NCERT Solutions for Class 9

NCERT Solutions for Class 9- All Subjects

Have you ever felt less than adequately prepared for an examination and felt it making you extremely nervous and anxious? When we are under-prepared for a test or examination, it can take a toll on us mentally and make us do badly in an examination. This feeling of nervousness can even make us make mistakes in answers whose answers we do know. This is the reason why NCERT Solutions for Class 9 hold incredible importance in the life of a student. Having such NCERT Class 9 Book Solutions in our reach can help us avoid being under-prepared by allowing us to make sure that we study everything there is to be studied.

NCERT Solutions Class 9 Maths, Science, English, Hindi & Social Science

Class 9 NCERT Solutions hold utmost importance to a student because Class 9 is the year where things really start to heat up for the student, academics-wise. This is when parents and teachers begin to put pressure on students for doing well in the boards that will come the next year, so that students start preparing themselves for the academic rigorously  that the board exams require. It is the introduction to the first make or break year in a student’s life, and this is why Class 9th NCERT Solutions are so important for the student. In addition, these Class 9 NCERT Solutions provide a great basis for studying for the students. We, at VRC, have provided NCERT Class 9 Solutions PDFs for every student to ensure that you all fare exceptionally well in your exams.

Class 9th NCERT Solutions Explanation

Here, we have provided you with Class 9 NCERT Solutions for all the subjects, namely, Social Science, Mathematics, Science, Hindi and English. Studying every subject thoroughly is necessary in order to score fantastic marks in an examination, and our Class 9th NCERT Solutions for each subject of Class 9 will help you do the same. Here is a brief breakdown of the subjects for which we have provided NCERT Solutions of Class 9:

NCERT Class 9 Solutions for Maths

The NCERT Class 9 Maths solutions consist of all the chapters and their solutions from the Class 9 NCERT textbook. The solutions cover all the topics and important points that are present. There are a total of 15 chapters present in the Class 9 Maths. All these chapters are properly explained by experts in the Class 9 Maths NCERT solutions. The Maths Class 9 Solutions are designed in such a way that they will help students learn and understand the concept. This will also help students score well in the examination.

Chapters and Topics Covered in Class 9 Maths NCERT Solutions: Chapter-wise Importance of  NCERT Class 9 Maths

NCERT textbook of Class 9 Maths consists of 15 chapters.  These chapters will help the students to have a clear understanding of the topics and will make them well prepared for the class 9 Math topics.

NCERT Class 9 Maths Chapter 1 –  Number System

This chapter is a continuation of the chapter Number Line that you studied in earlier standards. This chapter will also teach you how to place various types of numbers on the number line. In Class 9 Chapter 1 will also focus on where to put the square roots of 2 and 3 on the number line, rational numbers, the laws of rational exponents and integral powers.

Some of the topics that are covered in this chapter are terminating decimals and their examples, non-rational numbers, rationalization, laws of exponents. You must learn about natural numbers, whole numbers, integers, etc. Practice questions and examples from the exercises. Learn the properties and characteristics of rational numbers and irrational numbers. You must also learn the laws of radicals from this chapter.

NCERT Class 9 Maths Chapter 2 – Polynomials

This chapter walks you through polynomial algebraic expressions and the terminology associated with them. This chapter covers the definition and examples of polynomials, as well as the coefficient, degrees, and terms used in a polynomial. NCERT Class 9 Chapter 2  will also focus on different types of polynomials such as quadratic polynomials, linear constants, cubic polynomials, factor theorems, and factorization theorems.

Some of the topics that are covered in this chapter are, coefficients of a polynomial, degree of the polynomial, cubic polynomials, quadratic polynomials, linear polynomials. Solve as many questions as possible from this chapter and learn all the definitions and formulas. Learn about zero polynomials and practice all the theorems. You can also solve additional questions from the NCERT solutions Maths Class 9. Factor and remainder theorems are important topics and you must practice them from the solutions. 

NCERT Class 9 Maths Chapter 3 –  Coordinate Geometry

This chapter has three exercises that will help you learn coordinate geometry in greater depth. In this chapter, you will learn about the Cartesian plane, and several terms linked with the coordinate plane. You’ll also learn how to plot a point in the XY plane and how to name that point.

This chapter is important and some of the topics that are covered in this chapter are the cartesian coordinates, coordinates of a point, plotting points on a plane, etc. Learn how to write points in different quadrants, signs of all the four quadrants, etc. You should also learn how to plot a graph and point on the Cartesian plane. Solve as many questions as possible and practice the examples to get an idea of the exercise questions.

NCERT Class 9 Maths Chapter 4 –  Linear Equations in Two Variables

Class 9 Maths Chapter 4 will teach you to represent a linear equation using a graph plot along with finding solutions to linear equations with two variables.  

Students need to practice questions related to this chapter and be thorough with the formulas. Learn how to represent a linear equation in two variables using a graph. You must be thorough with the following topics from this chapter: lines passing through origin lines parallel to coordinate axes and solution of the linear equation in two variables on a graph. Practice and solve exercise questions also go through the examples before you start solving the exercise questions.

NCERT Class 9 Maths Chapter 5 – Introduction to Euclid’s Geometry

This chapter introduces several geometrical terminology and shapes. There are two exercises in this chapter where you will learn the relationship between theorems, postulates, and axioms.

Students have to show relations between axioms and theorems. This chapter is important in the class 9th NCERT. Learn all the postulates and theorems. Go through the examples to understand the concepts better. This chapter is easy and you can score well. There are only two exercises in this chapter and you should be thorough with them both. 

NCERT Class 9 Maths Chapter 6 – Lines and Angles

Class 9 Maths Chapter 6 includes several theorems and procedures to prove these theorems which are based on angles and lines. There are 2 exercises included in this chapter.

Some of the topics that are covered in this chapter are, the sum of the angles of a triangle is always 1800, the sum of two interior opposite angles gives an exterior angle, etc. As you already know that this chapter is one of the most important chapters and you need to be very attentive while learning this chapter. You need to solve and practice questions from all the exercises. Topics such as linear pair, lines parallel to the same line, etc. are some of the basic topics of this chapter. Learn the types and properties of the angles and triangles. You need to have a clear understanding of the concepts from this chapter and you can use the NCERT Class 9 Maths solutions to learn all the above topics. 

NCERT Class 9 Maths Chapter 7 – Triangles

Chapter 7 of NCERT Class 9 Maths will help the students learn about rules of congruence, properties of triangles and inequalities. 

This chapter is very important. To score well you have to be through with this chapter and practice all the topics and their questions and examples. Some of the topics that are very important in this chapter are as follows-side of triangles, hypotenuse theorem and prove SSS, ASA, SAS congruence. Learn all the properties of triangles, inequalities of triangles, LHS and RHS criteria for congruence. 

NCERT Class 9 Maths Chapter 8 – Quadrilaterals

This chapter will help you understand the properties of quadrilaterals along with their combination with triangles.

This chapter also requires students to prove theorems and formulas. You have to learn about the types of quadrilaterals and their formulas. There will be both short and long answer questions from this chapter. Learn how to calculate angles of quadrilaterals and practice questions from the exercises.

NCERT Class 9 Maths Chapter 9 – Areas of Triangles and Parallelogram

This chapter of Class 9 Maths is very important to get an understanding of the area and how to find the area of triangles as well as parallelograms.

This chapter is also very important. You can score well in your exam if you prepare this chapter well. There are three exercises in this chapter and you have to solve all of them. Practice as many examples as possible from this chapter. You will be asked to prove the conditions of the given diagrams and check whether they satisfy or not. This chapter has many theorems thus, you have to study and practice this chapter properly.

NCERT Class 9 Maths Chapter 10 – Circles

Class 9 Chapter 10 is an interesting chapter for the students as well as an important one. It will help you learn about circles, chords, subtended angles and also to calculate the distance between the chord and the centre of a circle.

Learn the definition of a circle. You also have to learn formulas for finding the area, perimeter, circumference, perimeter, etc. of the circle. There are some theorems and proofs that you must learn and practice. Go through the properties and solve examples before starting the exercise questions. 

NCERT Class 9 Maths Chapter 11 – Constructions

This is a very important chapter and will majorly focus on the construction of triangles, bisectors on a line segment and measuring angles such as 45°, 60° and 90°.

This chapter is very important and the questions from this chapter will carry more marks compared to others. Some topics such as the construction of triangles and bisector of line segments will be covered in this.

NCERT Class 9 Maths Chapter 12 – Heron’s Formula

In this chapter, you will learn how to find the area of triangles, various types of polygons and quadrilaterals. 

Here, you will learn the area of the triangle using Heron’s formula.

NCERT Class 9 Maths Chapter 13 – Surface Areas and Volume

In previous standards, every one of you had already studied mensuration. As a result, you must be aware of surface areas, which are included in this chapter. Some of the other important topics include the volume of cubes, cylinders, cuboids, cones, hemispheres, and spheres. In addition, you will learn how to convert one figure to another and compare the volumes of two figures in this chapter.

Cube, cuboids, sphere surface areas, and volumes. Learn how to find the total and lateral surface areas of a cube and cuboid. Some of the important topics that you must learn and practice are as follows; right circular cone, right circular cylinder, etc. practice questions related to volume and capacity. 

NCERT Class 9 Maths Chapter 14 – Statistics

This chapter will teach you about descriptive statistics and the collection of data. This is useful for interpreting any data and presenting the results obtained from it.

In this chapter, you have to learn how to deal with the collection, interpretation, and analysis of data. You must learn how to sort and group data. Some of the topics that you need to learn and practice for the exam are; bar graph, frequency polygon, histogram, etc. You also have to learn about mean, mode, and median. Solve exercise questions and practice graphs. 

NCERT Class 9 Maths Chapter 15 – Probability

It is important to solve Class 9 Maths Chapter 15 because all the questions included in this chapter are very interesting and are based on our daily life situations. This will make us understand Probability in a much easier manner. 

This chapter is also very important and students need to practice properly. Thus, students who follow the Class 9 NCERT solutions will be able to score well.

NCERT Class 9 Solutions for Science

Under Science in Class 9 NCERT Solutions, we have provided you with notes for Chemistry, Physics as well as Biology. All three subjects hold equal importance, especially for the students who wish to take up the Science stream in their post matriculation. There are 15 chapters in the Class 9 NCERT Science Solutions. Following are some of the important chapters and topics in the Class 9 NCERT science solutions:

Matter in Our Surroundings: as we already know that all three subjects are included in the class 9 science syllabus, chemistry, physics, and biology. The matter in our surroundings is an important chapter in chemistry and Class 9 Science. You have to prepare to learn the states of matter, characteristics of the particles, etc. try to understand the concepts and learn them thoroughly.

Atoms and Molecules: learn what an atom is. Learn the laws of chemical combinations, and how to write them. Study molecular and mole concepts. This chapter is important and questions will be asked from this chapter. Prepare well and you can score well in the exam.

Tissues: this chapter is in Biology and it is one of the most important chapters. Learn the types of tissues and what they are made of. Practice and learn both plant and animal tissues. You also have to practice diagrams of the tissues. Solve all the exercise questions from the NCERT science solutions. 

Why Do We Fall Ill: this is a chapter that you can easily learn and prepare. You can score well in this chapter and you must take advantage of it.

Motion: this chapter is from physics and you have to be very thorough with it. Learn about velocity, displacement, and acceleration. You also have to learn about the graphical representation of motion. Practice all the formulas and equations. Solve the exercise questions and use the NCERT solutions to your benefit. The topic circular motion is also a crucial topic and you must not neglect it.

Work, Power, and Energy: this chapter is numerical based thus, you have to practice as many numerical questions as possible. Solve the exercise questions and study the examples. Learn formulas for work, energy, and power. You also have to learn about kinetic and potential energy.

Sound: you have to be very thorough with this chapter and learn all the topics present. Practice the exercise questions and examples. Some important topics that you have to be thorough with are as follows: production and propagation of sound, the reflection of sound, and applications of ultrasound. The topic, structure of the human ear is also important and it is a sure question in the Class 9 Science exam.

Natural Resources: this chapter is also very easy and you will be able to learn fast and score well in it. Learn about the types of resources and their use. Topics that you have to be careful with are the ozone layer, biogeochemical cycles, and minerals in the soil. Use the NCERT science solutions to practice all the exercises and additional questions. 

Above all the chapters are from the science subject and you can study them from the Class 9 NCERT Science Solutions. Prepare the chapters and their topics using the solutions as it will benefit you and help you to prepare properly for your exams. 

The Social Science part of NCERT Class 9 Solutions PDFs is inclusive of the solutions for all four books that come under the syllabus. These books are, namely, History, Civics, Economics and Geography, all of which hold great importance for a cultural and historical understanding of the world in which we live. These notes are especially important for those looking to take up Humanities or Arts later on. Students can use the NCERT solutions for Class 9 to prepare.

Mathematics is an important part of every student’s life, whether they choose to continue it forward into their studies or not. Class 9 NCERT Solutions provided for you by VRC create the base for more complex Mathematics to be learned later on in higher classes.

NCERT Solutions of Class 9 Benefits

There are so many great benefits of the NCERT Solutions of Class 9. We have listed a few of them below:

  • They are completely free and downloadable notes and are also suitable for taking printouts so that they are handier for you.

  • All the solutions have been provided in a detailed manner, leaving no room for the student to miss out on anything from the textbooks. NCERT Solutions Class 9 pdf can be downloaded for free.

  • The Class 9th NCERT Solutions are systematically given, making the process of studying much easier and direct.


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 do I need to use NCERT Solutions for Class 9 by VRC?

The VRC’s NCERT Solutions for Class 9 have been written down by seasoned professionals who know the topic about which they have provided solutions inside and out. The solutions provided here will be helpful for students because they are highly detailed and the points from the textbooks have been systematically broken down to provide better understanding of the subjects. These Class 9 NCERT Solutions are designed to make the lives of students easier. They are even downloadable and printable, totally free of cost.

2. Which are the subjects for which VRC has provided Class 9 NCERT Solutions?

VRC has provided Class 9 NCERT Solutions for all subjects to ensure that there is no topic left untouched by the student and no room left to be under-prepared for exams. There are notes for the subjects of Physics, Chemistry and Biology under Science; Economics, History, Civics and Geography under Social Science, Mathematics, and English language as well as Hindi language. All the NCERT Class 9 Book Solutions that a student may need have been provided for their understanding and ease of scoring well in the examinations.

3. What are the important topics covered in the NCERT Solutions for Class 9 Maths?

All topics taught in the Class 9 Maths syllabus hold equal importance in building the base of the subject. The NCERT Solutions Class 9 Maths covers all important topics. The following topics hold a higher weightage in the exams.

  • Non-terminating Numbers
  • Laws Of Exponents
  • Rationalization
  • Zeros Of Polynomials
  • Algebraic Identities
  • Remainder Theorem
  • Coordinate Geometry
  • Euclid’s Geometry
  • Heron’s Formula
  • Angle Sum Property Of A Triangle
  • Pair of Linear Equations In Two Variable.

4. Why are the NCERT Solutions for Class 9 Maths important?

NCERT books are the most important source available for the preparation of exams. Exercises and questions in Class 9 Maths NCERT books are very helpful in scoring. Students should solve and practice regularly. NCERT Solutions are equally important since students might face difficulties in understanding or solving the questions correctly so, referring to these solutions can help them get a proper understanding of the methods used in solving the questions.

5. How can I get NCERT Solutions for Class 9th?

Students can access the NCERT Solutions on VRC when they need help while attempting the questions provided in NCERT books. They can access  NCERT Solutions Class 9 Maths on VRC’s app. All the resources are free of cost. Also, referring to these solutions will help students to understand the mathematical concepts well and they will be able to score good marks in exams.

6. Where can I get Chapter-wise Solutions for NCERT Class 9 Maths? 

NCERT Solutions for Class 9 Maths have been provided by VRC and can be accessed by students who require help in answering the questions provided in various exercises in the NCERT Book for Class 9 Maths. Students can find step-by-step solutions for all questions and exercises given in each chapter of the syllabus for Class 9. These solutions can be accessed and downloaded free of cost here.

7. Do I need to practice all the questions provided in Class 9 Mathematics NCERT Solutions?

Questions provided in the NCERT books are very important for students to gain a proper understanding of the different and complex concepts of the Class 9 Maths syllabus. Question papers are also strictly designed on the basis of NCERT questions. Ignoring any of the questions can lead to a loss of marks in the exams. Hence, it is necessary to practice all the Class 9 Maths NCERT Solutions at least twice.

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

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2. Uncollected checks are also known as?

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3. A Bank Reconciliation Statement is:

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4. Passbook is a copy of:

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5. Bank Reconciliation Statement is prepared:

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6. 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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7. A bank reconciliation statement is mainly prepared for:

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

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

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

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12. 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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13. Unfavourable bank balance means

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14. A bank reconciliation statement is prepared by

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

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

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17. 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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18. 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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19. Unfavourable bank balances means:

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20. 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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21. 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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22. 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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23. Bank statement also called?

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

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26. 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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