NCERT Solutions Class 11 Maths
NCERT Solutions For Class 11 Maths
When it comes to academics, classes 10, 11, and 12 are undoubtedly the most important years for a student. While classes 10 and 12 are critical from the point of view of board exams, class 11 is crucial as it helps prepare you for class 12 exams. Then, it becomes vital to have a solid grip on the various subjects in class 11 as it sets your basics right. The in-depth knowledge of fundamentals you gain in class 11 will only help you ace your board examinations, which will ultimately help you pursue your chosen career from a top college.
Maths is perhaps the most feared subject among many students, and yet it is also the most scored one. If you are also struggling with certain concepts in Maths, NCERT solutions class 11 Maths from Extramarks will prove to be an excellent resource in preparing you for the examinations. Extramarks offers comprehensive solutions for all classes – from NCERT solutions class 1 to NCERT solutions class 12 – helping you ace your exams with top scores!
The NCERT solutions class 11 are designed systematically, covering all the 16 chapters included in the CBSE syllabus. We aim at providing a comprehensive learning experience for the student and the overall development of the various concepts. This is why, in our NCERT class 11 Maths solutions, you will find detailed explanations, step-by-step solutions to Maths problems, practice questions, shortcut tips, quizzes, and more. Now, you can clear your doubts and become a Maths wizard with a strong hold on basic mathematical concepts!
Class 11 Maths NCERT Solutions
The NCERT solutions class 11 Maths are specially solved and organised by subject matter experts with years of experience in CBSE board education. These solutions have been developed to help you clear your doubts and provide you with a step-by-step guide to solving complex maths questions.
All the chapters in the NCERT class 11 textbook include unique maths concepts which need regular practice. The key to scoring higher marks in maths is being consistent. Solving as many questions as you can, given at the end of every chapter will increase your speed and develop your problem-solving skills. Hence, you must access the NCERT Solutions from Extramarks to enhance your preparation level.
With Extramarks’ NCERT Solutions, you can get access to all the 16 chapters in the class 11 NCERT Maths book in a downloadable format. In addition to your textbook exercises, in-text solved examples, and guide books, these solutions will be a valuable study resource, preparing you for different types of questions asked in the examination. You can download the NCERT Maths book class 11 solutions by clicking on the link given, free of cost, and start studying at any time!
NCERT Solutions for Class 11 Maths Chapters
The class 11 NCERT Maths book consists of a total of 16 chapters. If you have any confusion regarding any of the maths concepts, you can refer to our NCERT class 11 Maths solutions to have an all-round and more concise understanding of the various chapters as a whole. These solutions will provide accurate guidance, written in an easy-to-understand language and systematically organised. When you download the solutions from Extramarks, you can navigate chapter-wise as well as exercise-wise Maths solutions as per your convenience.
NCERT Solutions for Class 11 Maths
Looking for accurate study resources to help you prepare better for your class 11 Maths examination? If yes, then you’re at the right place! To make it even more convenient for you, we offer detailed solutions to the class 11 Maths NCERT book exercises. Created by top-notch and experienced faculty in a simple language, these solutions will come in handy when you sit down to study.
Once you are through with the CBSE Maths syllabus and have a clear understanding of the fundamentals, it is best to start solving several sample papers and revising the various concepts for a deeper understanding. With reliable study material available at your disposal, this will become extremely easy. The chapter-wise solutions ensure that you can start with the basic concepts, move on to the more complex topics, and utilise your time judiciously. To ensure better learning, our experts have provided easy solutions to even the most complex questions in a logical manner.
Moreover, our solutions and study materials are designed in accordance with the latest CBSE curriculum and NCERT textbook exercises. With the rigorous practice of the different concepts, you can achieve higher marks in your class 11 exams. In addition, the solutions are 100% accurate and as per the CBSE guidelines, so rest assured that you can attempt all the difficult questions in the exam with ease.
Needless to say, NCERT Maths book class 11 solutions is all you need to be the top scorer in class 11 Maths exams.
NCERT Solutions Maths Chapter 1 Class 11 – Sets (Term I)
This chapter introduces the concept of sets. The important topics in this chapter include equal sets, empty sets, subsets, universal sets, and power sets. Along with this, you will learn about various set operations and how to draw a Venn diagram. The fundamentals of this chapter will be useful when studying the second chapter – relations and functions. It will also help you understand the concepts of probability, geometry, sequences, and more. The properties of different types of sets are also covered in this chapter. This chapter includes a total of 6 exercises, along with a miscellaneous exercise, covering a wide range of questions to strengthen your learning.
Maths NCERT Solutions Class 11 Chapter 2 – Relations and Functions (Term II)
This chapter illustrates the concept of connecting pairs of objects from two different sets and establishing relations between these objects. Along with this, you will also learn about functions, which is one of the most important topics in the class 11 Maths NCERT book. Various concepts in this chapter include functions as a special type of relation, domain and range of functions, pictorial representation, domain and co-domain of relations, Cartesian product of sets, functions and their graphs, and more.
Class 11 Maths NCERT Solutions Chapter 3 – Trigonometric Functions (Term II)
In the third chapter, you will learn about the concept of trigonometric ratios and trigonometric functions as well as their properties. The chapter begins with the basics of trigonometric identities, trigonometric ratios of different angles, trigonometric functions of sum and difference of two angles, trigonometric equations, the domain and range of trigonometric functions and their graphs, and the application of these concepts. All these topics are covered among the 4 exercises, along with a miscellaneous exercise. Through the various numerical questions, you get to understand the dynamic world of trigonometry.
NCERT Solutions Maths Class 11 Chapter 4 – Principle of Mathematical Induction
If you are interested in mathematical induction, this chapter will get you familiar with the various concepts which will also be useful when you pursue higher studies. It includes different unique topics such as the steps of the principle of mathematical induction, induction, the process of proving the induction, and several examples to explain these concepts thoroughly. All the problems in this chapter are mostly application-based.
NCERT Solutions for Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations (Term I)
This chapter discusses the concepts of real numbers, complex numbers, and the square root of negative numbers. The concept of a complex number is critical for higher maths, so it is best to put extra focus when revising this chapter. You will be introduced to topics like algebraic properties of complex numbers, the fundamental theorem of algebra, solutions of quadratic equations in the complex number system, and the square root of the complex number. With so many topics to cover, Extramarks’ NCERT class 11 Maths solutions will be a useful resource in preparing for the exam.
NCERT Solutions Maths Chapter 6 Class 11 – Linear Inequalities (Term II)
The sixth chapter can be interesting to study, once you are thorough with the various concepts. As the name suggests, it explores the concept of how two quantities can be unequal rather than being equivalent. In the NCERT Maths book class 11 solutions, you will find detailed solutions to different topics like algebraic solutions to linear inequalities in one variable, their representation on the number line, rules of inequality, and the graphic representation of linear equations in two variables. There are a total of 3 exercises along with a miscellaneous exercise covered in this chapter.
NCERT Class 11 Maths Solutions Chapter 7 – Permutation and Combination (Term II)
The concepts of permutation and combination apply to a variety of fields apart from maths. That is why having a strong grip on these concepts is absolutely crucial.A permutation is each of the several possible ways in which a series of objects can be arranged. Whereas, combination is the way of selecting different objects from a set where the order of selection doesn’t matter. This chapter will discuss topics like fundamental principles of counting, factorial, the derivation of the formula of permutation and combination, and their application.
NCERT Solutions Class 11 Maths Chapter 8 – Binomial Theorem
The Binomial Theorem is used to solve complex numerical and difficult computations for higher powers. This chapter will discuss the history and proof of the binomial theorem for positive integral indices. You may use the simplified expression of (a + b)n, where n is a rational number. Along with this, you will study Pascal’s triangle, the middle term, the binomial theorem for any index, the general and middle terms in binomial expansion, and their simple application.
NCERT Solutions Class 11 Maths Chapter 9 – Sequences and Series (Term I)
Chapter 9 of the Class 11 Maths NCERT book is an important chapter and carries a high weightage in the exam. The arranged list of numbers is a sequence and the sum of all terms in a sequence is a series. This chapter introduces you to the concepts of Arithmetic Progression (A.P.), Geometric Progression (G.P.), Arithmetic Mean (A.M.), terms of a G.P., the sum of the first n numbers of a G.P., formulae for the sum of special series, infinite G.P. and its sum- Geometric Mean (G.M.), the relation between A.M. and G.M., and more. To score better in this chapter, you need to understand and memorise several formulas to accurately solve the questions.
NCERT Solutions Class 11 Maths Chapter 10 – Straight Lines (Term I)
Learn about straight lines and their properties in this chapter. This is an important chapter for geometry where regular practice is the key to scoring better. Chapter 10 of the NCERT Class 11 Maths solutions comprises topics like the distance formula, section formula, area of a triangle, slope formula, conditions of collinearity of three points, equation of a straight line, parallel and perpendicular lines, etc. The various exercises will help you understand this chapter better.
NCERT Solutions Class 11 Maths Chapter 11 – Conic Sections (Term II)
In maths, the conic section is the curve obtained from the intersection of the surface of a cone and a plane. Conics include curves like circles and ovals, as well as conic segments, hyperbolas, and parabolas. In addition, the chapter will also introduce you to the concept and application of the x, y, and z-axis. The NCERT Maths book class 11 solutions cover various topics like the difference between various conics, the definition of parabola, line and a parabola, tangents to a parabola, ellipse, eccentric circles, etc.
NCERT Solutions Maths Class 11 Chapter 12 – Introduction to Three Dimensional Geometry (Term II)
This chapter extensively deals with coordinate geometry in a three-dimensional space. A point in space has three coordinates. This chapter introduces you to the concepts of coordinate axes and coordinate planes, coordinates of a point, the distance between two points, direction ratios of a line, the relationship between direction cosines of a line, section formula, etc. This is a highly scoring chapter where regular practice can help you ace the exam.
NCERT Solutions Maths Class 11 Chapter 13 – Limits and Derivatives (Term II)
The chapter, Limits and Derivatives, is an introduction to Calculus. Calculus is the study of changes in the value of a function as the points in the domain change. To begin with, you will get the basic idea of limits and derivatives along with some definitions of the algebra of limits.. The chapter includes several important theorems that you will need to learn to improve your understanding of the chapter and score well. You can study using the NCERT class 11 Maths solutions from Extramarks.
Class 11 Maths NCERT Solutions Chapter 14 – Mathematical Reasoning
This is a relatively easy chapter that deals with some basic ideas of mathematical reasoning. In this chapter, you are required to arrive at solutions to problems as per the scenario provided, using deductive reasoning. This chapter is extremely engaging and also important for upcoming competitive exams. Here, you will learn the basics of mathematical reasoning, open and compound statements, logic, statements, tables for basic logical connections, quantifiers and quantified statements, and more.
Class 11 Maths NCERT Solution Chapter 15 – Statistics (Term I)
When it comes to higher maths, statistics is a crucial chapter. In this chapter, you will learn about some measures of dispersion and methods of calculation for grouped and ungrouped data. The different concepts introduced in this chapter include measures of dispersion, mean deviation, range, variance, and standard deviation of grouped and ungrouped data, analysis of frequency distributions, and more. Once you are clear with the topics and methods of attempting the questions, you can easily score better.
NCERT Solutions Class 11 Maths Chapter 16 – Probability (Term II)
Probability is a much-used concept in various fields, and this chapter explores this topic in great detail using real-life examples. You should ensure a solid understanding of the core concepts and applications in this chapter to solve the maximum number of questions from this chapter. It revolves around concepts such as probability, events, types of events, random experimenting, simple and compound events, sure and impossible events, the probability of ‘and’, ‘not’, and ‘or’ events, and so on. The NCERT class 11 Maths solutions from Extramarks cover all the important topics and NCERT exercises from this chapter.
Class 11 Maths Solutions for Students
Most students fear Maths because it can be a tricky subject to prepare for. It can be a highly scoring subject only when you practice similar types of questions regularly. While your class 11 Maths NCERT book should be your main focus, practising extra questions can also prove to be helpful. Various subject experts at Extramarks have compiled and solved all the Maths NCERT textbook questions in a logical manner.
Moreover, the solutions are organised chapter-wise, which makes it easier for you to navigate and find the exercises you are looking for. And the best part is that the downloadable format allows you to access these solutions conveniently, anytime, from anywhere. So rest assured, you will be learning from the best resources available with a single click.
Chapter-Wise Weightage of Marks Class 11 Maths
When you’re preparing for an exam, knowing the marking scheme and the chapter-wise distribution of marks can really help you prepare better. This way, you can put extra effort and focus on your weak chapters that carry a high weightage.
The chapter-wise marks weightage for class 11 Maths is as below-
Unit No. | Unit Name | Marks |
I | Sets and Functions | 29 |
II | Algebra | 37 |
III | Coordinate Geometry | 13 |
IV | Calculus | 06 |
V | Mathematical Reasoning | 03 |
VI | Statistics and Probability | 12 |
Total | 100 |
Marking Scheme for Class 11 Maths – First Term
CBSE has divided the curriculum into two terms along with the syllabus, with 7 chapters in Term I out of 16 chapters. The Maths class 11 exam is of a total of 50 marks in both terms I and II. Here, the internal assessment carries 10 marks while the written examination has 40 marks in each term.
Here is the marking scheme for Term I of Class 11 Maths
S.No. | Chapters | Marks |
1. | Chapter 1- Sets | 11 |
2. | Chapter 2- Relations and Function | |
3. | Chapter 5- Complex Numbers and Quadratic Equations | 13 |
4. | Chapter 9- Sequences and Series | |
5. | Chapter 10- Straight Lines | 6 |
6. | Chapter 13- Limits and Derivatives (Only Limits) | 4 |
7. | Chapter 15- Statistics | 6 |
Total | 40 | |
Internal Assessment | 10 | |
Grand Total | 50 |
Internal Assessment Class 11 Term I
Internal Assessment | Marks |
Periodic/Unit tests | 05 marks |
Activities and Projects- Activity file + term end assessment + viva | 05 marks |
Total | 10 |
Marking Scheme for Class 11 Maths – Second Term
For a total of 40 marks in the written exam, the second term includes 7 chapters from a total of 16 chapters in the Maths NCERT syllabus.
Here is the marking scheme for the second term of the class 11 Maths exam-
S.No. | Chapters | Marks |
1. | Chapter 3- Trigonometric Functions | 8 |
2. | Chapter 6- Linear Inequalities | 11 |
3. | Chapter 7- Permutation and Combination | |
4. | Chapter 11- Conic Sections | |
5. | Chapter 12- Introduction to Three-Dimensional Geometry | 9 |
6. | Chapter 13- Limits and Derivatives (Derivatives only) | 6 |
7. | Chapter 16- Probability | 6 |
Total | 40 | |
Internal Assessment | 10 | |
Grand Total | 50 |
Internal Assessment Class 11 Term II
Internal Assessment | Marks |
Periodic/Unit tests | 05 marks |
Activities and Projects- Activity file + term end assessment + viva | 05 marks |
Total | 10 |
You can achieve better marks and improve your academic performance with consistent practice and a smart approach to studying. The NCERT class 11 Maths solutions will give you a competitive edge in preparing for your exam with their smart approach.
Solutions for Future Reference
When you download NCERT solutions class 11 Maths, you not only get access to study material to ace your class 11 examinations, but you can also use these for your future reference. The chapters covered in the class 11 Maths NCERT book are an essential part of the various competitive exams like JEE Main, JEE Advanced, CAT, CET, etc. All the questions covered will act as valuable revision notes when you start preparing for these entrance exams.
Moreover, they are created in a straightforward language, which will allow you to understand the complex topics very easily and retain them for longer. With this in-depth knowledge, you can surely appear for your competitive exam with increased confidence and concentration.
So, once you download the NCERT Solutions, you can save them for future reference. These solutions will provide guidance for an enhanced learning experience and you can practice these chapters regularly to ace your exams!
Covering All Chapters in One Solution
The NCERT Maths book class 11 solutions is a key study resource that covers all the chapters from the NCERT textbook in a single set. You can access 100% accurate solutions to different chapters including, sets, relations and functions, complex numbers, linear inequalities, quadratic equations, limit and derivatives, introduction to three-dimensional geometry, and more. All the NCERT exercise questions are solved by experienced faculty, providing you with step-by-step methods to solve a particular question.
With all the solutions available in one place, you don’t have to search in different places for different chapters when you begin studying. All you have to do is download the NCERT solutions class 11 and get instant access. All the concepts are explained in great detail which will clear your doubts and increase your confidence while attempting different questions during the actual examination.
Help in Exam Preparation
As a class 11 student, you must be aware that the mathematical concepts learned in class 11 will also be useful when you reach class 12. Not only that, but class 11 Maths questions are also a crucial part of several competitive exams. Since our NCERT solutions are provided systematically, you can grasp the theory behind each topic quickly while at the same time improving your time management skills. This will eventually help you in the actual exam, where time management and a thorough understanding of the difficult topics are essential for achieving higher marks.Moreover, remember that being consistent should be your top priority. The more you practise, the better you get at quickly solving questions.
Key Benefits of NCERT Solutions Class 11 Maths
- NCERT solutions from Extramarks are available in downloadable format, free of cost. This allows you to study at your own pace, completing each topic by devoting the proper time
- These solutions are compatible with all devices. So you can download them on your desktop, tablet, or smartphone and prepare for exams within your comfort zone
- The NCERT class 11 Maths solutions will also assist your classroom studies by providing a reference for your homework and assignments
- Certain chapters like probability, statistics, 3D geometry, sets, linear inequalities, etc., are relatively simple topics that you can easily master with enough practice and revision. Our comprehensive NCERT solutions class 11 Maths will help you do the needful
- The detailed solutions will also help you prepare faster for the exam. This is because whenever you get stuck on a question, you can simply refer to these solutions to clear your doubts or understand how the problem was solved
- Since Maths is a complex subject, having accurate solutions at your disposal can ease your worries in preparing for the exam
Moreover, not just maths, but Extramarks also offers complete NCERT solutions for all the class 11 subjects in a simple language, ready to download. And if that’s not enough, you can also access complete study resources for all classes, including NCERT solutions class 12, NCERT solutions class 10, NCERT solutions class 9, NCERT solutions class 7, and so on. Needless to say, Extramarks is your one-stop solution for valuable study material for all classes and subjects.
Extramarks Gives You Competitive Edge
Extramarks’ NCERT Solutions Class 11 Maths, as well as other subjects, gives you the confidence, clarity, and knowledge to attempt several difficult questions based on unique mathematical concepts with ease. Various education boards, including CBSE, design their school curriculum for classes 11 and 12 based on the NCERT textbooks for students. The concepts covered in the textbook offer you comprehensive knowledge of the basics, which can help you grasp even the most critical topics effortlessly.
And to further help you with that, NCERT class 11 Maths solutions by Extramarks also help you better understand the NCERT topics, improving your speed of learning. Students can use our detailed solutions to prepare notes for self-study and last-minute revisions and get ahead of their peers with their preparation.
These solutions are designed methodically which allows you to practice all the exercise questions in a logical manner and improve your mathematical skills. And not only that. With regular practice and by solving different types of questions, you get to improve your speed, concentration level as well as time management skills.
NCERT Solutions for Class 11 Maths – Preparation Tips
Preparing for a subject like maths can be overwhelming as well as tricky. Yet it is one of the most scoring subjects. You can score well only if you have a solid understanding of the fundamentals as well as the regular practice of solving various questions. Here are some effective tips you can follow to prepare efficiently and achieve higher marks in the exam-
- Create a study schedule to devote time to all the chapters and keep track of your progress. You can check the marking scheme to dedicate more time to your weak topics or chapters that carry a higher weightage of marks
- Having the best study resources can only take your exam preparation to the next level. You can use the NCERT solutions from Extramarks to boost your understanding and solve various types of questions easily
- Try to make short notes while revising as it will not only help you gain clarity but also identify any doubts you may have about any topic
- Once you are through with the NCERT syllabus, make sure to attempt as many questions and sample papers as you can to enhance your learning process
- While attempting the sample papers or mock tests, time yourself to evaluate how much time you are spending on different questions and if you’re able to complete the paper in the standard 3 hours. This way, you can improve your speed and time management skills by practicing more for topics that take time to solve. When preparing, completing the syllabus on time is extremely important as you must take some time for revision as well
- Regular self-assessment will help you judge your preparation level and identify the key areas where you need more practice
- Preparing for Maths can be overwhelming, so it is always important to keep your cool and take regular breaks in between studies to relax and unwind your brain
- Remember, for a subject like Maths, consistency is the key. Practice on a regular basis and revise several times to easily pass your class 11 exams.
FAQs (Frequently Asked Questions)
1. How can I prepare better for the class 11 Maths examination?
The syllabus for class 11 Maths can differ widely from the class 10 syllabus which can overwhelm the students as they are introduced to many new and unique concepts. So, it becomes important to put extra focus and prepare systematically. First, you need to thoroughly complete the NCERT Maths book as most of the exam is inspired by NCERT exercises. After this, you can start revising with NCERT solutions from Extramarks or guide books to practise different types of questions with varying degrees of difficulty.
2. Do the NCERT solutions cover all the topics discussed?
Yes, the NCERT solutions for class 11 by Extramarks include all 16 chapters of the textbook. You can find the solutions as well as extra practice questions as per the board guidelines for a comprehensive learning experience.
3. How many exercises are there in the Class 11 Maths textbook?
There are a total of 16 chapters in the class 11 Maths NCERT book and a total of 53 exercises. You can access the chapter-wise solutions to these exercises from Extramarks. With these solutions at your disposal, learning new concepts will become easy and you will be able to complete your syllabus in no time. Practising these solutions will give you the confidence to attempt various difficult questions that may be asked in the examination.
4. Is it necessary to solve sample papers for the class 11 Maths examination?
While practising sample papers is not required, doing so will greatly benefit you on the exam. Ideally, when you are done with the NCERT syllabus and exercises, you should start revising and practising different sample papers, mock tests, as well as previous years’ questions to boost your preparation level. This will also help you understand the exam pattern, marking scheme, types of questions asked, the difficulty level of the questions, important topics covered, etc. Besides, when you solve the papers, it allows you to improve your time management skills and speed of solving for better performance during the actual exam.
5. What are some of the important concepts covered in Chapter 9 of NCERT solutions for class 11?
The ninth chapter of the Maths NCERT textbook is on sequences and series, which introduces you to the concept of Arithmetic Progression and Geometric Progression. The chapter includes 4 exercises that can help strengthen your knowledge of the chapter as you solve the questions. Some of the important topics covered in this chapter include A.P., G.P., Arithmetic Mean, general terms of a G.P., infinite G.P. and its sum, the sum of the first n numbers of a G.P., Geometric Mean, relations between A.M. and G.M., and formulae for special series.
6. Is the class 11 examination based on the NCERT textbook?
Yes, class 11 examinations are completely based on the NCERT textbook. The class 11 Maths NCERT book covers a variety of unique mathematical concepts and provides a detailed explanation in a simple language. Besides, the textbook contains several exercises in each chapter to test your knowledge of the topics discussed so far. Practising these exercise questions regularly will help you gain in-depth knowledge and score higher as most of the questions in the exam come directly or indirectly from the NCERT book only. So, the best way to prepare for your exams would be to first complete the NCERT textbook and then move on to the revision using extra study materials.
7. Where can I get the solutions for class 11 Maths NCERT questions?
With Extramarks, you can get the well-explained solutions to all the NCERT textbook questions for Maths as well as other subjects. You can visit our website, find the chapter or exercise you are looking for, and click on the download link to get access to the solutions for free. The solutions will offer you the convenience of studying at your own pace and will prove to be a valuable study resource when you are preparing for any competitive exams in the future.
Moreover, all the questions are solved step-by-step by experienced professionals. So rest assured, you’ll get 100% accurate and reliable solutions. So don’t wait and download your copy today.
8. How many chapters are covered in the class 11 NCERT textbook?
As per the latest CBSE Maths syllabus, the NCERT textbooks cover a total of 16 chapters. These chapters are Sets, Relations and Functions, Trigonometric Functions, Principle of Mathematical Induction, Complex Numbers and Quadratic Equations, Linear Inequalities, Permutation and Combination, Binomial Theorem, Sequences and Series, Straight Lines, Conic Sections, Introduction to Three Dimensional Geometry, Limits and Derivatives, Mathematical Reasoning, Statistics, and Probability.
9. How will Extramarks’ NCERT solutions for class 11 Maths help in scoring better marks?
The class 11 solutions provided by Extramarks are solved and created by subject matter experts as per the latest CBSE guidelines. A detailed explanation of difficult concepts is provided to make it easier for you to solve the questions step-by-step. These solutions will aim to develop your problem-solving skills as well as boost your knowledge of the basics. For your convenience, the questions are available chapter-wise as well as topic-wise.