the marks weightage provided by the CBSE in mind.

Will the NCERT Solutions for Class 10 Maths make it easier for me to tackle the problems?

Ans. The Class 10 test is a watershed moment in the lives of learners. Mathematics is a topic that mainly consists of numerical, and comprehending ideas helps to obtain higher grades. Students should first comprehend the academic year's syllabus and then master the topics based on it for better performance. Students' logical thinking and analytical abilities will develop as they solve textbook problems using the answers PDF.

How can I obtain the NCERT Solutions for Class 10 Maths PDF?

Ans. Class 10 books  provide students with NCERT Solutions for Class 10 Maths PDF. Subject matter experts prepare the solutions with the students' learning capacity in mind. The primary goal of developing solutions is to assist students in learning complicated ideas without trouble. Students can also cross-check their answers while working through textbook problems to obtain a sense of other approaches to resolving topics quickly.

Are the NCERT Solutions for 10th Grade Maths beneficial to CBSE board students?

Ans. Some of the specific applications of the NCERT Maths Solutions for Class 10 -

  • It establishes solid basics of essential topics and boosts confidence for term-based tests.
  • The strategy for addressing complicated issues is simple to learn.
  • It is an ideal study tool for students who want to complete their assignments on time and get higher grades in their term examinations.

How can I acquire a sense of the key concepts in the NCERT Solutions for Class 10 Maths?

Ans. Students should download and read the CBSE curriculum before the start of each academic year to have a thorough grasp of the subjects that will be assessed. Students must tackle NCERT Textbook issues by selecting the appropriate study resource that meets their needs. Students' problem-solving abilities improve when they practice the problems on a regular basis using the NCERT Solutions for Class 10 Maths.

Is it necessary to use the NCERT Solutions for Class 10 Maths?

Ans . NCERT Solutions for Class 10 Maths are designed in such a way that students may quickly comprehend the concepts and solve their difficulties. The answers include detailed explanations to help students understand the subject. Students can get PDF solutions and utilize them to strengthen their conceptual understanding.

Are the NCERT Solutions for Class 10 Maths the finest resource for CBSE students?

Ans . Students should choose the best study material for their needs from the many options available on the market. Class 10 books NCERT Solutions for Class 10 Maths are widely regarded as the finest reference tool for CBSE students. The solutions are given in chapter and practice forms, which students may download and utilize. Students can view the PDF links without regard to time limits.

Why do students require NCERT Solutions for Class 10 study material to qualify for the board exam?

Ans. Class 10 is an important time in a student's life since the grades they receive determine their future profession. It might be challenging to achieve good results in board examinations without adequate study materials. NCERT Solutions for Class 10 in a subject-by-subject manner. Students who are having problems answering textbook questions can use these solutions to ace the board test easily.

Explain the significance of class 10 books NCERT Solutions for Class 10.

Ans . The significance of class 10 books NCERT Solutions for Class 10 is as follows:

  • NCERT Solutions are created in accordance with the CBSE syllabus.
  • All of the textbook questions are answered so that students have no problem answering them.
  • The experienced team of members creates solutions with the goal of offering high-quality study materials to pupils in grades 10.

How can one obtain free NCERT Solutions for Class 10 PDFs from OSWAAL?

Ans . As class 10 is a critical phase in students’ life, students should choose the appropriate study material that meets their demands. Keeping this in mind, the team of subject matter experts curate solutions that are clear and easy to grasp. The solutions include step-by-step explanations to enable students of all IQ levels to understand the ideas. The PDFs of the answers may be downloaded by visiting the our website. By inputting the necessary information, students will have access to both online and offline study resources for a particular subject.

Will the board exam questions be drawn from NCERT Solutions for Class 10 Maths?

Ans. The NCERT Solutions for Class 10 Maths provide the most questions in the board exam. Students can refer to the solutions offered by the professors at class 10 while answering textbook problems to gain a better knowledge of the subject. The answers are designed so that students may easily comprehend complicated concepts. Students can utilize online and offline solutions with no time limits.

How many exercises are there in the Grade 10 th Maths Chapter 12?

Ans . There are three exercises are present in the 10 th Grade Maths Chapter 12, i.e., Areas Related to Circles.

How many problems are present in each NCERT Exemplar Solutions for Class 10 Maths Chapter 12 exercise?

Ans. Three problems are included in Chapter 12 of the NCERT Solutions for Class 10 Maths . Exercise 12.1 consists of five questions, whereas Exercise 12.2 consists of 14 questions. 12.3 comprises 16 questions. Every problem is addressed with the utmost attention to give students accurate solutions following CBSE norms.

Explain the circumference of a circle in Chapter 12 of NCERT Exemplar Solutions for Class 10 Maths?

Ans.  A circle's perimeter is the linear distance travelled around the circle. The perimeter of a circle is known by a unique name, Circumference. The circumference multiplied by the diameter is given by the formula 2πr.

Where can I get online NCERT Exemplar Solutions for Class 10 Maths Chapter 12?

Ans.  Yes, the NCERT Exemplar Solutions for Class 10 Maths Chapter 12 are available on our website . Subject specialists evaluate the solutions to all problems to give students the most significant reference material. You can download chapter-by-chapter or exercise-by-exercise answers to understand better the problem-solving approaches used while solving textbook questions

Which chapter in class 10 math is the most difficult?

Ans. The most challenging chapter is trigonometry.

In Class 10, how many hours should I study?

Ans. A student should study between 7 and 10 hours every day. It is probable that if you dedicate more time, you may become weary. As a result, the maximum amount of time you should commit to your studies is 7 – 10 hours.

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NCERT Solutions for Class 10 Maths Updated 2023-24

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Mathematics is a crucial subject, but many students find it challenging to grasp. To address this, the Physics Wallah team has developed comprehensive NCERT solutions for Class 10 Maths . Our primary goal is to simplify math concepts and make them easily understandable, boosting students' confidence in their mathematical abilities. These solutions are designed to be invaluable resources for improving math scores and overall performance.

Students can access the NCERT Solutions for class 10 Maths in PDF format using the given links. This allows them to study and review the material at their own pace, making it more convenient for them. With our dedicated efforts, we aim to make mathematics an enjoyable and accessible subject for all students, instilling a strong foundation that will serve them well in their academic and professional pursuits.

NCERT Solutions for Class 10 Maths Chapter-Wise List

The Class 10 Mathematics syllabus comprises 15 chapters, as outlined in the table provided. NCERT Solutions for Class 10 Maths are essential tools that play a crucial role in helping students comprehend the concepts with ease. These solutions are presented simplified, making the subject more accessible and promoting effective learning and understanding. Students find great value in utilizing these resources to improve their grasp of the subject and enhance their overall performance.

NCERT Solutions for Class 10 Maths

NCERT Solutions for Class 10 Maths Chapter 1 - Real Numbers

In class 10 chapter 1 , students will explore real and irrational numbers. The chapter begins with Euclid's division lemma, which states that "given positive integers a and b, there exist unique integers qar satisfying a = bq + r, 0≤r<b". The Euclidean division algorithm is based on this lemma and is used to compute the HCF of two given positive integers. Therefore, the Fundamental Theorem of Arithmetic is defined, which is used to find the LCM and HCF of two positive integers. Then the concept of irrational number, rational number and decimal expansion of rational numbers is explained using the theorem.

Topics Covered in this chapter are- Fundamental Theorem of Arithmetic – statements after reviewing work done before and after illustrating and motivating through examples, Proofs of irrationality of √2, √3, √5.

NCERT Solution for class 10 Maths Chapter 1 Real number

Also, access the helpful resources for Class 10 Maths Chapter 1 Real Numbers at Physics Wallah

  • Important questions for class 10 Maths Chapter 1 Real Numbers
  • RD Sharma Solutions for Class 10 Chapter 1 Real Numbers
  • RS Aggarwal class 10 solutions Chapter 1 Real Numbers

NCERT Solutions for Class 10 Maths Chapter 2 - Polynomials

In Polynomials, the chapter begins by defining the degree of a polynomial, a linear polynomial, a quadratic polynomial, and a cubic polynomial. This chapter consists of 4 exercises, including an optional exercise. Exercise 2.1 contains questions about finding the number of zeros in a graph. It requires understanding the geometric meaning of the zeros of a polynomial. Exercise 2.2 is based on the Relationship between Zeros and Coefficients of a Polynomial, where students must find the zeros of a quadratic polynomial. In some questions, they have to find a quadratic polynomial. In Exercise 2.3, the term division algorithm is defined, and students will find related questions. Additional exercise 2.4 consists of questions from all concepts of chapter 2.

Topics Covered in this chapter are- Zeros of a polynomial, Relationship between zeros and coefficients of quadratic polynomials.

Also, access the helpful resources for Class 10 Maths Chapter 2 Polynomials at Physics Wallah

  • Important questions for class 10 Maths Chapter 2 Polynomials
  • RD Sharma Solutions for Class 10 Chapter 2 Polynomials
  • RS Aggarwal class 10 solutionsChapter 2 Polynomials

NCERT Solutions for Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables

This chapter explains the concept of a pair of linear equations in two variables. This chapter contain a total of 7 exercises, and in these exercises, different methods of solving a pair of linear equations are described. Exercise 3.1 describes how to represent the situation algebraically and graphically. Exercise 3.2 explains methods for solving a pair of linear equations using the graphical method. And exercises 3.3, 3.4, 3.5, and 3.6 describe the algebraic method, the elimination method, the cross-multiplication method, and the substitution method. Exercise 3.7 is an optional exercise that contains all types of questions. Students must practice these exercises to master the method of solving linear equations.

Topics Covered in this chapter are- Pair of linear equations in two variables and graphical method of their solution, consistency/ inconsistency. Algebraic conditions for number of solutions. Pair of linear equations in two variables solution – by substitution, by elimination. Simple situational problems.

Also, access the helpful resources for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables at Physics Wallah

  • Important questions for class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables
  • RD Sharma Solutions for Class 10 Chapter 3 Pair of Linear Equations in Two Variables
  • RS Aggarwal class 10 solutions Chapter 3 Pair of Linear Equations in Two Variables

NCERT Solutions for Class 10 Maths Chapter 4 - Quadratic Equations

In this chapter, students will discuss the standard form of writing a Quadratic Equation. The chapter properly explain the method of solving the quadratic equation through the completing the square method and factorization method. The chapter finish with the topic on finding the nature of roots which means, a quadratic equation ax² + bx + c = 0 has:

  • Two distinct real roots, if b² – 4ac > 0
  • Two equal roots, if b² – 4ac = 0
  • No real roots, if b² – 4ac < 0

Topics Covered in this chapter are- Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots.

Also, access the helpful resources for Class 10 Maths Chapter 4 Quadratic Equations at Physics Wallah

  • Important questions for class 10 Maths Chapter 4 Quadratic Equations
  • RD Sharma Solutions for Class 10 Chapter 4 Quadratic Equations
  • RS Aggarwal class 10 solutions Chapter 4 Quadratic Equations

NCERT Solutions for Class 10 Maths Chapter 5 - Arithmetic Progressions

This chapter introduces students to the new topic of Arithmetic Progression or AP. The chapter contains a total of 4 exercises. In Exercise 5.1, students will find questions about representing a situation in AP form, finding the first term and difference of an AP, and determining whether a series is an AP or not. Exercise 5.2 contains questions on finding the nth term of an AP using the following formula:

a n = a + (n-1) d

In the next exercise i.e., 5.3, contains the questions on finding the sum of first n terms of an AP. The last exercise includes higher-level questions based on AP to enhance students’ analytical and problem-solving skills.

Topics Covered in this chapter are- Arithmetic Progression, Derivation of the nth term and the sum of the first n terms of A.P. and their application in solving daily life problems.

Also, access the helpful resources for Class 10 Maths Chapter 5 Arithmetic Progressions at Physics Wallah

  • Important questions for class 10 Maths Chapter 5 Arithmetic Progressions
  • RD Sharma Solutions for Class 10 Chapter 5 Arithmetic Progressions
  • RS Aggarwal class 10 solutions Chapter 5 Arithmetic Progressions

NCERT Solutions for Class 10 Maths Chapter 6 - Triangles

Chapter 6 of Class 10 covers the topic of triangles. It focuses on figures with the same shape but different sizes, explaining the concept of similarity in triangles and the associated theorems. The chapter also introduces the idea of congruent triangles. Moreover, it explains the theorems concerning triangle areas, the Pythagorean theorem, and the converse of the Pythagorean theorem.

Students must be familiar with the following theorems for their exam preparation:

  • Theorem of Proportionality: If a line is drawn parallel to one side of a triangle and intersects the other side at distinct points, the two sides are divided in the same ratio.
  • Parallel Line Theorem: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
  • Similar Triangles Theorem: If the corresponding angles of two triangles are equal, their corresponding sides are in the same ratio, making the triangles similar.
  • Proportional Sides Theorem: If the sides of one triangle are proportional to the sides of another triangle, their corresponding angles are equal, and the triangles are similar.
  • Angle-Side Similarity Theorem: If one angle of a triangle is equal to one angle of another triangle, and the sides, including these angles, are proportional, then the two triangles are similar.
  • Area Ratio Theorem: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
  • Right Triangle Perpendicular Theorem: In a right triangle, if a perpendicular is drawn from the right-angle vertex to the hypotenuse, the resulting triangles on both sides of the perpendicular are similar to the whole triangle and each other.
  • Pythagorean Theorem: In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
  • Converse of the Pythagorean Theorem: In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.
  • Understanding these theorems will help students excel in their studies and perform well in the examination.

Also, access the helpful resources for Class 10 Maths Chapter 6 Triangles at Physics Wallah

  • Important questions for class 10 Maths Chapter 6 Triangles
  • RD Sharma Solutions for Class 10 Chapter 6 Triangles
  • RS Aggarwal class 10 solutions Chapter 6 Triangles

NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry

In the chapter 7, students will learn how to find the distance between two points whose coordinates are given and the area of ​​the triangle formed by the three given points. Students will also learn how to find the coordinates of a point that bisects a line joining the two given points in a given ratio. In the end, students will be introduced to the distance formula, the section formula, and the area of ​​a triangle in this Coordinate Geometry chapter.

Topics Covered in this chapter are- the concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

Also, access the helpful resources for Class 10 Maths Chapter 7 Coordinate Geometry at Physics Wallah

  • Important questions for class 10 Maths Chapter 7 Coordinate Geometry
  • RD Sharma Solutions for Class 10 Chapter 7 Coordinate Geometry
  • RS Aggarwal class 10 solutions Chapter 7 Coordinate Geometry

NCERT Solutions for Class 10 Maths Chapter 8 - Introduction to Trigonometry

In Chapter 8 of NCERT Solutions, students are introduced to trigonometry, which involves studying the ratios of right triangles with respect to their acute angles. These ratios are called trigonometric ratios. The chapter explains trigonometric ratios for angles such as 0° and 90°, and students are taught how to calculate these ratios for given angles. Additionally, they are introduced to some important trigonometric identities.

This chapter serves as a fundamental introduction to trigonometry, and it is beneficial for students not only in Class 10 but also in higher classes like Class 11 and 12. Students are taught introductory trigonometry formulas, which help them establish a solid foundation for their future studies in the subject.

Furthermore, the chapter explains the relationship between trigonometric ratios and angles. Students are introduced to important complementary angle trigonometric ratios, such as sin (90° – A) = cos A, cos (90° – A) = sin A, tan (90° – A) = cot A, cot (90° – A) = tan A, sec (90° – A) = cosec A, and cosec (90° – A) = sec A.

Additionally, they learn fundamental trigonometric identities, such as sin^2 A + cos^2 A = 1, sec^2 A – tan^2 A = 1 for 0° ≤ A < 90°, and cosec^2 A = 1 + cot^2 A for 0° < A ≤ 90°. These concepts are essential tools for solving trigonometry problems and understanding the relationship between different trigonometric functions.

Also, access the helpful resources for Class 10 Maths Chapter 8 Introduction to Trigonometry at Physics Wallah

  • Important questions for class 10 Maths Chapter 8 Introduction to Trigonometry
  • RD Sharma Solutions for Class 10 Chapter 8 Introduction to Trigonometry
  • RS Aggarwal class 10 solutions Chapter 8 Introduction to Trigonometry

NCERT Solutions for Class 10 Maths Chapter 9 - Some Applications of Trigonom

In Chapter 9, we build upon the concepts learned in Chapter 8 and explore the practical applications of trigonometry in our daily lives. In this chapter, trigonometry calculates the height and distance of various objects in real-world situations. It shows how trigonometry is crucial in navigation, helping us find directions and positions accurately. Additionally, the chapter demonstrates the application of trigonometry in construction projects, allowing us to calculate angles and distances for creating structures.

Furthermore, trigonometry is widely used in geography and mapping, enabling us to determine the positions of various locations based on their latitude and longitude coordinates. This chapter sheds light on how trigonometry is practically applied to solve real-world problems and enhance our understanding of the world around us. The skills gained from this chapter can be valuable in numerous fields, making trigonometry a versatile and important topic to teach.

Also, access the helpful resources for Class 10 Maths Chapter 9 Some Applications of Trigonometry at Physics Wallah

  • Important questions for class 10 Maths Chapter 9 Some Applications of Trigonometry
  • RD Sharma Solutions for Class 10 Chapter 9 Some Applications of Trigonometry
  • RS Aggarwal class 10 solutions Chapter 9 Some Applications of Trigonometry

NCERT Solutions for Class 10 Maths Chapter 10 - Circles

In Class 10 Maths, Chapter 10 builds upon the knowledge of circles studied in previous classes. This chapter introduces the concept of tangents and explores the number of tangents that can be drawn from a point on a circle.

This chapter covers two important theorems:

  • Theorem 1: At any point on a circle, the tangent drawn is always perpendicular to the radius passing through that point of contact.
  • Theorem 2: When drawing tangents from an external point to a circle, the lengths of these tangents will be equal.

Understanding these theorems is crucial, as they help determine various properties and relationships between circles and tangents. Understanding the concept of tangents and their relationship with circles is a crucial step in studying circles. This knowledge is a foundation for more advanced concepts taught in higher classes.

Also, access the helpful resources for Class 10 Maths Chapter 10 Circles at Physics Wallah

  • Important questions for class 10 Maths Chapter 10 Circles
  • RD Sharma Solutions for Class 10 Chapter 10 Circles
  • RS Aggarwal class 10 solutions Chapter 10 Circles

NCERT Solutions for Class 10 Maths Chapter 11 - Constructions

Chapter 11 is an exciting and practical chapter on constructing various geometric figures. In this lesson, students will learn how to divide a line segment and draw tangents to a circle. The chapter provides clear and detailed explanations of the construction methods, making it easier for students to grasp the concepts.

The chapter presents step-by-step methods and plenty of examples before each exercise for constructing tangents to a circle. These examples are designed to aid students in better-comprehending construction techniques and the underlying theorems. By following the examples and practicing the exercises, students can enhance their skills in geometric constructions and gain confidence in solving construction-based problems. This chapter provides valuable hands-on experience, which is interesting and lays a strong foundation for more complex constructions in higher classes.

Also, access the helpful resources for Class 10 Maths Chapter 11 Constructions at Physics Wallah

  • Important questions for class 10 Maths Chapter 11 Constructions
  • RD Sharma Solutions for Class 10 Chapter 11 Constructions
  • RS Aggarwal class 10 solutions Chapter 11 Constructions

NCERT Solutions for Class 10 Maths Chapter 12 - Areas Related to Circles

In this chapter, we delve into the concepts of the perimeter and area of a circle. We will explore how to calculate a sector's area and a circle's segment. Moreover, the chapter covers finding the area of figures containing either a whole circle or a part of it.

Some important formulas to remember and practice within this chapter are:

  • Circumference = 2πr (where r is the radius of the circle)
  • Area of the circle = πr^2 (where r is the radius of the circle)
  • Area of a sector of angle θ = (θ/360) × πr^2 (where θ is the angle of the sector and r is the radius of the circle)
  • Length of an arc of a sector of angle θ = (θ/360) × 2πr (where θ is the angle of the sector and r is the radius of the circle)

Understanding and applying these formulas will enable students to calculate the perimeter and area of circles easily. They can also find areas of different shapes involving circles or circular segments. This chapter equips students with practical skills to solve circle-related problems in various scenarios.

Also, access the helpful resources for Class 10 Maths Chapter 12 Areas Related to Circles at Physics Wallah

  • Important questions for class 10 Maths Chapter 12 Areas Related to Circles
  • RD Sharma Solutions for Class 10 Chapter 12 Areas Related to Circles
  • RS Aggarwal class 10 solutions Chapter 12 Areas Related to Circles

NCERT Solutions for Class 10 Maths Chapter 13 - Surface Areas and Volumes

Chapter 13 of Class 10 Maths NCERT book PDF solution deals with surface areas and volumes of various objects and shapes. In this chapter, five exercises involve finding the surface area of complex objects formed by combining two or more solid shapes. The solid shapes covered in the exercises are cuboid, cone, sphere, hemisphere, and cylinder. Students also learn how to find the volume of objects of different solid shapes and convert them from one shape to another.

Key formulas used for calculating surface areas and volumes of different objects:

Total Surface Area (TSA) of a new solid = Curved Surface Area (CSA) of one hemisphere + CSA of cylinder + CSA of another hemisphere.

Diameter of a sphere = 2r (where r is the radius).

Surface Area of a sphere = 4πr².

Volume of a sphere = (4/3)πr³.

Curved Surface Area of a cylinder = 2πrh (where r is the radius and h is the height).

Area of two circular bases of a cylinder = 2πr².

Total Surface Area of a cylinder = Circumference of cylinder + Curved Surface Area of cylinder = 2πrh + 2πr².

The volume of a cylinder = πr²h.

The slant height of a cone = l = √(r² + h²) (where r is the radius and h is the height).

Curved Surface Area of a cone = πrl.

Total Surface Area of a cone = πr(l + r).

Volume of a cone = (1/3)πr²h.

The perimeter of a cuboid = 4(l + b + h) (where l, b, and h are the length, breadth, and height, respectively).

Length of the longest diagonal of a cuboid = √(l² + b² + h²).

Total Surface Area of a cuboid = 2(lb + bh + lh) (where l, b, and h are the length, breadth, and height, respectively).

The volume of a cuboid = lbh (where l, b, and h are the length, breadth, and height, respectively).

By understanding and applying these formulas, students can efficiently solve problems related to surface areas and volumes of various shapes and objects. These concepts are widely applicable in real-life scenarios, making this chapter practical and relevant.

Also, access the helpful resources for Class 10 Maths Chapter 13 Surface Areas and Volumes at Physics Wallah

  • Important questions for class 10 Maths Chapter 13 Surface Areas and Volumes
  • RD Sharma Solutions for Class 10 Chapter 13 Surface Areas and Volumes
  • RS Aggarwal class 10 solutions Chapter 13 Surface Areas and Volumes

NCERT Solutions for Class 10 Maths Chapter 14 - Statistics

In this chapter, students explore the fascinating world of representing data numerically, whether in grouped or ungrouped form. They learn valuable techniques for calculating the mean, median, and mode of a given dataset, which helps in understanding the central tendencies of the data.

The subsequent exercise delves into the concept of cumulative frequency distribution, allowing students to create cumulative frequency curves. These curves visually represent the cumulative data frequencies, providing a more comprehensive understanding of the dataset's distribution.

Overall, this chapter equips students with essential tools for analyzing and interpreting data, making it a crucial aspect of mathematics that finds applications in various fields. By learning these techniques, students will be able to make informed decisions based on data and gain valuable insights from it.

Also, access the helpful resources for Class 10 Maths Chapter 14 Statistics at Physics Wallah

  • Important questions for class 10 Maths Chapter 14 Statistics
  • RD Sharma Solutions for Class 10 Chapter 14 Statistics
  • RS Aggarwal class 10 solutions Chapter 14 Statistics

NCERT Solutions for Class 10 Maths Chapter 15 - Probability

Chapter 15 of NCERT Solutions for Class 10 Maths is all about probability. It covers two main types of probability: experimental probability and theoretical probability. The chapter uses numerous examples to help learners understand the concept of probability effectively.

Probability is a crucial chapter for students to focus on, as it serves as a foundation for future discussions and new topics in higher classes. A strong grasp of the basics in class 10 makes it easier for students to understand the formulas and concepts introduced in advanced classes. Probability becomes a chapter where students can score well in exams with proper understanding and sufficient practice.

By mastering probability, students develop essential skills to analyse uncertainties and make informed decisions based on data. Understanding probability is beneficial in various fields of study and real-life situations. Therefore, devoting time and effort to grasp the concepts in this chapter will be valuable in the long run.

Also, access the helpful resources for Class 10 Maths Chapter 15 Probability at Physics Wallah

  • Important questions for class 10 Maths Chapter 15 Probability
  • RD Sharma Solutions for Class 10 Chapter 15 Probability
  • RS Aggarwal class 10 solutions Chapter 15 Probability

NCERT Solutions For Class 10 Maths PDF

Class 10 Maths covers a total of 15 chapters. here we are providing students NCERT Solutions for class 10 Maths. That will help students to enhance their maths skills easily and conveniently. Check below the NCERT Solution for Class 10 Maths PDF.

Benefits of Class 10 Math NCERT Books and Solutions

Class 10 Math NCERT books and solutions offer several benefits to students, making them an essential resource for their mathematical journey. Some key benefits include

  • Comprehensive Coverage: NCERT books cover all essential Class 10 Math topics, providing a structured syllabus and step-by-step explanations for easier learning.
  • Clear and Concise Language: The simple and clear language in NCERT books helps students understand complex mathematical concepts better.
  • Alignment with Curriculum: NCERT strictly follows educational board curriculums, ensuring students cover necessary topics for exams.
  • Builds Strong Fundamentals: NCERT solutions focus on building a strong foundation by explaining concepts in-depth, benefiting higher classes and other fields of study.
  • Numerous Examples and Exercises: The books include many examples and exercises for practice and reinforcing understanding.
  • Exam-Oriented Approach: NCERT solutions prepare students effectively for exams with exam-oriented questions matching competitive exam patterns.
  • Authentic and Reliable: NCERT is reputable and experienced educators and subject matter experts prepare its books.
  • Conceptual Clarity: NCERT solutions emphasize conceptual clarity, enabling the practical application of knowledge.

Preparation Tips for Class 10 Maths

Preparing for Class 10 Maths can be both exciting and challenging. As you embark on this academic journey, we have compiled a set of valuable preparation tips to help you succeed in your mathematics studies. With a strong foundation in math, you can not only excel in exams but also develop problem-solving and analytical skills that are essential for various aspects of life. Below are some preparation tips that will pave the way for a successful and fulfilling learning experience in Class 10 Maths.

  • Understand the syllabus thoroughly.
  • Create a well-structured study schedule.
  • Master the basic concepts and formulas.
  • Practice regularly to reinforce learning.
  • Seek help and clarify doubts promptly.
  • Use reliable study materials and resources.
  • Improve mental calculations for faster problem-solving.
  • Focus on problem-solving techniques and strategies.
  • Take mock tests to assess preparation level.
  • Analyze mistakes and learn from them.
  • Revise regularly to retain information effectively.

Why Physics Wallah is Best for NCERT Solutions for Class 10 Maths

Physics Wallah is a highly esteemed platform for NCERT Solutions for Class 10 Maths, and students prefer it for various reasons:

  • Success-Oriented Approach: Physics Wallah's solutions are designed to help students excel in Class 10 Maths exams by promoting a deep understanding of the subject.
  • Trusted by Toppers: Academic toppers consistently choose Physics Wallah, which speaks to the platform's credibility and effectiveness.
  • Focus on Important Questions: Physics Wallah's solutions highlight essential questions, enabling students to concentrate on crucial topics and concepts during exam preparation.
  • Convenient PDF Format: The NCERT solutions are available in PDF format, ensuring easy access across different devices and enabling sharing with friends for collaborative learning.
  • Accessible time, Anywhere: Physics Wallah's solutions can be accessed on smartphones, tablets, and laptops, allowing students to study at their convenience and pace.
  • Simple Sign-Up Process: Students can quickly sign up on the Physics Wallah platform, eliminating unnecessary delays and ensuring a smooth learning experience.
  • Leading Education Portal: Physics Wallah is a well-known and reputable education portal recognised for its exceptional academic resources and reliable student support.

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NCERT Solutions For Class 10 Maths FAQs

Q1. What are NCERT Solutions for Class 10 Maths?

Ans. The NCERT Solutions for Class 10 Maths provide in-depth and comprehensive explanations of the mathematical concepts found in the Class 10 NCERT Math textbook. They help students understand and solve the exercises and problems in the textbook.

Q2. Why are NCERT Solutions important for Class 10 Maths?

Ans. NCERT Solutions are essential as they provide step-by-step explanations and solutions to textbook problems. They help students better understand concepts, prepare for exams, and improve their problem-solving skills.

Q3. What topics are covered in Class 10 Maths NCERT Solutions?

Ans. Class 10 Maths NCERT Solutions cover many topics, including real numbers, polynomials, pair of linear equations, quadratics, trigonometry, coordinate geometry, probability, and more.

Q4. How can NCERT Solutions for Class 10 Maths benefit me?

Ans. NCERT Solutions can benefit students by providing clear explanations, helping them grasp complex concepts, improving their exam preparation, and enhancing their overall performance in mathematics.

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  • chapter-3 Pair of Linear Equations in Two Variables Exercise 3.4
  • chapter-3 Pair of Linear Equations in Two Variables Exercise 3.5
  • chapter-3 Pair of Linear Equations in Two Variables Exercise 3.6
  • chapter-3 Pair of Linear Equations in Two Variables Exercise 3.7
  • chapter-4 Quadratic Equations Exercise 4.1
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  • chapter-5 Arithmetic Progressions Exercise 5.1

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CBSE Class 10 Maths Practice Paper 2024 Solved: Download for Important Questions and Last Minute Revision

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CBSE Class 10 Maths Standard Practice Paper PDF: CBSE Class 10 Maths Exam 2024 is scheduled for March 11, 2024. This is going to be one of the most crucial exams for class 10 students in deciding their overall performance in CBSE 10th class and their future educational pursuits. To perform well in this important exam, students are advised to thoroughly practice with the sample papers, previous years’ question papers and the practice papers. We have provided here the CBSE Class 10 Maths Standard Practice Paper which has been curated by subject experts analysing the previous years' question patterns and the latest CBSE syllabus. By solving this comprehensive practice paper, students can assess their preparedness for the CBSE Class 10 Maths Exam 2024 and enhance their problem-solving skills. Solutions to all questions are also provided here to facilitate a better understanding of the concepts and help students identify and rectify any errors in their answers. Download the practice paper and solutions in PDF here.

CBSE Class 10 Maths 50 Most Important MCQs for Board Exam 2024

CBSE Class 10 Maths Standard Practice Paper 2024

1. What is the degree of the constant polynomial?

(a) 2                  

(b)  1                   

(c)  0                 

(d)  4

Answer: (c)  0 

2. Which of the following cannot be the probability of an event?

(a) 23             

(b) –1.5                

(c) 15          

Answer: (b) –1.5 

3. Which one of the following options is true?

y =3x+5 has:

(a) unique solution     

(b) infinite solutions                  

(c) two solution         

Answer: (b) infinite solutions

4. For what values of k will the following pair of linear equations have infinitely many solutions?

(i)  kx + 3y – (k – 3) = 0               

(ii) 12x + ky – k = 0

(a) -6              

(b) 0             

(c)  6                

(d) All of these

Answer: (d)  All of these 

5. What is the common difference of following AP:

3, 3+√2, 3+2√2, 3+3√2, ...............

(a) 3               

(b) 2                 

(c) √2                

Answer: (c) √2 

6. If Tn is the nth term of an AP and Tn = 2n -3  then what is the common difference of the A.P?

(a) -2             

(b) 5                  

(c)  3               

(d)  2

Answer: (d)  2

7. If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠ PTQ is equal to:                             

(a) 60°                

(b) 70°              

(c) 80°              

Answer: (b) 70°

8. Find the value of k for which the quadratic equation 2x 2 -kx+k=0  has equal roots.

(a) only 0              

(b) only  8         

(c) 0 and  8         

(d) can’t find

Answer: (c) 0 and  8

9. What is the product of zeroes of the polynomial 2x 2 -7x+6?

(a) 12               

(b) 9             

(c)  3              

Answer: (c)  3   

10. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is :   

(a)5  units          

(b) 12 units              

(c) 11 units        

(d) (7 + 5)  units

Answer: (b) 12 units  

11. In a ∆ABC, If tan A = cot B, then  A + B  is equal to :

(a) 60°                   

(b) 120°                   

(c) 90°               

Answer: (c) 90°

12. If sin A = 35  then cosA is equal to :

(a) 0               

(b) 1                 

(c) 45                    

Answer: (c) 45

13. On comparing the ratios  a1/a2, b1/b2 and c1/c2 find out whether the following pair of linear equations is consistent, or inconsistent.

2 x + 5 y - 5 = 0   and    4 x + 10 y + 7 = 0

(a) Consistent      

(b) Inconsistent    

(c) Nothing to say      

Answer: (b) Inconsistent 

14. If  x= 1/√3 is a root of the equation Px 2 + (√3- √2)x -1=0 , then the value of  P 2  +1 is :

(a) 6           

(b) 6        

(c) 7                  

Answer: (a) 6

15. In the given figure, PA and PB are tangents to the given circle such that PA = 5 cm and ∠APB = 60°. The length of chord AB is :

(a) 5√2 cm                

(b) 5 cm             

(c) 5√3 cm          

Answer: (b) 5 cm

16. If two positive integers p and q can be expressed as p = ab 2 and q = a 3 b, where a, b being prime numbers, then LCM (p, q) is equal to:

(a) ab              

(b) a 2 b 2                

(c) a 3 b 2                            

(d) a 3 b 3

Answer: (c) a 3 b 2    

17. Simplest rationalizing factor of  √8 is:

(a) √8               

(b) √2       

(c) 3√2                 

Answer: (b) √2  

18. If  LCM of 12 and 42 is 10 m +4 then value of m  is :

(a) 6                  

(b) 7                  

(c) 0             

Answer: (d) 8

Direction: In the question number 19 and 20, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct option

19. Statement A (Assertion):  Ravi goes 30 m due East and then 40 m due North. His distance from the starting point is 50 m. 

Statement R( Reason):  In right angled triangle ABC, right angled at B, AB 2 =  BC 2  + AC 2

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

(c) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

Answer: (c) Assertion (A) is true but reason (R) is false.

20. If Sn is the sum of the first n terms of an A.P., then its nth term an is given by an = S n  – S n-1

Reason: The 10th term of the A.P. 5, 8, 11, 14, ………………. is 35.

To check all questions and answers, go to the following links:

Also Check:

CBSE Class 10 Maths Sample Paper for Board Exam 2024

CBSE Class 10 Maths Additional Questions by CBSE for Board Exam 2024

CBSE Class 10 Maths Important MCQs for All Chapters

CBSE Class 10 Maths Deleted Syllabus for Board Exam 2024

CBSE Class 10 Maths Mind Maps for Quick Revision of All Chapters

Revised NCERT Book for CBSE Class 10 Maths

Updated NCERT Solutions for CBSE Class 10 Maths

CBSE Class 10 Maths Practice Paper 2024 Solved: Download for Important Questions and Last Minute Revision

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CBSE Class 10 Hindi A Solved Practice Paper 2024: Best for Last Minute Revision, Download PDF Now!

CBSE Class 10 Hindi A Practice Paper 2024: Download here the CBSE Class 10 Hindi A practice paper with solutions to prepare for the upcoming CBSE Class 10 Hindi Exam 2024. These questions are best for last minute revision and assess your preparedness for the exam.

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Prominent features of CBSE Class 10 Hindi A Practice Paper 2024

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  • Questions are based on the important topics from the prescribed syllabus.
  • Questions have been curated by experienced subject teachers.
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CBSE Class 10 Hindi A Practice Paper 2024

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CBSE Class 10 Hindi A Sample Paper for Board Exam 2024

CBSE Class 10 Hindi A Additional Questions by CBSE for Board Exam 2024

CBSE Class 10 Hindi A Deleted Syllabus for Board Exam 2024

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math solved exercises class 10

CBSE Class 10 Science Sample Paper 2024: Solve this paper to score 95+ marks

Solve the cbse class 10 science sample paper for 2024 as a valuable resource to achieve a score high marks in your exam. working through this sample paper will enable you to familiarise yourself with the exam pattern, enhance your time management skills, and grasp the anticipated difficulty level..

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CBSE Class 10 Science Sample Paper 2024: Solve this paper to score 95+ marks

The Central Board of Secondary Education, CBSE, has released the sample paper and marking scheme for CBSE Class 10 Science for the academic session 2023-2024. Solving the sample papers helps students understand the exam pattern, manage time effectively, and gauge the expected level of difficulty.

The CBSE board exams 2024 are scheduled to take place starting from February 15, 2024.

CBSE CLASS 10 SCIENCE SAMPLE PAPER 2024

math solved exercises class 10

Maths Questions for Class 10

Those who are preparing for Class 10 Maths exams should practise more questions, as it will clear their doubts instantly. These CBSE Important Questions for Class 10 Maths given here will help you prepare well and score good marks in the Maths exam. You can get some preparation tips for the 10th Maths exam here.

Also, get Class 10 Maths MCQs for all chapters here.

CBSE Important Questions for Class 10 Maths are given here based on the NCERT syllabus. These questions are prepared as per the latest exam pattern. You must practise these CBSE Important Questions for Class 10 Maths to boost your preparation for the Maths paper. There is a high probability of coming across a few of these questions in the board exam. Click on the links below to access the Maths chapter-wise CBSE Important Questions for Class 10 . Each chapter contains a set of solved questions and additional questions for practice.

Practise these CBSE Important Questions for Class 10 Maths daily to build a better understanding of the concepts for Mathematics subject. You can also practise the CBSE Class 10 Question Paper . Download the BYJU’S App to get personalised videos based on Maths concepts.

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COMMENTS

  1. Class 10 Maths Notes, Solved Exercises Solutions, MCQ's

    Class 10 Maths Notes, Solved Exercises Solutions, MCQ's Now, you are a matric student of part two and you have an idea how a question paper will be and how will you prepare for it. Let's discuss some important tips for preparing exams of mathematics subject.

  2. NCERT Solutions for Class 10 Maths Updated for 2023-24 Exams

    NCERT Solutions for Class 10 Maths for all the exercises from Chapters 1 to 15 are provided here. These NCERT Solutions are curated by our expert faculty to help students in their exam preparations. Students looking for the NCERT Solutions of Class 10 Maths can download all chapter-wise PDFs to find a better approach to solving the problems.

  3. NCERT Solutions for Class 10 Maths

    Learn CBSE NCERT Solutions for Class 10 Maths - Class 10 Maths NCERT Solutions NCERT Solutions for Class 10 Maths are solved by experts of LearnCBSE.in in order to help students to obtain excellent marks in their board examination. All the questions and answers that are present in the CBSE NCERT Books has been included in this page.

  4. NCERT Solutions For class 10 Maths (All Exercise)

    Chapter 1 - Real Numbers Chapter 2 - Polynomials Chapter 3 - Pair of Linear Equations in Two Variables Chapter 4 - Quadratic Equations Chapter 5 - Arithmetic Progressions Chapter 6 - Triangles Chapter 7 - Coordinate Geometry Chapter 8 - Introduction to Trigonometry Chapter 9 - Some Applications of Trigonom

  5. NCERT Solutions for Class 10 Maths

    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.

  6. NCERT Solutions for Class 10 Maths

    Click on any of the links below to start learning from Teachoo ... Chapter 1 Class 10 Real Numbers Chapter 2 Class 10 Polynomials Chapter 3 Class 10 Pair of Linear Equations in Two Variables Chapter 4 Class 10 Quadratic Equations Chapter 5 Class 10 Arithmetic Progressions Chapter 6 Class 10 Triangles Chapter 7 Class 10 Coordinate Geometry

  7. NCERT Solutions for Class 10 Maths

    The Class 10 Maths NCERT Solution PDFs cover all the Exercises from Chapters 1 - 15 present in the NCERT books. These Class 10 Maths solutions are written according to the CBSE exam guidelines to increase the students understanding of the subject and help them to score well.

  8. NCERT Solutions for Class 10 Maths

    NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers. In Chapter 1 of NCERT Class 10 Maths, 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.

  9. NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations

    Solutions: Let the present age of Aftab be 'x'. And, the present age of his daughter be 'y'. Now, we can write, seven years ago, Age of Aftab = x-7 Age of his daughter = y-7 According to the question, x−7 = 7 (y−7) ⇒x−7 = 7y−49 ⇒x−7y = −42 ……………………… (i)

  10. NCERT Solutions for Class 10 Maths

    Class 10 Maths Chapter 4 Quadratic Equations Solutions. In this chapter, you will study quadratic equations in depth. Furthermore, you will study to find the roots of quadratic equations. There are also some of the daily life applications of quadratic equations in this chapter. A total of 4 exercises are there in this chapter.

  11. NCERT Solutions for Class 10

    NCERT Solutions for Class 10 Maths covers all exercise questions mentioned in the NCERT Maths textbook. These solutions for Maths are prepared by our highly skilled subject experts to help students while preparing for their exams.

  12. NCERT Solutions for Class 10 Maths PDF Free Download

    NCERT Solutions for Class 10 Maths covering all the exercise questions is made available for you for free of cost. Subject Experts have created these 10th Class Maths NCERT Solutions to complement your board exam preparation. Know a better approach to solve all your problems by referring to our Chapterwise Class 10th Maths NCERT Book Solutions PDF.

  13. NCERT Solutions For Class 10 Maths Chapter 1 Real Numbers

    Solution: Ex 1.1 Class 10 Maths Question 2. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. Solution Ex 1.1 Class 10 Maths Question 3. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns.

  14. 10th Class Math Notes

    10th Class Math Notes contains solved exercises, review questions, MCQs, important board questions, and solution notes. class 10 math key book. ... Finally, circulate forward to the exercises of the chapter of maths class 10 notes. Practice every question of an exercise completely. You can do all the exercises in this manner.

  15. NCERT Solutions for Class 10 Maths

    This solved exercise has very helpful for your exam. NCERT Solutions Class 10 Maths All Chapters: NCERT Solutions Class 10 Maths Chapter 1 Real Numbers. ... Three problems are included in Chapter 12 of the NCERT Solutions for Class 10 Maths. Exercise 12.1 consists of five questions, whereas Exercise 12.2 consists of 14 questions. 12.3 comprises ...

  16. NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

    Solution: In a given triangle ABC, right angled at B = ∠B = 90° Given: AB = 24 cm and BC = 7 cm According to the Pythagoras Theorem, In a right- angled triangle, the squares of the hypotenuse side is equal to the sum of the squares of the other two sides. By applying Pythagoras theorem, we get AC 2 =AB 2 +BC 2 AC 2 = (24) 2 +7 2 AC 2 = (576+49)

  17. NCERT Solutions for Class 10

    NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Chapter 2 Polynomials Chapter 3 Pair of Linear Equations in Two Variables Chapter 4 Quadratic Equations Chapter 5 Arithmetic Progressions Chapter 6 Triangles Chapter 7 Coordinate Geometry Chapter 8 Introduction to Trigonometry Chapter 9 Applications of Trigonometry Chapter 10 Circle

  18. Mathematics

    Class 10 maths notes according to FBISE syllabus. Contains solved exercises, review questions, MCQs, important board questions and chapter overview.

  19. NCERT Solutions for Class 10 Maths Updated 2023-24

    NCERT Solutions for Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables. This chapter explains the concept of a pair of linear equations in two variables. This chapter contain a total of 7 exercises, and in these exercises, different methods of solving a pair of linear equations are described.

  20. CBSE Class 10 Maths Practice Paper 2024 Solved: Download for ...

    By solving this comprehensive practice paper, students can assess their preparedness for the CBSE Class 10 Maths Exam 2024 and enhance their problem-solving skills.

  21. CBSE Class 10 Maths Practice Paper 2024 Solved: Download for Important

    CBSE Class 10 Maths Standard Practice Paper PDF: CBSE Class 10 Maths Exam 2024 is scheduled for March 11, 2024. This is going to be one of the most crucial exams for class 10 students in deciding ...

  22. NCERT Solutions For Class 10 Maths Chapter 10 Circles

    Answer: (i) A tangent to a circle intersects it in one point (s). (ii) A line intersecting a circle in two points is called a secant. (iii) A circle can have two parallel tangents at the most. (iv) The common point of a tangent to a circle and the circle is called the point of contact. 3.

  23. NCERT Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1

    Solution: There can be infinitely many tangents to a circle. Ex 10.1 Class 10 Maths Question 2. Fill in the blanks: (i) A tangent to a circle intersects it in ………… point (s). (ii) A line intersecting a circle in two points is called a ………… . (iii) A circle can have ………………. parallel tangents at the most.

  24. CBSE Class 10 Hindi A Solved Practice Paper for Board Exam 2024

    CBSE Class 10 Hindi A Solved Practice Paper 2024: Best for Last Minute Revision, Download PDF Now! ... CBSE Class 10 Maths Top 50 MCQs for Board Exam 2024: Best for Last Minute Revision; Get Free ...

  25. NCERT Solutions for Class 10 Maths Chapter 6 Triangles

    1. Fill in the blanks using correct word given in the brackets:- (i) All circles are __________. (congruent, similar) Answer: Similar (ii) All squares are __________. (similar, congruent) Answer: Similar (iii) All __________ triangles are similar. (isosceles, equilateral) Answer: Equilateral

  26. CBSE Class 10 Science Sample Paper 2024 Solve this paper to score 95

    Solve the CBSE Class 10 Science Sample Paper for 2024 as a valuable resource to achieve a score high marks in your exam. Working through this sample paper will enable you to familiarise yourself with the exam pattern, enhance your time management skills, and grasp the anticipated difficulty level.

  27. CBSE Important Questions for Class 10 Maths Chapter-wise

    2,92,836 Maths Questions for Class 10 Those who are preparing for Class 10 Maths exams should practise more questions, as it will clear their doubts instantly. These CBSE Important Questions for Class 10 Maths given here will help you prepare well and score good marks in the Maths exam.