# NCERT Solutions

**NCERT Solutions** maths give young minds the most articulate and well-researched guide that can be consulted throughout their school lives. Each solution has been painstakingly prepared by mathematical geniuses in order to ensure that kids get the most out of their educational journey. The NCERT solutions maths include study tips, quick tricks to check if a student has arrived at the correct answer, mnemonics to memorize formulas, formula charts, and interesting facts to maintain a child’s enthusiasm. More importantly, each exercise problem is solved with adequate descriptions so as to combat confusion and superficial understanding of concepts.

NCERT Solutions maths are extremely helpful and sufficient for students preparing for any type of exams such as home, boards, and competitive tests. These solutions are not only useful for children belonging to the CBSE board but also help other students get a thorough insight into various mathematical topics. The benefits of using these solutions, as a reliable means of preparation, are endless. The NCERT solutions maths are driven towards aiding kids in getting a deep-seated and in-depth knowledge of Mathematics that will make them capable of solving the most complex problems within seconds.

## NCERT Solutions Maths Class 6 to 12 PDF Download

Perhaps the most tangible feature of the NCERT solutions maths, apart from many others, is that they promote the development of several skills such as visualization powers, problem-solving techniques, critical as well as computational thinking, and auxiliary abilities. These are not only useful for Mathematics but helps kids through many other subjects as well. Students can build a logical mindset while solving problems that will be useful in all walks of life. Given below are the class-wise links to the solutions of all mathematical chapters covered in the NCERT textbook.

### NCERT Solutions for Class 6 to 12 Maths

- NCERT Solutions for maths class 6 - PDF Download
- NCERT Solutions for maths class 7 - PDF Download
- NCERT Solutions for maths class 8 - PDF Download
- NCERT Solutions for maths class 9 - PDF Download
- NCERT Solutions for maths class 10 - PDF Download
- NCERT Solutions for maths class 11 - PDF Download
- NCERT Solutions for maths class 12 - PDF Download

The most important step in knowledge retention is regular practice. All the chapters in mathematics, throughout the grades, are interlinked. If a child has a shaky conceptual understanding of a certain topic chances are that he might not be able to successfully solve mathematical problems thus instilling fear. To address this challenge kids must periodically revise the NCERT solutions maths. It is also advised that students must first try the NCERT textbook questions on their own before tallying their results to ensure mastery of the subject. Given below are the links to all NCERT math textbooks.

>> Download CBSE Class 6 Maths NCERT Book

>> Download CBSE Class 7 Maths NCERT Book

>> Download CBSE Class 8 Maths NCERT Book

>> Download CBSE Class 9 Maths NCERT Book

>> Download CBSE Class 10 Maths NCERT Book

>> Download CBSE Class 11 Maths NCERT Book

>> Download CBSE Class 12 Maths NCERT Book

## NCERT Solutions for Class 12 Maths

NCERT solutions for class 12 maths comprise all the important and necessary chapters that will not only be helpful for a student while attempting boards as well as competitive exams but will also carry them through college. Given below are the exercise-wise links of all chapters that can be accessed to build an ironclad mathematical foundation.

### Class 12 Maths NCERT Solutions Chapter 1 to 13

### NCERT Solutions Class 12 Maths Chapter 1 Relations and Functions

- Class 12 Maths Chapter 1 Exercise 1.1
- Class 12 Maths Chapter 1 Exercise 1.2
- Class 12 Maths Chapter 1 Exercise 1.3
- Class 12 Maths Chapter 1 Exercise 1.4
- Class 12 Maths Chapter 1 Miscellaneous Exercise

### NCERT Solutions Class 12 Maths Chapter 2 Inverse Trigonometric Functions

- Class 12 Maths Chapter 2 Exercise 2.1
- Class 12 Maths Chapter 2 Exercise 2.2
- Class 12 Maths Chapter 2 Miscellaneous Exercise

### NCERT Solutions Class 12 Maths Chapter 3 Matrices

- Class 12 Maths Chapter 3 Exercise 3.1
- Class 12 Maths Chapter 3 Exercise 3.2
- Class 12 Maths Chapter 3 Exercise 3.3
- Class 12 Maths Chapter 3 Exercise 3.4
- Class 12 Maths Chapter 3 Miscellaneous Exercise

### NCERT Solutions Class 12 Maths Chapter 4 Determinants

- Class 12 Maths Chapter 4 Exercise 4.1
- Class 12 Maths Chapter 4 Exercise 4.2
- Class 12 Maths Chapter 4 Exercise 4.3
- Class 12 Maths Chapter 4 Exercise 4.4
- Class 12 Maths Chapter 4 Exercise 4.5
- Class 12 Maths Chapter 4 Exercise 4.6
- Class 12 Maths Chapter 4 Miscellaneous Exercise

### NCERT Solutions Class 12 Maths Chapter 5 Continuity and Differentiability

- Class 12 Maths Chapter 5 Exercise 5.1
- Class 12 Maths Chapter 5 Exercise 5.2
- Class 12 Maths Chapter 5 Exercise 5.3
- Class 12 Maths Chapter 5 Exercise 5.4
- Class 12 Maths Chapter 5 Exercise 5.5
- Class 12 Maths Chapter 5 Exercise 5.6
- Class 12 Maths Chapter 5 Exercise 5.7
- Class 12 Maths Chapter 5 Exercise 5.8
- Class 12 Maths Chapter 5 Miscellaneous Exercise

### NCERT Solutions Class 12 Maths Chapter 6 Application of Derivatives

- Class 12 Maths Chapter 6 Exercise 6.1
- Class 12 Maths Chapter 6 Exercise 6.2
- Class 12 Maths Chapter 6 Exercise 6.3
- Class 12 Maths Chapter 6 Exercise 6.4
- Class 12 Maths Chapter 6 Exercise 6.5
- Class 12 Maths Chapter 6 Miscellaneous Exercise

### NCERT Solutions Class 12 Maths Chapter 7 Integrals

- Class 12 Maths Chapter 7 Exercise 7.1
- Class 12 Maths Chapter 7 Exercise 7.2
- Class 12 Maths Chapter 7 Exercise 7.3
- Class 12 Maths Chapter 7 Exercise 7.4
- Class 12 Maths Chapter 7 Exercise 7.5
- Class 12 Maths Chapter 7 Exercise 7.6
- Class 12 Maths Chapter 7 Exercise 7.7
- Class 12 Maths Chapter 7 Exercise 7.8
- Class 12 Maths Chapter 7 Exercise 7.9
- Class 12 Maths Chapter 7 Exercise 7.10
- Class 12 Maths Chapter 7 Exercise 7.11
- Class 12 Maths Chapter 7 Miscellaneous Exercise

### NCERT Solutions Class 12 Maths Chapter 8 Application of Integrals

- Class 12 Maths Chapter 8 Exercise 8.1
- Class 12 Maths Chapter 8 Exercise 8.2
- Class 12 Maths Chapter 8 Miscellaneous Exercise

### NCERT Solutions Class 12 Maths Chapter 9 Differential Equations

- Class 12 Maths Chapter 9 Exercise 9.1
- Class 12 Maths Chapter 9 Exercise 9.2
- Class 12 Maths Chapter 9 Exercise 9.3
- Class 12 Maths Chapter 9 Exercise 9.4
- Class 12 Maths Chapter 9 Exercise 9.5
- Class 12 Maths Chapter 9 Exercise 9.6
- Class 12 Maths Chapter 9 Miscellaneous Exercise

### NCERT Solutions Class 12 Maths Chapter 10 Vector Algebra

- Class 12 Maths Chapter 10 Exercise 10.1
- Class 12 Maths Chapter 10 Exercise 10.2
- Class 12 Maths Chapter 10 Exercise 10.3
- Class 12 Maths Chapter 10 Exercise 10.4
- Class 12 Maths Chapter 10 Miscellaneous Exercise

### NCERT Solutions Class 12 Maths Chapter 11 Three Dimensional Geometry

- Class 12 Maths Chapter 11 Exercise 11.1
- Class 12 Maths Chapter 11 Exercise 11.2
- Class 12 Maths Chapter 11 Exercise 11.3
- Class 12 Maths Chapter 11 Miscellaneous Exercise

### NCERT Solutions Class 12 Maths Chapter 12 Linear Programming

- Class 12 Maths Chapter 12 Exercise 12.1
- Class 12 Maths Chapter 12 Exercise 12.2
- Class 12 Maths Chapter 12 Miscellaneous Exercise

### NCERT Solutions Class 12 Maths Chapter 13 Probability

- Class 12 Maths Chapter 13 Exercise 13.1
- Class 12 Maths Chapter 13 Exercise 13.2
- Class 12 Maths Chapter 13 Exercise 13.3
- Class 12 Maths Chapter 13 Exercise 13.4
- Class 12 Maths Chapter 13 Exercise 13.5
- Class 12 Maths Chapter 13 Miscellaneous Exercise

## NCERT Solutions for Class 11 Maths

NCERT solutions for class 11 maths have chapters that build the base for the upcoming grade. The syllabus covered in this class has very close ties to class 12 because it acts as a base for those chapters thus, kids must make it a point to be thorough with their understanding of all topics. The links to these exemplar exercise-wise solutions can be found below:

### NCERT Solutions for Class 11 Maths Chapter 1 to 16

### NCERT Solutions Class 11 Maths Chapter 1 Sets

- Class 11 Maths Chapter 1 Exercise 1.1
- Class 11 Maths Chapter 1 Exercise 1.2
- Class 11 Maths Chapter 1 Exercise 1.3
- Class 11 Maths Chapter 1 Exercise 1.4
- Class 11 Maths Chapter 1 Exercise 1.5
- Class 11 Maths Chapter 1 Exercise 1.6
- Class 11 Maths Chapter 1 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 2 Relations and Functions

- Class 11 Maths Chapter 2 Exercise 2.1
- Class 11 Maths Chapter 2 Exercise 2.2
- Class 11 Maths Chapter 2 Exercise 2.3
- Class 11 Maths Chapter 2 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 3 Trigonometric Functions

- Class 11 Maths Chapter 3 Exercise 3.1
- Class 11 Maths Chapter 3 Exercise 3.2
- Class 11 Maths Chapter 3 Exercise 3.3
- Class 11 Maths Chapter 3 Exercise 3.4
- Class 11 Maths Chapter 3 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 4 Principle of Mathematical Induction

### NCERT Solutions Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations

- Class 11 Maths Chapter 5 Exercise 5.1
- Class 11 Maths Chapter 5 Exercise 5.2
- Class 11 Maths Chapter 5 Exercise 5.3
- Class 11 Maths Chapter 5 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 6 Linear Inequalities

- Class 11 Maths Chapter 6 Exercise 6.1
- Class 11 Maths Chapter 6 Exercise 6.2
- Class 11 Maths Chapter 6 Exercise 6.3
- Class 11 Maths Chapter 6 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 7 Permutations and Combinations

- Class 11 Maths Chapter 7 Exercise 7.1
- Class 11 Maths Chapter 7 Exercise 7.2
- Class 11 Maths Chapter 7 Exercise 7.3
- Class 11 Maths Chapter 7 Exercise 7.4
- Class 11 Maths Chapter 7 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 8 Binomial Theorem

- Class 11 Maths Chapter 8 Exercise 8.1
- Class 11 Maths Chapter 8 Exercise 8.2
- Class 11 Maths Chapter 8 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 9 Sequences and Series

- Class 11 Maths Chapter 9 Exercise 9.1
- Class 11 Maths Chapter 9 Exercise 9.2
- Class 11 Maths Chapter 9 Exercise 9.3
- Class 11 Maths Chapter 9 Exercise 9.4
- Class 11 Maths Chapter 9 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 10 Straight Lines

- Class 11 Maths Chapter 10 Exercise 10.1
- Class 11 Maths Chapter 10 Exercise 10.2
- Class 11 Maths Chapter 10 Exercise 10.3
- Class 11 Maths Chapter 10 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 11 Conic Sections

- Class 11 Maths Chapter 11 Exercise 11.1
- Class 11 Maths Chapter 11 Exercise 11.2
- Class 11 Maths Chapter 11 Exercise 11.3
- Class 11 Maths Chapter 11 Exercise 11.4
- Class 11 Maths Chapter 11 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry

- Class 11 Maths Chapter 12 Exercise 12.1
- Class 11 Maths Chapter 12 Exercise 12.2
- Class 11 Maths Chapter 12 Exercise 12.3
- Class 11 Maths Chapter 12 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 13 Limits and Derivatives

- Class 11 Maths Chapter 13 Exercise 13.1
- Class 11 Maths Chapter 13 Exercise 13.2
- Class 11 Maths Chapter 13 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 14 Mathematical Reasoning

- Class 11 Maths Chapter 14 Exercise 14.1
- Class 11 Maths Chapter 14 Exercise 14.2
- Class 11 Maths Chapter 14 Exercise 14.3
- Class 11 Maths Chapter 14 Exercise 14.4
- Class 11 Maths Chapter 14 Exercise 14.5
- Class 11 Maths Chapter 14 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 15 Statistics

- Class 11 Maths Chapter 15 Exercise 15.1
- Class 11 Maths Chapter 15 Exercise 15.2
- Class 11 Maths Chapter 15 Exercise 15.3
- Class 11 Maths Chapter 15 Miscellaneous Exercise

### NCERT Solutions Class 11 Maths Chapter 16 Probability

- Class 11 Maths Chapter 16 Exercise 16.1
- Class 11 Maths Chapter 16 Exercise 16.2
- Class 11 Maths Chapter 16 Exercise 16.3
- Class 11 Maths Chapter 16 Miscellaneous Exercise

## NCERT Solutions for Class 10 Maths

NCERT solutions maths class 10 has a detailed explanation of each and every textbook question. These solutions have been given by math experts with the sole purpose of aiding students in scoring the best possible marks in their board exams. To get an insight into the lessons access the exercise-wise links to all chapters given below.

### NCERT Solutions for Class 10 Maths Chapter 1 to 15

### NCERT Solutions Class 10 Maths Chapter 1 Real Numbers

- Class 10 Maths Chapter 1 Exercise 1.1
- Class 10 Maths Chapter 1 Exercise 1.2
- Class 10 Maths Chapter 1 Exercise 1.3
- Class 10 Maths Chapter 1 Exercise 1.4

### NCERT Solutions Class 10 Maths Chapter 2 Polynomials

- Class 10 Maths Chapter 2 Exercise 2.1
- Class 10 Maths Chapter 2 Exercise 2.2
- Class 10 Maths Chapter 2 Exercise 2.3
- Class 10 Maths Chapter 2 Exercise 2.4

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

- Class 10 Maths Chapter 3 Exercise 3.1
- Class 10 Maths Chapter 3 Exercise 3.2
- Class 10 Maths Chapter 3 Exercise 3.3
- Class 10 Maths Chapter 3 Exercise 3.4
- Class 10 Maths Chapter 3 Exercise 3.5
- Class 10 Maths Chapter 3 Exercise 3.6
- Class 10 Maths Chapter 3 Exercise 3.7

### NCERT Solutions Class 10 Maths Chapter 4 Quadratic Equations

- Class 10 Maths Chapter 4 Exercise 4.1
- Class 10 Maths Chapter 4 Exercise 4.2
- Class 10 Maths Chapter 4 Exercise 4.3
- Class 10 Maths Chapter 4 Exercise 4.4

### NCERT Solutions Class 10 Maths Chapter 5 Arithmetic Progressions

- Class 10 Maths Chapter 5 Exercise 5.1
- Class 10 Maths Chapter 5 Exercise 5.2
- Class 10 Maths Chapter 5 Exercise 5.3
- Class 10 Maths Chapter 5 Exercise 5.4

### NCERT Solutions Class 10 Maths Chapter 6 Triangles

- Class 10 Maths Chapter 6 Exercise 6.1
- Class 10 Maths Chapter 6 Exercise 6.2
- Class 10 Maths Chapter 6 Exercise 6.3
- Class 10 Maths Chapter 6 Exercise 6.4
- Class 10 Maths Chapter 6 Exercise 6.5
- Class 10 Maths Chapter 6 Exercise 6.6

### NCERT Solutions Class 10 Maths Chapter 7 Coordinate Geometry

- Class 10 Maths Chapter 7 Exercise 7.1
- Class 10 Maths Chapter 7 Exercise 7.2
- Class 10 Maths Chapter 7 Exercise 7.3
- Class 10 Maths Chapter 7 Exercise 7.4

### NCERT Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry

- Class 10 Maths Chapter 8 Exercise 8.1
- Class 10 Maths Chapter 8 Exercise 8.2
- Class 10 Maths Chapter 8 Exercise 8.3
- Class 10 Maths Chapter 8 Exercise 8.4

### NCERT Solutions Class 10 Maths Chapter 9 Some Applications of Trigonometry

### NCERT Solutions Class 10 Maths Chapter 10 Circles

### NCERT Solutions Class 10 Maths Chapter 11 Constructions

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

- Class 10 Maths Chapter 12 Exercise 12.1
- Class 10 Maths Chapter 12 Exercise 12.2
- Class 10 Maths Chapter 12 Exercise 12.3

### NCERT Solutions Class 10 Maths Chapter 13 Surface Areas and Volumes

- Class 10 Maths Chapter 13 Exercise 13.1
- Class 10 Maths Chapter 13 Exercise 13.2
- Class 10 Maths Chapter 13 Exercise 13.3
- Class 10 Maths Chapter 13 Exercise 13.4
- Class 10 Maths Chapter 13 Exercise 13.5

### NCERT Solutions Class 10 Maths Chapter 14 Statistics

- Class 10 Maths Chapter 14 Exercise 14.1
- Class 10 Maths Chapter 14 Exercise 14.2
- Class 10 Maths Chapter 14 Exercise 14.3
- Class 10 Maths Chapter 14 Exercise 14.4

### NCERT Solutions Class 10 Maths Chapter 15 Probability

## NCERT Solutions for Class 9 Maths

NCERT solutions for class 9 maths bridges the knowledge of chapters that kids have learned in middle school with newer and more intensive topics that will be used throughout the remainder of their school careers. The solutions are written in a way to ease students into more complicated topics that are based on previous concepts thus, helping them work with these chapters quickly and efficiently. Given below are the links to all exercise-wise solutions.

### NCERT Solutions for Class 9 Maths Chapter 1 to 15

### NCERT Solutions Class 9 Maths Chapter 1 Number Systems

- Class 9 Maths Chapter 1 Exercise 1.1
- Class 9 Maths Chapter 1 Exercise 1.2
- Class 9 Maths Chapter 1 Exercise 1.3
- Class 9 Maths Chapter 1 Exercise 1.4
- Class 9 Maths Chapter 1 Exercise 1.5
- Class 9 Maths Chapter 1 Exercise 1.6

### NCERT Solutions Class 9 Maths Chapter 2 Polynomials

- Class 9 Maths Chapter 2 Exercise 2.1
- Class 9 Maths Chapter 2 Exercise 2.2
- Class 9 Maths Chapter 2 Exercise 2.3
- Class 9 Maths Chapter 2 Exercise 2.4
- Class 9 Maths Chapter 2 Exercise 2.5

### NCERT Solutions Class 9 Maths Chapter 3 Coordinate Geometry

- Class 9 Maths Chapter 3 Exercise 3.1
- Class 9 Maths Chapter 3 Exercise 3.2
- Class 9 Maths Chapter 3 Exercise 3.3

### NCERT Solutions Class 9 Maths Chapter 4 Linear Equations in Two Variables

- Class 9 Maths Chapter 4 Exercise 4.1
- Class 9 Maths Chapter 4 Exercise 4.2
- Class 9 Maths Chapter 4 Exercise 4.3
- Class 9 Maths Chapter 4 Exercise 4.4

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

### NCERT Solutions Class 9 Maths Chapter 6 Lines and Angles

- Class 9 Maths Chapter 6 Exercise 6.1
- Class 9 Maths Chapter 6 Exercise 6.2
- Class 9 Maths Chapter 6 Exercise 6.3

### NCERT Solutions Class 9 Maths Chapter 7 Triangles

- Class 9 Maths Chapter 7 Exercise 7.1
- Class 9 Maths Chapter 7 Exercise 7.2
- Class 9 Maths Chapter 7 Exercise 7.3
- Class 9 Maths Chapter 7 Exercise 7.4
- Class 9 Maths Chapter 7 Exercise 7.5

### NCERT Solutions Class 9 Maths Chapter 8 Quadrilaterals

### NCERT Solutions Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles

- Class 9 Maths Chapter 9 Exercise 9.1
- Class 9 Maths Chapter 9 Exercise 9.2
- Class 9 Maths Chapter 9 Exercise 9.3
- Class 9 Maths Chapter 9 Exercise 9.4

### NCERT Solutions Class 9 Maths Chapter 10 Circles

- Class 9 Maths Chapter 10 Exercise 10.1
- Class 9 Maths Chapter 10 Exercise 10.2
- Class 9 Maths Chapter 10 Exercise 10.3
- Class 9 Maths Chapter 10 Exercise 10.4
- Class 9 Maths Chapter 10 Exercise 10.5
- Class 9 Maths Chapter 10 Exercise 10.6

### NCERT Solutions Class 9 Maths Chapter 11 Constructions

### NCERT Solutions Class 9 Maths Chapter 12 Heron’s Formula

### NCERT Solutions Class 9 Maths Chapter 13 Surface Areas and Volumes

- Class 9 Maths Chapter 13 Exercise 13.1
- Class 9 Maths Chapter 13 Exercise 13.2
- Class 9 Maths Chapter 13 Exercise 13.3
- Class 9 Maths Chapter 13 Exercise 13.4
- Class 9 Maths Chapter 13 Exercise 13.5
- Class 9 Maths Chapter 13 Exercise 13.6
- Class 9 Maths Chapter 13 Exercise 13.7
- Class 9 Maths Chapter 13 Exercise 13.8
- Class 9 Maths Chapter 13 Exercise 13.9

### NCERT Solutions Class 9 Maths Chapter 14 Statistics

- Class 9 Maths Chapter 14 Exercise 14.1
- Class 9 Maths Chapter 14 Exercise 14.2
- Class 9 Maths Chapter 14 Exercise 14.3
- Class 9 Maths Chapter 14 Exercise 14.4

### NCERT Solutions Class 9 Maths Chapter 15 Probability

## NCERT Solutions for Class 8 Maths

NCERT solutions for class 8 maths help students in taking a complete look at the various formulas and types of problems that can appear on an examination. The different techniques used to solve questions encourage children to think out of the box and approach a sum with creative vigor. Given below are the solutions to all the exercises in each chapter.

### NCERT Solutions for Class 8 Maths Chapter 1 to 16

### NCERT Solutions Class 8 Maths Chapter 1 Rational Numbers

### NCERT Solutions Class 8 Maths Chapter 2 Linear Equations in One Variable

- Class 8 Maths Chapter 2 Exercise 2.1
- Class 8 Maths Chapter 2 Exercise 2.2
- Class 8 Maths Chapter 2 Exercise 2.3
- Class 8 Maths Chapter 2 Exercise 2.4
- Class 8 Maths Chapter 2 Exercise 2.5
- Class 8 Maths Chapter 2 Exercise 2.6

### NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals

- Class 8 Maths Chapter 3 Exercise 3.1
- Class 8 Maths Chapter 3 Exercise 3.2
- Class 8 Maths Chapter 3 Exercise 3.3
- Class 8 Maths Chapter 3 Exercise 3.4

### NCERT Solutions Class 8 Maths Chapter 4 Practical Geometry

- Class 8 Maths Chapter 4 Exercise 4.1
- Class 8 Maths Chapter 4 Exercise 4.2
- Class 8 Maths Chapter 4 Exercise 4.3
- Class 8 Maths Chapter 4 Exercise 4.4
- Class 8 Maths Chapter 4 Exercise 4.5

### NCERT Solutions Class 8 Maths Chapter 5 Data Handling

- Class 8 Maths Chapter 5 Exercise 5.1
- Class 8 Maths Chapter 5 Exercise 5.2
- Class 8 Maths Chapter 5 Exercise 5.3

### NCERT Solutions Class 8 Maths Chapter 6 Squares and Square Roots

- Class 8 Maths Chapter 6 Exercise 6.1
- Class 8 Maths Chapter 6 Exercise 6.2
- Class 8 Maths Chapter 6 Exercise 6.3
- Class 8 Maths Chapter 6 Exercise 6.4

### NCERT Solutions Class 8 Maths Chapter 7 Cubes and Cube Roots

### NCERT Solutions Class 8 Maths Chapter 8 Comparing Quantities

- Class 8 Maths Chapter 8 Exercise 8.1
- Class 8 Maths Chapter 8 Exercise 8.2
- Class 8 Maths Chapter 8 Exercise 8.3

### NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities

- Class 8 Maths Chapter 9 Exercise 9.1
- Class 8 Maths Chapter 9 Exercise 9.2
- Class 8 Maths Chapter 9 Exercise 9.3
- Class 8 Maths Chapter 9 Exercise 9.4
- Class 8 Maths Chapter 9 Exercise 9.5

### NCERT Solutions Class 8 Maths Chapter 10 Visualising Solid Shapes

- Class 8 Maths Chapter 10 Exercise 10.1
- Class 8 Maths Chapter 10 Exercise 10.2
- Class 8 Maths Chapter 10 Exercise 10.3

### NCERT Solutions Class 8 Maths Chapter 11 Mensuration

- Class 8 Maths Chapter 11 Exercise 11.1
- Class 8 Maths Chapter 11 Exercise 11.2
- Class 8 Maths Chapter 11 Exercise 11.3
- Class 8 Maths Chapter 11 Exercise 11.4

### NCERT Solutions Class 8 Maths Chapter 12 Exponents and Powers

### NCERT Solutions Class 8 Maths Chapter 13 Direct and Inverse Proportion

### NCERT Solutions Class 8 Maths Chapter 14 Factorisation

- Class 8 Maths Chapter 14 Exercise 14.1
- Class 8 Maths Chapter 14 Exercise 14.2
- Class 8 Maths Chapter 14 Exercise 14.3
- Class 8 Maths Chapter 14 Exercise 14.4

### NCERT Solutions Class 8 Maths Chapter 15 Direct and Inverse Proportion

- Class 8 Maths Chapter 15 Exercise 15.1
- Class 8 Maths Chapter 15 Exercise 15.2
- Class 8 Maths Chapter 15 Exercise 15.3

### NCERT Solutions Class 8 Maths Chapter 16 Playing with Numbers

## NCERT Solutions for Class 7 Maths

NCERT solutions for class 7 maths give stepwise solutions to all NCERT textbook problems. Kids can use these to improve their understanding of the concepts encompassed in this grade. Further, they can utilize these well-structured solutions as a cross-reference guide to check their answers as well as get an idea of the procedure used to attempt a particular sum. The links given below allow for easy access to the exercise solutions of each chapter.

### NCERT Solutions for Class 7 Maths Chapter 1 to 15

### NCERT Solutions Class 7 Maths Chapter 1 Integers

- Class 7 Maths Chapter 1 Exercise 1.1
- Class 7 Maths Chapter 1 Exercise 1.2
- Class 7 Maths Chapter 1 Exercise 1.3
- Class 7 Maths Chapter 1 Exercise 1.4

### NCERT Solutions Class 7 Maths Chapter 2 Fractions and Decimals

- Class 7 Maths Chapter 2 Exercise 2.1
- Class 7 Maths Chapter 2 Exercise 2.2
- Class 7 Maths Chapter 2 Exercise 2.3
- Class 7 Maths Chapter 2 Exercise 2.4
- Class 7 Maths Chapter 2 Exercise 2.5
- Class 7 Maths Chapter 2 Exercise 2.6
- Class 7 Maths Chapter 2 Exercise 2.7

### NCERT Solutions Class 7 Maths Chapter 3 Data Handling

- Class 7 Maths Chapter 3 Exercise 3.1
- Class 7 Maths Chapter 3 Exercise 3.2
- Class 7 Maths Chapter 3 Exercise 3.3
- Class 7 Maths Chapter 3 Exercise 3.4

### NCERT Solutions Class 7 Maths Chapter 4 Simple Equations

- Class 7 Maths Chapter 4 Exercise 4.1
- Class 7 Maths Chapter 4 Exercise 4.2
- Class 7 Maths Chapter 4 Exercise 4.3
- Class 7 Maths Chapter 4 Exercise 4.4

### NCERT Solutions Class 7 Maths Chapter 5 Lines and Angles

### NCERT Solutions Class 7 Maths Chapter 6 The Triangle and its Properties

- Class 7 Maths Chapter 6 Exercise 6.1
- Class 7 Maths Chapter 6 Exercise 6.2
- Class 7 Maths Chapter 6 Exercise 6.3
- Class 7 Maths Chapter 6 Exercise 6.4
- Class 7 Maths Chapter 6 Exercise 6.5

### NCERT Solutions Class 7 Maths Chapter 7 Congruence of Triangles

### NCERT Solutions Class 7 Maths Chapter 8 Comparing Quantities

- Class 7 Maths Chapter 8 Exercise 8.1
- Class 7 Maths Chapter 8 Exercise 8.2
- Class 7 Maths Chapter 8 Exercise 8.3

### NCERT Solutions Class 7 Maths Chapter 9 Rational Numbers

### NCERT Solutions Class 7 Maths Chapter 10 Practical Geometry

- Class 7 Maths Chapter 10 Exercise 10.1
- Class 7 Maths Chapter 10 Exercise 10.2
- Class 7 Maths Chapter 10 Exercise 10.3
- Class 7 Maths Chapter 10 Exercise 10.4
- Class 7 Maths Chapter 10 Exercise 10.5

### NCERT Solutions Class 7 Maths Chapter 11 Perimeter and Area

- Class 7 Maths Chapter 11 Exercise 11.1
- Class 7 Maths Chapter 11 Exercise 11.2
- Class 7 Maths Chapter 11 Exercise 11.3
- Class 7 Maths Chapter 11 Exercise 11.4

### NCERT Solutions Class 7 Maths Chapter 12 Algebraic Expressions

- Class 7 Maths Chapter 12 Exercise 12.1
- Class 7 Maths Chapter 12 Exercise 12.2
- Class 7 Maths Chapter 12 Exercise 12.3
- Class 7 Maths Chapter 12 Exercise 12.4

### NCERT Solutions Class 7 Maths Chapter 13 Exponents and Powers

- Class 7 Maths Chapter 13 Exercise 13.1
- Class 7 Maths Chapter 13 Exercise 13.2
- Class 7 Maths Chapter 13 Exercise 13.3

### NCERT Solutions Class 7 Maths Chapter 14 Symmetry

- Class 7 Maths Chapter 14 Exercise 14.1
- Class 7 Maths Chapter 14 Exercise 14.2
- Class 7 Maths Chapter 14 Exercise 14.3

### NCERT Solutions Class 7 Maths Chapter 15 Visualising Solid Shapes

- Class 7 Maths Chapter 15 Exercise 15.1
- Class 7 Maths Chapter 15 Exercise 15.2
- Class 7 Maths Chapter 15 Exercise 15.3
- Class 7 Maths Chapter 15 Exercise 15.4

## NCERT Solutions for Class 6 Maths

Grade 6 marks the start of middle school and the NCERT solutions for class 6 maths allows for an easy transition so that kids get the chance to revise the concepts they have learned in lower classes and relate them to complex topics. The solutions provide a step-by-step and illustrative approach to all questions enabling students to get a better understanding of the chapter at hand. The links given below can be used to access a PDF format of all solutions easily.

### Class 6 Maths NCERT Solutions Chapter 1 to 14

### NCERT Solutions Class 6 Maths Chapter 1 Knowing Our Numbers

- Class 6 Maths Chapter 1 Exercise 1.1
- Class 6 Maths Chapter 1 Exercise 1.2
- Class 6 Maths Chapter 1 Exercise 1.3

### NCERT Solutions Class 6 Maths Chapter 2 Whole Numbers

- Class 6 Maths Chapter 2 Exercise 2.1
- Class 6 Maths Chapter 2 Exercise 2.2
- Class 6 Maths Chapter 2 Exercise 2.3

### NCERT Solutions Class 6 Maths Chapter 3 Playing With Numbers

- Class 6 Maths Chapter 3 Exercise 3.1
- Class 6 Maths Chapter 3 Exercise 3.2
- Class 6 Maths Chapter 3 Exercise 3.3
- Class 6 Maths Chapter 3 Exercise 3.4
- Class 6 Maths Chapter 3 Exercise 3.5
- Class 6 Maths Chapter 3 Exercise 3.6
- Class 6 Maths Chapter 3 Exercise 3.7

### NCERT Solutions Class 6 Maths Chapter 4 Basic Geometrical Ideas

- Class 6 Maths Chapter 4 Exercise 4.1
- Class 6 Maths Chapter 4 Exercise 4.2
- Class 6 Maths Chapter 4 Exercise 4.3
- Class 6 Maths Chapter 4 Exercise 4.4
- Class 6 Maths Chapter 4 Exercise 4.5
- Class 6 Maths Chapter 4 Exercise 4.6

### NCERT Solutions Class 6 Maths Chapter 5 Understanding Elementary Shapes

- Class 6 Maths Chapter 5 Exercise 5.1
- Class 6 Maths Chapter 5 Exercise 5.2
- Class 6 Maths Chapter 5 Exercise 5.3
- Class 6 Maths Chapter 5 Exercise 5.4
- Class 6 Maths Chapter 5 Exercise 5.5
- Class 6 Maths Chapter 5 Exercise 5.6
- Class 6 Maths Chapter 5 Exercise 5.7
- Class 6 Maths Chapter 5 Exercise 5.8
- Class 6 Maths Chapter 5 Exercise 5.9

### NCERT Solutions Class 6 Maths Chapter 6 Integers

- Class 6 Maths Chapter 6 Exercise 6.1
- Class 6 Maths Chapter 6 Exercise 6.2
- Class 6 Maths Chapter 6 Exercise 6.3

### NCERT Solutions Class 6 Maths Chapter 7 Fractions

- Class 6 Maths Chapter 7 Exercise 7.1
- Class 6 Maths Chapter 7 Exercise 7.2
- Class 6 Maths Chapter 7 Exercise 7.3
- Class 6 Maths Chapter 7 Exercise 7.4
- Class 6 Maths Chapter 7 Exercise 7.5
- Class 6 Maths Chapter 7 Exercise 7.6

### NCERT Solutions Class 6 Maths Chapter 8 Decimals

- Class 6 Maths Chapter 8 Exercise 8.1
- Class 6 Maths Chapter 8 Exercise 8.2
- Class 6 Maths Chapter 8 Exercise 8.3
- Class 6 Maths Chapter 8 Exercise 8.4
- Class 6 Maths Chapter 8 Exercise 8.5
- Class 6 Maths Chapter 8 Exercise 8.6

### NCERT Solutions Class 6 Maths Chapter 9 Data Handling

- Class 6 Maths Chapter 9 Exercise 9.1
- Class 6 Maths Chapter 9 Exercise 9.2
- Class 6 Maths Chapter 9 Exercise 9.3
- Class 6 Maths Chapter 9 Exercise 9.4

### NCERT Solutions Class 6 Maths Chapter 10 Mensuration

- Class 6 Maths Chapter 10 Exercise 10.1
- Class 6 Maths Chapter 10 Exercise 10.2
- Class 6 Maths Chapter 10 Exercise 10.3

### NCERT Solutions Class 6 Maths Chapter 11 Algebra

- Class 6 Maths Chapter 11 Exercise 11.1
- Class 6 Maths Chapter 11 Exercise 11.2
- Class 6 Maths Chapter 11 Exercise 11.3
- Class 6 Maths Chapter 11 Exercise 11.4
- Class 6 Maths Chapter 11 Exercise 11.5

### NCERT Solutions Class 6 Maths Chapter 12 Ratio and Proportion

- Class 6 Maths Chapter 12 Exercise 12.1
- Class 6 Maths Chapter 12 Exercise 12.2
- Class 6 Maths Chapter 12 Exercise 12.3

### NCERT Solutions Class 6 Maths Chapter 13 Symmetry

- Class 6 Maths Chapter 13 Exercise 13.1
- Class 6 Maths Chapter 13 Exercise 13.2
- Class 6 Maths Chapter 13 Exercise 13.3

### NCERT Solutions Class 6 Maths Chapter 14 Practical Geometry

- Class 6 Maths Chapter 14 Exercise 14.1
- Class 6 Maths Chapter 14 Exercise 14.2
- Class 6 Maths Chapter 14 Exercise 14.3
- Class 6 Maths Chapter 14 Exercise 14.4
- Class 6 Maths Chapter 14 Exercise 14.5
- Class 6 Maths Chapter 14 Exercise 14.6

## Important Formulas in NCERT Solutions Maths

Throughout a child’s school career, he is introduced to several formulas. These formulas in the NCERT solutions maths can be seen as tools used for simplification of a problem. Each class takes a detailed look at the required formulas along with providing the derivations and corresponding analysis. The common denominator throughout all grades is that students must make it a practice to understand the concept behind the formula before memorizing and making a note of it. Given below are some of the class-wise important formulas:

Class 6

- Associative property: p + (q + r) = (p + q) + r
- Commutative property: p + q = q + p
- Area of a square = (side)
^{2}

Class 7

- Distributive Property: a × (b + c) = a × b + a × c
- Multiplicative Identity: 1 × a = a × 1 = a
- Area of a square = side × side
- Area of a rectangle = length × breadth

Class 8

- (a
^{ m})^{ n}= a^{ mn} - a
^{ 0}= 1 - Probability = (Number of outcomes that make an event) / (Total number of outcomes of the experiment)
- Discount = Marked Price – Sale Price
- Sales tax = Tax% of Bill Amount
- (a – b)
^{ 2}= a^{ 2}– 2ab + b^{ 2} - (a + b)
^{ 2}= a^{ 2}+ 2ab + b^{ 2}

Class 9

- (√a + √b)(√a - √b) = a - b
- (√a + √b)
^{2}= a + b + 2√(ab) - x
^{ 2}– y^{ 2}= (x + y) (x – y) - (x + a) (x + b) = x
^{ 2}+ (a + b)x + ab - Area of a triangle = ½ * base * height
- Area of a parallelogram = base * height

Class 10

- Area of a circle = πr
^{2} - Area of sector = θ/360 × πr
^{2} - HCF (p, q) × LCM (p, q) = p × q
- nth term of AP: a
_{n}= a + (n – 1) d - Sum of n terms: S = n/2[2a + (n – 1) d]
- LSA of frustum of a cone = √[h
^{2}+ (r_{1}- r_{2})^{2}]

Class 11

- (A ∪ B)′ = A′ ∩ B′
- ( A ∩ B )′ = A′ ∪ B′
- n (A ∪ B) = n (A) + n (B)
- Equation of a Parabola: y
^{ 2}= 4ax - Equation of an Ellipse: x
^{2}/a^{2}+ y^{2}/b^{2}= 1 - sin (x – y) = sin x cos y – cos x sin y
- sin (– x) = – sin x
- z
_{ 1}+ z_{ 2}= (a + c) + i (b + d) where z_{1}= a + ib, z_{2}= c + id

Class 12

- d/dx (tan
^{-1}x) = 1/(1 + x^{2}) - d/dx (cot
^{-1}x) = 1/(1 + x^{2}) - (A + B) + C = A + (B + C); [A, B, C are matrices]
- k(A + B) = kA + kB; [A, B are matrices]

## Importance of NCERT Solutions Maths

Maths NCERT Solutions are extremely important for students as they provide fun and easy to solve all questions. These solutions have been written by subject matter experts who ensure that the language used is simple to read and easy to understand facilitating holistic educational development amongst students. A few of the reasons why NCERT solutions are of such importance are given below:

**Time - Management**- The NCERT solutions maths help students in organizing themselves in the most efficient way. Kids can gauge the amount of time that will need to be allotted for solving a certain question and time themselves accordingly thus, enabling them to streamline their studying process.**Quick Revision**- During examination days when students do not have the time to revisit each and every question again, they can use the NCERT solutions maths to get a quick overview of topics as well as the associated formulas. This saves time and maximizes knowledge retention.**Better marks**- There are several methods to solve a particular question and the NCERT solutions maths give the most optimized way to reach an answer. Further, all the steps have been clearly explained. By adhering to the techniques given in these solutions students can get an idea of how to attempt their examination papers be it school, boards, or competitive. By presenting their test papers in a well-coherent manner kids can increase the probability of getting a good score.

## FAQs on NCERT Solutions Maths

### How CBSE Students can utilize Maths NCERT Solutions effectively?

The first step is to understand the theory behind any given section. Next, is to go through the formulas, understand the derivation as well as the ideology behind it, and then memorize them. Kids should then apply these concepts to the exercise problems and finally, use the Maths NCERT solutions to tally their answers and check the steps.

### Do I Need to Practice all Questions Provided in NCERT Solutions Maths?

Each question associated with the NCERT Solutions Maths has been handpicked by experts and placed in the textbook with a purpose. These problems are meant to give a student a complete understanding of the section that they are studying. Thus, it is vital to practice all sums in order to build a robust mathematical foundation.

### Do I Need to Make Notes while Referring to NCERT Solutions Maths?

It is highly recommended that kids should make notes while using the NCERT Solutions Maths as it gives them a way to recall concepts quickly. While attempting certain sums students should make notes against it outlining mnemonics, an easier explanation of concepts in their own words, and so on. This enables them to complete their revision at twice the pace and absorb twice the amount of information as opposed to studying without notes.

### How are NCERT Solutions Maths Promoting Problem Solving in Students?

NCERT solutions maths typically try to break down problems into smaller chunks and solve them in parts. Further, they place focus on understanding concepts thoroughly as well as grasping what the question is asking a student to do before actually solving it. By using these solutions kids can instill these values and improve their problem-solving skills.

### What are the Best Ways to Learn Concepts Covered in NCERT Solutions Maths?

The best way to learn the concepts in NCERT solutions maths is through constant practice and due diligence. It is necessary to build a crystal clear understanding of these topics before attempting exercise problems. Continuous revision of the theories, formulas, and sums will help kids build the confidence required to solve any type of examination as they will have a strong conceptual foundation.

### Where Can I Get class-wise NCERT Solutions Maths?

Students can access the well-explained class-wise NCERT Solutions Maths from the links that are given in this article. For the reader’s convenience, all the links have further been divided into the exercises pertaining to each chapter. Kids can use these to get the easy-to-download, scrollable PDF version of all solutions that can be used both online as well as offline and is compatible with all electronic devices.

### Are NCERT Solutions Maths Sufficient for CBSE Boards Exams?

All CBSE examinations irrespective of what class, follow the syllabus set by the experts at NCERT. Thus, the textbooks have questions that have a high probability of appearing in a test. The NCERT solutions maths are designed to help kids prepare well for any exam by providing a range of study tips and interesting facts. For the purpose of board exams, however, students can consult other supplementary material such as sample papers.

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