NCERT Solutions for Class 11

Subject-Wise NCERT Solutions Class 11

You can access NCERT Class 11 PDFs to crack desired score in your academics exams. Class 11th is a base for class 12 and it is also considered as an important class. It helps you to prepare better for class 12. Students try to find out comprehensive study material for the preparation of exams. They feel very nervous if they did not get any good and efficient resources. Here our panel of experts have designed comprehensive NCERT Solutions for Class 11 to make learning better and enjoyable.  All the PDF solutions are available for all subjects, along with additional question banks to help students to crack good marks. Now visit our official webpage to clear your bulk of doubts and download the PDFs of  desired chapters.

NCERT Solutions for Class 11 Maths

The NCERT Solutions for Mathematics are well explained which are easily understandable. There are 16 chapters in class 11 Mathematics You can easily download chapter-wise NCERT solutions PDF  of Mathematics.

Chapter 1 – Sets and functions

In this chapter, This is the first chapter and there are a total of 3 exercises. This chapter holds 23 marks and you need to be thorough with your preparation. You have to learn about sets and their representation, types of sets, etc., practice examples, and the exercise questions. In the next exercise, you have to learn relations and functions. You also have to learn the sum, difference, quotient, etc. of functions. Solve the exercise examples to understand the concept properly and then you can proceed towards solving the exercise questions. Practice diagrams, domain, and range of functions. The last exercise is trigonometric functions, learn about positive and negative angles and solve examples and related questions. Learn how to measure angles in radians and degrees and also their conversion. 

Signs of trigonometric functions are also an important topic and you have to be thorough with it. Practice the domain and range functions along with their graphs. Learn the general solutions of trigonometric equations. In the topic sets. You also need to practice power sets, Venn diagrams, properties, etc. In the exercise relation and function, you have to learn pictorial diagrams, range of a relation, etc., practice-related examples and questions. Use the NCERT solutions for additional help and explanations.

1. Algebra 

This is the second unit and there are 6 chapters in it. The first chapter is on Mathematical Induction. Learn the principle of mathematical induction and applications. Complex numbers and quadratic equations is the 2nd chapter and there are 6 exercises in it. This chapter is very important and you have to prepare for it properly. 

Learn about complex numbers and their needs. You also have to learn the algebraic properties of complex numbers, and solve the given examples in the exercise. You also have to know the polar representation of complex numbers. Practice questions related to quadratic equations in complex numbers and the square root of complex numbers. You can always use the NCERT solutions for difficult topics and exercise questions. 

The 3rd chapter is Linear Inequalities, in this chapter and there are 4 exercises in this chapter. Learn about linear inequalities and go through plus one question paper and answers. In the next exercise, you have to learn algebraic solutions of linear inequalities in one and two variables. You also have to learn graphical solutions for two variables. Practice all the exercise questions and examples. 

Permutation and combinations is the 4th chapter in this unit. There are 5 exercises in this chapter. You will learn the fundamental principle of counting, derivation, and simple applications. Solve the exercise questions and use the NCERT solutions as reference. In permutations and combinations, you have to practice as many questions as possible.  

The 5th chapter is Binomial Theorem, there are 5 exercises and you have to solve and learn all the topics. Learn about pascal’s triangle, general and middle term binomial expression, and solve questions related to it. Also learn simple applications and solve exercise questions and practice. 

Sequence and series is the 6th chapter and there are 9 exercises. This chapter is very important and you have to prepare it properly to score well in it. Learn about arithmetic and geometric progression. Practice their formulas and solve questions related to them. 

You also have to focus on topics like arithmetic and geometric mean. Be very thorough with this chapter and revise daily. This unit holds 37 marks in total and thus requires proper preparations. The NCERT solutions also have additional questions plus one question paper and answers.

Chapter 3 – Matrices

This chapter is an easiest chapter in comparison with all chapters. you can easily crack good score with well planned preparation. There are total eight exercises in  this particular chapter. While going through this chapter You will be able to about the types of matrices and do solve questions related to the matrics. You will be able to earn about the elementary operation and invertible matrices as well. Kindly Solve  examples first for your better understanding of the concepts and practice as many questions as you would like. After wrapping the all examples, kindly solve short and long questions. Use the NCERT solutions for Class 12 for solving the textbook questions along with extra questions.

2. Coordinate geometry

This is the third unit and there are 3 chapters in it. This unit holds 13 marks. The first chapter in this unit is straight lines and there are 4 major exercises in it. Learn about the shifting of origin, the slope of a line, etc. 

Practice all the formulas and general forms. You also have to learn equations of the line parallel to the axis, point-slope form, etc. Solve all the examples and cover all the salient concepts before starting the exercise questions. You can use the NCERT solutions for the exercise questions and topics. The second chapter is conic sections, where you will learn about circles, ellipses, parabola, etc. 

Practice their formulas and solve related examples for understanding the concept properly. You also have to learn the standard equations and properties of a parabola, ellipse, and hyperbola. The last exercise in this chapter discusses the standard equation of a circle. Solve the exercise questions only after the completion of every topic. 

The 3rd chapter is three-dimensional geometry and there are 3 exercises in this chapter. In the first exercise, you have to learn about coordinate axes and coordinate planes in three dimensions. You also have to learn the coordinates of a point and distance and section formulas. Practice the given examples and exercise questions using the NCERT solutions for Class 11. 

3. Calculus – This is the 4th unit and there is only one chapter. This unit holds 6 marks and there are 5 exercises in this chapter. You have to learn the limits of polynomial and rational functions. You also have to learn derivation, practice examples, and exercise questions. This chapter is important and you will be studying it in higher classes also. Thus, you need to be thorough with it and properly learn it. Practice the formulas and memorize the properties.

Mathematical Reasoning – This is the 5th unit and there is one chapter in it. Practice the examples and learn the salient concepts properly. Solve the exercise questions after the completion of the chapter. For all the above units and chapters, the NCERT solutions provide the best explanation and you can use it to your advantage by preparing from it. 


The subjects which come under Humanities for Class 11 Solution are compulsorily History and Political Science. Class 11th NCERT Solutions are available for these subjects in full detail for Humanities/Arts students.


The textbook for Class 11 History is Themes in World History. Its contents are as follows:

Political Science

The textbook for Political Science is Indian Constitution at Work. Its contents are as follows:


Business Studies and Accountancy are the main or compulsory subjects under the Commerce stream and VRC provides some great Class 11th NCERT Solutions for the same. Some of the important chapters and topics that are included in class 11.

NCERT Commerce Solutions are as Follows:

Theoretical framework – In this chapter, you will be introduced to accounting and its concepts. You have to learn the functions, merits, and demerits, classifications, the role of an accountant, etc. Also, practice the equations and formulas. Solve the exercise questions and use the NCERT solutions for them. 

  • Theory of base accounting – In this chapter, you have to learn the different features of accounting principles, types of accounting principles, etc. You also have to have an idea of the accounting base, accounting standards, and objectives. Practice the exercise questions and try to maintain a separate note for the topic. 

  • Recording of transactions – In this chapter, you have to learn the basic steps required for recording transactions and the rules. Practice as exercise questions from the NCERT solutions. In the last topic, you have to learn the importance of the source documents.

  • Bank reconciliation statement – In this chapter, you will learn the basic difference between a cash book and a passbook, types of differences caused by time gap, etc. This chapter is important and you can score well with proper preparation. Solve the exercise questions and practice the examples.

  • Trial balance and rectification of errors – In this chapter, you will learn about trial balance, how it is prepared, the format of trial balance, etc. You also have to learn how to rectify errors and practice a few examples related to them. Solve the exercise questions and be thorough with your preparation.

  • Applications of computers in accounting – Learn the importance and use of computers in accounting. Capabilities of a computer and transaction processing system are some of the salient topics that you should be thorough with. Study the chapter with the help of NCERT solutions. Learn the features of a computerized accounting system and practice them. 

  • Structuring database for accounting – In this chapter, you have to learn the process and steps involved. You need to understand and memorize the steps and processes. Practice the exercise questions. 

There are 15 chapters in the class 11 commerce syllabus. To score well, you have to prepare all the chapters properly. The NCERT solutions have a proper and thorough explanation for all the chapters and they also comprise additional examples and questions. The NCERT solutions are the best material that you can use for both preparing and revising. The NCERT solutions are available in PDF form and you can download them for free. 


Under Science NCERT Solution for Class 11, there are the subjects Physics, Chemistry and Biology, which are compulsory for Science students. Biology is optional but is a pure science subject and is therein included. The science solutions also cover all the chapters and topics. You can use it to prepare your physics and chemistry. Preparing from the NCERT solutions will help you to keep track of the topics and will also help you to revise fast. Thus, it is recommended that you use the NCERT solutions during your preparation. 

Physics and Chemistry are compulsory subjects for Class 11 science students. Students can opt for any subject from Mathematics and Biology (PCM or PCB) or even opt for both (PCMB).

Common Subjects

Some common subjects are Psychology, Geospatial Technology, Legal Studies and Mass Communication, from which students from each stream are allowed to select one. Economics is a compulsory subject for Commerce as well as Humanities students, and English is a compulsory subject for all students. NCERT Solutions Class 11 PDFs provided for these subjects holds great importance to all students of Class 11.


The Class 11 English Syllabus is in following parts:

  • Literature

  • Hornbill (prose/poetry):


The following topics will be covered in this section:

  • Modals

  • Clauses

  • Change of Voice

  • Error Correction

  • Editing task/cloze passages

  • Re-ordering/transformation of sentences.


Practise the following reading-based skills:

  • Unseen Passage

  • Note Making

  • Summary


The following writing skills are to be practised:

  • Notice

  • Advertisement

  • Poster

  • Letter

  • Composition

Class 11 Solution Weightage Marks

All subjects of Class 11 amount to a total of 100 marks, from which 20 marks go from an internal assessment and 80 marks are from the written examination conducted at the end of the year by the CBSE board. The internal assessment includes an average of the midterm marks scored by the student and marks awarded for projects and other practical activities. The question paper for each subject is of 80 marks, its weightage marks divided chapter and topic-wise. Studying for these final year board exams is where the VRC’s NCERT Solution for Class 11 comes in handy.

NCERT 11th Solution Benefits

There are several benefits of Class 11th NCERT Solutions, some of which are listed as follows:

    • Written NCERT Solution for Class 11 can be soothing for the anxiousness and nervousness which comes with studying for exams.

    • NCERT 11th Solutions are given in a detailed and systematic manner which erases the student’s need to scour through textbooks to look for precise points.

    • The Class 11th NCERT Solutions provide samples for how questions should be answered in an exam.

    • VRC keeps the NCERT Solutions Class 11 PDFs completely free of cost and fully downloadable and printable.

    • The Class 11 Solutions allow the student to settle more easily into a stream which they have just chosen.


Revision Notes for Class 12

Important Questions for Class 12

CBSE Previous Year Question Paper for Class 12

CBSE Sample Paper for Class 12 

NCERT Exemplar Question for Class 12

Class 12 Maths Formula

CBSE Syllabus for Class 12

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FAQs (Frequently Asked Questions)

1. Why Choose VRC’s NCERT Solutions PDF?
VRC’s NCERT solutions PDF is a free PDF available online to help students from class 1 to 12 in their preparations for their final exams. The PDF is written under the CBSE guidelines to help you score well in these exams. In order to encourage concept-based learning, additional emphasis is given on understanding of the subject with a focus on each topic and each concept. After going through the PDF, students will find themselves well prepared to appear in the examinations. The NCERT solution PDF is a complete study material guide available for the students.
2. Why do Students Need NCERT Solutions PDF?
VRC’s NCERT solutions PDF is a must-have for all the students of classes from 1 to 12. Extensively explained solutions are available to students in this PDF. This PDF is reliable and recommended by teachers. Students should regularly go through the PDF to increase their understanding of the subject and their score in the examinations. The PDF helps you save your valuable time in searching for answers to the questions in your textbook as solutions to all the problems are available in the PDF well-categorized chapter wise and subject-wise.
4. Do I need to practice all the questions provided in Class 11 NCERT Solutions?
 It is indeed very crucial to practice as much as possible since Class 11 is primarily focused on fundamentals which can be challenging and it would be quite difficult for you to complete the syllabus and score well if you do not grasp the concepts. NCERT questions are also well-structured and created with strict respect to the CBSE syllabus for Class 11. You can get the NCERT Solutions for Class 11 free of cost. 
7. How many Chapters are there in the NCERT Solutions Class 11 Economics?

The NCERT Class 11 Indian Economic Development book has ten chapters. Each chapter covers a certain area and its topics, which are adequately expanded and explained, as well as carefully structured and conform strictly to the CBSE syllabus. From the standpoint of the test, it is critical to understand all of the principles, study the NCERT book thoroughly, and practice all of the exercises. Please refer to the link NCERT Solutions for Class 11 on VRC website ( for additional information.

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1. Unfavourable bank balances means:

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2. Pass Book of the account holder is a copy of

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3. Ravi’s bank reconciliation statement shows cheques deposited but not credited by bank of Rs. 3,800 and cheques issued but not presented by suppliers of Rs. 3,500. His bank balance as per Cash Book is Rs. 25,000. Balance as per pass book statement is

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4. Passbook is a copy of:

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5. Bank charges Rs.5,000 debited twice in pass book. What should be done in BRS if overdraft as per cash book is starting point?

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6. If balance in the bank statement shows Rs. 3,000 (Dr.) and there are deposits of Rs. 800 not yet credited and unpresented cheques totalling Rs. 500, the balance in the Cash Book should be:

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7. A bank reconciliation statement is mainly prepared for:

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8. Find out the Bank Balance as per Cash Book from the following particulars :
(i) Overdraft as per Pass Book = Rs. 5,000.
(ii) Cheques deposited into the bank but not credited = Rs.2,000

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9. Customer’s copy of the account provided by the bank to the depositor to record deposits and withdrawals is called:

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10. A bank reconciliation statement is prepared by

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11. ‘NSF’ marked in cheque sent back by the bank indicates

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12. Cash book balance was Rs. 1,790 (Dr.). When compared with the bank statement, it was identified that unpresented cheques were Rs. 1,040 and deposits not credited were Rs. 820. Balance of the bank statement will

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13. Bank statement also called?

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14. A Bank Reconciliation Statement is:

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15. Bank Reconciliation Statement is prepared:

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16. Overdraft as per Cash Book is Rs. 10,000. Cheques deposited but not credited Rs.2,500. Cheques issued but not encashed Rs.3,500. What is the balance as per Pass Book?

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17. Payment done by the account holder through issuing a cheque is entered in

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18. When check is not paid by the bank, it is called?

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19. Following details are related to a firm’s banking transactions at 31st March, 2019. Balance as per bank statement Rs. 22,650; uncleared lodgements Rs. 3,110; unpresented cheques Rs. 6,290. Bank credit recorded twice by bank in error as Rs. 650.
Which balance for cash at bank should appear in the Balance Sheet as at 31st March, 2019?

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20. VRC Ltd. receives a check for Rs. 100 records it in cash book and deposits it on the same day. A statement sent by the bank that day does not show this Rs. 100. How is this shown on the bank reconciliation statement?

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21. Unfavourable bank balance means

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22. Current account shows Rs. 1,000 as overdrawn. When bank statement is received, it was identified that one of debtors has deposited Rs. 400 into the account and bank charges of Rs. 20 had been debited to the account. Bank Statement balance is

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23. A business receives its bank statement showing the closing balance as Rs. 8,500 overdrawn. It is found that there were unpresented cheques amounting to Rs. 2,000 and uncredited deposits amounted to Rs. 1,500. Overdraft as per Cash Book is:

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24. The cheque which is issued to creditor but is not presented for payment is called?

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25. Uncollected checks are also known as?

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26. The balance on the debit side of the bank column of cash book indicates?

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