NCERT Solutions
We provide solutions for all the questions that are present in the NCERT math textbooks for Classes 6 to 12. The solutions are detailed and provide stepbystep explanations for all the problems. Specifically, we review each question by taking into consideration the knowns and the unknowns (information/data/values), difficulty level, and the required steps for reasoning. This approach makes it easier for both the students and the teachers to understand the solution of each problem. Many questions that need pictorial explanation are also provided with diagrams and theoretical solutions. These solutions will help the students for the purpose of both homework and exams.
NCERT Solutions Class 6 to 12
Download PDF's NCERT Solutions for Class 6 to 12  

☛ NCERT Solutions for Class 6 Maths ☛ NCERT Solutions for Class 7 Maths ☛ NCERT Solutions for Class 8 Maths ☛ NCERT Solutions for Class 9 Maths ☛ NCERT Solutions for Class 10 Maths 
NCERT Solutions for Class 6,7,8,9,10,11 & 12 Maths Chapterwise PDFs
NCERT Solutions for Class 7 Maths Chapter 1 to 15
NCERT Solutions for Class 8 Maths Chapter 1 to 16
NCERT Solutions for Class 9 Maths Chapter 1 to 15
NCERT Solutions for Class 10 Maths Chapter 1 to 15
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What is unique about Cuemath's NCERT math solutions?
A guide to the best math learning practices
Designed according to best student learning practices, Cuemath’s NCERT Math solutions are a highly effective way of scoring higher in exams.
Highquality errorfree video solutions
These NCERT solutions are well explained with highquality and errorfree video solutions for each and every question.
Clear indepth coverage of all the topics
Designed in a concise yet explanatory manner, our solutions give a clear and indepth understanding of each Math topic.
Develop problemsolving approach
These solutions are prepared by our inhouse Math experts, from IIT and Cambridge University with over 15 years of experience in teaching Math.
Concepts for future competitive exams
Designed according to NCERT guidelines, our reliable and highly effective solutions develop a strong conceptual foundation in students for JEE,Math Olympiad, etc.
Cuemath is India’s Number 1 Math learning program providing the best online classes to students from classes 712. Our classes are highly interactive and conducted on a onetoone basis with our highly qualified and trained math expert, who inculcates selflearning among students to enhance their critical thinking and problemsolving skills. As a Cuemath student, you get personalized attention five times more than any normal class. Our curriculum is designed by experts from IIT & Cambridge university with simulations to make the sessions interactive and interesting for you Oftentimes, school teachers ask students to solve NCERT math problems so that a firm understanding of the fundamental concepts is developed or reinforced. Also, students can augment their knowledge about problemsolving methods by comparing solutions provided by their school teacher against the styles adopted by different providers (including Cuemath, which is a leader in the domain of math learning). Furthermore, while students are welcome to refer to different textbooks that are popular among the student communities, they must approach the NCERT books quite seriously as CBSE designs its question papers utilizing the concepts covered in these books. Equally significant is the fact that to design the board question paper, CBSE may select those teachers, who would align their style with the NCERT content.
Online math tuitions vs offline:
Online tutoring services have gained popularity all over India due to its affordability and convenience. Many parents these days prefer online math tuitions for their kids to formulate faster and better learning results. They provide many benefits over conventional tutoring including customized learning, quality tutoring, affordability of cost, no travel time, safety and comfort, etc. There are many online tutoring services available these days but not all of them offer the same quality and effectiveness. Online tuition classes can range anything from a prerecorded video assignment to an interactive session by an online expert. Due to this diversity of formats, it becomes tricky for parents to choose a suitable option for their children.
Before choosing any online tutoring program you should carefully consider if the online learning program:
 provides proper coverage of all the topics in a child's school syllabus
 tutors are well qualified and trained according to the requirement.
 has a basic structure and content designed to maximize the child’s learning potential.
Cuemath online math classes own all these qualities along with additional benefits including personalized attention, interactive animations, simulations, etc. To experience the quality of Cuemath online classes book a free class today!
Our NCERT App offers various math study materials for students such as math apps, NCERT solutions, educational videos, etc. to give an edge to your child’s exam journey and help them bag the highest marks! You can also easily promote your child’s interest in math with the Cuemath math games and interactive worksheets for students from classes K to 10. These educational games help children to grasp various math concepts faster and easier in a fun way. With the help of these interactive games, you can also reinforce school learning at home which develops a strong mental and cognitive ability of a child. These apps are absolutelyFREEfor everyone.
FAQs on NCERT Solutions
What is the difference between NCERT and CBSE syllabus?
CBSE or Central Board of Secondary Education is a board and is the governing body. NCERT or National Council of Educational Research and Training publishes textbooks for the board. Most of the schools are affiliated with the CBSE board in India.
Will the CBSE NCERT syllabus change from the 201819 session or the 201920 session?
According to HRD minister Prakash Javadekar, the NCERT syllabus was supposed to be reduced by half from the 2019 session. However, it will be cut by only 1015% for the academic year 20192020. Thus, it can be inferred that the goal of syllabus reduction will be achieved in phases. Importantly, the minister said that social sciences will have more cuts than science, mathematics, and languages.
How do I buy NCERT Books solutions online?
As a student, you don’t have to pay for NCERT solutions. You can download NCERT maths solutions for FREE by visiting this page. Our solutions are unique as we help you follow a systematic approach to problemsolving. Also, you will get help in gaining a deep understanding of the solutions as we provide additional reasoning for each problem.
Which is the best video solution for the class 9 maths NCERT?
The best video solutions for class 9 NCERT maths solutions are provided by Cuemath. These video solutions have been developed by Manan Khurma, who is the founder of Cuemath. Manan is an Electrical Engineer from IIT Delhi and he has taught thousands of students over a span of 15 years. He is one of the best Math experts in India. You can visit our YouTube channel to access NCERT maths video solutions.
Is NCERT enough for CBSE Class X Maths board examinations?
For maths, it is important that you understand the concepts covered in the NCERT book. Also, you must practice all the questions provided in the NCERT chapter exercises. However, if you want guaranteed improvement in maths, you must try Cuemath’s LEAP program. For a limited period, you can book a demo session with our expert teacher for FREE.
What is the best way to read NCERT books in order to score full in exams?
Tips to read NCERT books in a proper manner:
 Students must go through the syllabus and see the chapter content in the Index of the textbook
 Students should make a list of topics based on the level of difficulty
 Make a study plan based on the difficulty level
 Start reading the content of each chapter in depth as per the study plan for easy completion of the syllabus. Ensure that all concepts are clear
 The confidence of the students increase as they start practicing the difficult topics first and gradually move towards the easy ones
 Make important notes in a separate book when reading the chapters. This helps students to revise the difficult topics few days before the exam or even at the last minute
 Practice all the sample questions, sample papers, and exercises for each chapter. These questions help to understand the concept indepth and ace the exams
 Students can score high marks if they also go through the extra information given in the boxes like 'Did you know?‘ and 'Think out of the Box‘, Questions given at the end of each chapter
 Highlight the doubts and explore them separately with either your teacher or other resources from the internet or other reference books
You can also visit our Cuemath website which provides NCERT Solutions from Class 7 to Class 12 to explore the solutions for the questions which are left unsolved and get clarity on how to approach a given problem in the best way possible.
What is the exam pattern of the CBSE Class 10th Maths Question Paper?
The Exam pattern of the CBSE Class 10th Maths Question Paper is divided into Internal Assessment for 20 marks and Theory Paper for 80 marks. The Internal Assessment is conducted by the respective schools. Further, it consists of the following subdivisions:
Internal Assessment 
Marks allotted 
Periodic Tests and Multiple Assessment ● 3 Periodic tests are conducted in the school. ● Students are allotted their final marks based on the average of 2 periodic tests, i.e. on a total of 5 Marks. ● Multiple Assessment comprises Oral tests, Presentations, Group or Individual Assessment done in class. 
10 Marks (5+5 Marks) 
Portfolio ● Work done by the student throughout the year is part of Portfolio. ● It includes the neatness and presentation of notebooks, efforts put by the student to be creative, completeness of the work. 
5 Marks 
Math Lab activities from the textbook 
5 Marks 
The Theory Paper is for 80 Marks. It includes 4 Sections. Section A, B, C, and D. Section A consists of Multiple Choice Questions (MCQ) or the Objective Type for 20 Marks and the remaining Sections comprises Subjective Type Questions for 60 marks.
Sections 
No. of Questions 
Marks allotted per Question 
Total Marks 
Section A (MCQ type) 
20 Questions 
1 Mark 
20 Marks 
Section B 
6 Questions 
2 Mark 
12 Marks 
Section c 
8 Questions 
3 Mark 
24 Marks 
Section D 
6 Questions 
4 Mark 
24 Marks 
Total 
40 Questions 
80 Marks 

Internal Assessment 
Is it required to solve all the questions in NCERT given at the end of the chapter?
The NCERT textbooks are prescribed by the CBSE Board keeping in mind that children understand the concepts well. They can apply these concepts provided they learn it thoroughly which helps them to get through in their Board Exams and competitive exams like JEE, NEET, etc. In order to achieve this by the students across India, CBSE has prescribed a common study material to be referred to. This is published by the NCERT publishing body. Hence, it is essential to solving all the questions in the NCERT textbook given at the end of each chapter. All this helps them gain good fundamental knowledge on each topic and the subject overall.
What are the changes done for the Mathematics exam in the Class 10th CBSE Board in 2020?
Students go through immense pressure and stress to score full marks in maths, which is considered a difficult subject by the majority. To score full marks in Maths and get high scores overall in the Board Exams for Class 10th, in the academic year 201920, the CBSE Board has introduced two levels based on the difficulty for Mathematics Exam in Class 10th to make it easier. The two levels introduced are:
 Basic Mathematics
 Standard Mathematics
The syllabus and teaching in the Classroom remain the same for both levels. Students can opt for their choice of the type of Exam they would want to appear.
What is the Basic and Standard level option in the Class 10th CBSE Maths Exam?
The Basic and Standard level options for Maths in Class 10th counters to the level of difficulty of the Question Paper given in the Board Exams. Previously, students could only take Standard Maths, due to which they felt stressed out. Currently, the CBSE Board in the Academic year 201920 has helped the students relax to an extent by giving them options. The Question paper set for Basic maths is easier than Standard Maths. As compared to Basic Mathematics, Standard Maths assesses students for higher mathematical abilities.
What is the difference between the two levels in the 10 grade CBSE?
The Question paper set according to Basic Mathematics helps students give Maths Exam for Class 10th with less stress and strain. Here, the students cannot pursue any course that relates to Maths in Class 11 and 12. Standard Mathematics is similar to the previous Question Papers set by the CBSE Board for the Class 10th Maths Exam. As with previous years, Students can continue to pursue their choice of course in Class 11 and 12, which may or may not include Maths as a subject.
Can a student opt for both levels in Maths subject in the 10th grade CBSE Board exams?
No. Students have to make only one choice from either of the two levels.
Further, if a student chooses Basic Mathematics to appear for the Board Exam for Class 10th, then he/she cannot choose any course like Science or Commerce that includes Maths as a subject in the Senior Secondary School. If any student is interested in selecting a course with Maths in Senior Secondary School, they should pass Standard Mathematics in the Board Exams.
To add on to this, if a student has cleared Basic Mathematics in the Class 10th Board Exams, he/she can appear for Standard Mathematics in the Compartment Exams of Class 10th and clear it to opt for a course with Maths in Senior Secondary School.
What are the top 5 tips to get a perfect score in the Class 10th Maths Exam?
Maths is considered a strenuous subject by the majority of children in school. The beautiful aspect of Maths is that if the concepts, reasoning, and logic behind each problem are understood well, then it is the most simple subject. The preparation for the subject is half complete as we only have to implement those concepts in our solutions. Below are tips and tricks to achieve a perfect score in the Grade 10th Maths Exam:
★Solve all the Questions and Examples from the NCERT textbook as recommended by the CBSE Board for Class 10th Maths.
★Refer to the detailed NCERT Solutions provided on our Cuemath website in case of doubts. Students can also refer to ourYoutube Video Solutionswhich are prepared by our welltrained, expert teachers at Cuemath.
★Make a note of important Theorems, Formulae, Concepts, and strategies to solve tough problems as it is easy to revise (even at the last minute).
★Graphs are important as they help score marks easily. Avoid mistakes in this type of question.
★Understand the Question Paper Pattern and start answering the familiar Questions first and then move on to timeconsuming questions.
Last but not least, stay Calm, be Healthy, and Confident. Get a good sleep a day before the Exam. This helps students in their speed and accuracy when solving problems as their mind is fresh. Following the above points can help children attain a perfect score in the Grade 10th Maths Exam.
Important Note:
Maths Exam for Class 10th conducted by CBSE Board is on12th March 2020
How can I score full marks in the Class 10th CBSE Board?
The key aspects to score full marks in Maths arePreparation, Practice, andRevision. If students follow this, they can score full marks in the Class 10th Maths Exam conducted by CBSE Board.
Preparation:
For any task to be accomplished, Planning and Preparation are the most important. Refer to the Maths syllabus as prescribed by the CBSE Board for Class 10th. Make a Study Plan. Ensure that you allow the required time to Maths subject based on your understanding. As exams are fast approaching, the topics must be revised in a way depending on the knowledge of all topics and concepts which are studied throughout the year. Plan the timetable depending on the level of difficulty of each topic for the child.
Practice:
There is a quote that says ‘Practice makes a Man Perfect. Put this approach practically. As prescribed by the CBSE Board, refer to the NCERT textbooks. Solve all the Exemplars, Exercises behind each Chapter, Sample Questions, Model Papers thoroughly. Make Notes for easy accessibility to revise them before the exams. Develop a strategy to solve questions that are very difficult. This can be achieved by solving the previous years’ Question Papers. You can also refer to our Previous Years Solved Question Papers. To ace yourself in the Board exams, refer to the NCERT Solutions for Class 10th provided on the Cuemath website. These solutions for NCERT Maths offer a good, comprehensive, and errorfree approach to all the problems from NCERT textbooks.
Revision:
We tend to practice even after continuous practice. So Repetition or Revision is very important to score full marks. Revise all the important Concepts, Theorems, Formulae, Tricks to achieve a Centum in Maths. Maths being a concrete subject, you can assess yourself by answering Mock Exams which are timebound. Correct them to see your strong and weak areas in any of the topics. Revise weak topics again. You can also revise the important formulae available on our Cuemath website.
Students can score full marks in Grade 10th Maths Exam of CBSE Board if the above techniques are practiced with sincerity and dedication
What are the most important books to be referred to ace the Class 10th Math Board exam?
The most important books to refer to for the Class 10th Math Board Exam are the Standard NCERT textbooks prescribed by the CBSE Board.
Sl. No. 
Textbooks 
Author / Publications 
1. 
Mathematics Textbook for Class X 
NCERT Publications 
2. 
Mathematics Exemplar Problems For Class X 
NCERT Publications 
3. 
Laboratory Manual  Mathematics, the secondary stage 
NCERT Publications 
4. 
Guidelines for Mathematics Laboratory in Schools, class X 
CBSE Publications 
The Math textbook can also be downloaded as a PDF or can be read online on the NCERT website.
The belowmentioned study materials also help Class 10 students to excel in their upcoming CBSE Board Exams. Students across India refer to these textbooks to solve extra questions which helps them score full marks and understand the concepts thoroughly as they offer applicationbased questions.
Sl. No. 
Textbooks 
Author / Publications 
1. 
Mathematics for Class 10 
R.D. Sharma 
2. 
Secondary School Mathematics for Class 10 
R.S. Aggarwal 
3. 
All in one mathematics 
Arihant 
Are NCERT books enough for the JEE Main?
As a serious JEE aspirant, you must study and understand all the concepts and problems covered in NCERT books. However, only a proportion of JEE Main questions are directly based on NCERT material. Therefore, you must use additional material and practice questions to develop your thinking and attain success in the JEE Main examination.