# NCERT Solutions for Class 12 Maths

Class 12 is an important and core phase for your career as you gain the basic knowledge of many important subjects and topics. Math as a crucial subject plays a significant role in improving your overall percentage in exams. NCERT Solutions for Class 12 Maths can help you revise and practice Math concepts for your board exams.

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## Class 12 Mathematics Chapters 1 to 13:

Cuemath provides the most accurate and reliable chapter-wise NCERT Solutions to the various math problems covered in the Class 12 NCERT textbooks. Here is a brief context of the chapter-wise solutions for Class 12 Maths:

## Chapter-1 Relations and Functions:

Chapter 1 of the NCERT Maths textbook for Class 12 is Relations and Functions which includes the concept of  Types of Relations, Types of Functions, Composition of Functions, Invertible Function and Binary Operations. You will be easily able to understand and practice the concept of Empty relation, Universal relation, Reflexive relation, Symmetric relation, Transitive relation, Equivalence relation, the composition of functions, etc. with the help of Class 12 solutions provided by Cuemath. Download Relations and Functions PDF.

## Chapter-2 Inverse Trigonometric Functions:

Chapter 2 of the NCERT Maths textbook for Class 12 is Inverse Trigonometric Functions which includes basic concepts and properties of Inverse Trigonometric Functions. Our solutions to Chapter 2 includes solutions to all these exercises which will help you to understand and solve problems related to the domains and ranges of inverse trigonometric functions using both algebraic and graphical representation . Download Inverse Trigonometric Functions PDF

## Chapter-3 Matrices:

Chapter 3 of the NCERT Maths textbook for Class 12 is Matrices which includes concept of Matrix and its types, Operations on Matrices, Transpose of a Matrix, Symmetric and Skew Symmetric Matrices, Elementary Operation of a Matrix, Invertible Matrices. Our solutions to Chapter 3 includes solutions to all these exercises which will help you to understand and solve problems related to Matrix. Download Matrices PDF.

## Chapter-4 Determinants:

Chapter 4 of the NCERT Maths textbook for Class 12 is Determinants which includes concept of Determinant, properties of Determinants, area of a Triangle, Minors and Cofactors, Adjoint and Inverse of a Matrix. Our solutions to Chapter 4 includes solutions to all these exercises which will help you to understand and solve problems related to Applications of Determinants and Matrices. Download Determinants PDF.

## Chapter-5 Continuity and Differentiability:

Chapter 5 of the NCERT Maths textbook for Class 12 is Continuity and Differentiability. Our solutions to chapter 5 will help you to understand the concept of Continuity, Differentiability, Exponential and Logarithmic Functions, Logarithmic Differentiation, Derivatives of Functions in Parametric Forms, Second Order Derivative, Rolle’s Theorem, Mean Value Theorem. Download Continuity and Differentiability PDF.

## Chapter-6  Application of Derivatives:

Chapter 6 of the NCERT Maths textbook for Class 12 is Application of Derivatives. The solutions for chapter 6 include the concept of  Rate of Change of Quantities, Increasing and Decreasing Functions, Tangents and Normals, Approximations, Maxima and Minima. Download Application of Derivatives PDF.

## Chapter-7 Integrals:

Chapter 7 of the NCERT Maths textbook for Class 12 is Integrals. In this chapter 7, you’ll learn basic concept of Integration as an inverse process of Differentiation, Methods of Integration, Integrals of some Particular Functions, Integration by Partial Fractions, Integration by Parts, Definite Integral, Fundamental Theorem of Calculus, Evaluation of Definite Integrals by Substitution, Some Properties of Definite Integrals. Download Integrals PDF.

## Chapter-8 Application of Integrals:

Chapter 8 of the NCERT Maths textbook for Class 12 is Application of Integrals. Our solutions for Class 12 Maths Chapter 8 will help you to understand, learn and solve problems based on the application of Integrals, like area under simple curves, area between two curves. Download Application of Integrals PDF.

## Chapter-9 Differential Equations:

Chapter 9 of the NCERT Maths textbook for Class 12 is Differential Equations. This chapter includes the basic concepts, general and particular solutions of a Differential Equation, Formation of a Differential Equation whose general solution is given, Methods of solving First order, First Degree Differential Equations. Download Differential Equations PDF.

## Chapter-10 Vector Algebra:

Chapter 10 of the NCERT Maths textbook for Class 12 is Vector Algebra. In this chapter, you'll learn some basic concepts, types of Vectors, Addition of Vectors, Multiplication of a Vector by a Scalar, Product of Two Vectors, etc. Download Vector Algebra PDF.

## Chapter-11 Three Dimensional Geometry:

Chapter 11 of the NCERT Maths textbook for Class 12 is Three Dimensional Geometry, which has concepts based on the Direction Cosines and Direction Ratios of a line, Equation of a line in space, angle between two lines, shortest distance between two lines, Plane, coplanarity of two lines, angle between two planes, distance of a point from a plane, Angle between a Line and a plane, etc. Download Three Dimensional Geometry PDF.

## Chapter-12 Linear Programming:

Chapter 12 of the NCERT Class 12 Maths textbook is Linear Programming. In this chapter, you will learn some concepts based on problems related to Different Types of Linear Programming and its Mathematical Formulation. Our solutions for Chapter 12 of Class 12 Maths will help you to easily grasp these concepts for a thorough revision. Download Linear Programming PDF.

## Chapter-13 Probability:

Chapter 13 of the NCERT Class 12 Maths textbook is Probability. In this chapter, you will study Conditional Probability, Multiplication Theorem on Probability, Independent Events, Bayes' Theorem, Random Variables and its Probability Distributions, Bernoulli Trials and Binomial Distribution. Download Probability PDF.

## How are NCERT Solutions prepared and what edge do they provide?

NCERT Maths Solutions for Class 12 are a vital resource to prepare and secure good marks in board exams. These solutions are well prepared after extensive research by highly qualified and profound educators from across the country to provide an edge to the students. A perfect guide to ace CBSE Class 12 exams, these solutions are also meant to prepare children for various competitive exams including NTSE, Math Olympiad, JEE, etc. The solutions are created by the best math experts in the country after long research and analysis. These solutions are exclusively designed to impart a strong conceptual knowledge in students through continuous practice. Formulated to enhance mathematical proficiency, these solutions serve as an excellent resource for exam preparation. They not only help students in preparing for exams but also sets them on the right path for future success.

These solutions optimize practice and self-learning in kids. Structured in a very simple and easy to understand language, these solutions help in learning concepts in less time resulting in better time management during exams. Providing coverage to all the important topics and concepts, these solutions are helpful in preparing for various competitive exams including Math Olympiad, JEE, NTSE, etc. Cuemath provides the most reliable and highly effective math solutions from Class 7-12. Our solutions not only help students to prepare for exams but also help them in enhancing their problem-solving ability and reasoning power. With Cuemath solutions, it becomes simple and easy for students to grasp various concepts in detail.

## Why are Cuemath NCERT Math solutions the best?

Cuemath's NCERT Math Solutions are formulated by our in-house math experts to provide a competitive edge to the Class 12 students. You can easily refer to and learn from our high-quality, error-free video solutions and text solutions as they are created in a simple and easy to understand manner. These solutions give an in-depth knowledge of every topic in Class 12 Maths. Designed in a very concise yet explanatory manner, they are formulated to impart a clear conceptual knowledge as well as to develop reasoning and problem-solving approach in kids. Our solutions are an extremely reliable and highly effective guide to the best math learning practices. These Math videos and text solutions are also designed according to the NCERT guidelines to build a stronger conceptual foundation in students for future exams. It is also a highly efficient way of scoring the highest marks not only in board exams but also in various competitive exams including NTSE, Math Olympiad, JEE, etc.

## How are Cuemath solutions different from competitors?

Our NCERT Solutions are exclusively designed by highly qualified and experienced Maths experts, to strengthen the mathematical foundation of children. We offer the most effective math solutions for Class 12 students to help them prepare for their board exams. These solutions provide chapter wise coverage to various topics of Class 12 NCERT Maths textbook and are prepared according to the NCERT guidelines. Each topic is elaborated in a detailed, efficient and easy to understand format in-order to implement faster and better learning.

Our NCERT App offers various math study material for students such as Math apps, Video Solutions, Text Solutions, Concept videos, etc. to give an edge to your child’s exam journey and help them bag the highest marks! You can also easily promote your child’s interest in math with the Cuemath Math Games for students from Class K to 12. These educational games help children to grasp various math concepts faster and easier in a fun way. With the help of these interactive games, you can also reinforce school learning at home which develops a strong mental and cognitive ability of a child. These apps are absolutely FREE for everyone.

## When to refer to NCERT Solutions for Class 12?

Mathematics in Class 12 covers topics based on complicated domains including calculus, trigonometry, geometry, statistics, etc. Preparation for this type of learning requires thorough practice and a strong conceptual understanding of each and every topic. To achieve this conceptual proficiency, these solutions are the most reliable and useful reference for Class 12 students. These solutions not only help in learning math concepts better but also provide assistance to students for their homework and exam preparation. It has proven to be an efficient guide for self-learning in the absence of a tutor.

## How can NCERT Solutions help in Exam preparation?

NCERT Maths Solutions are the best way to attain the right approach for precisely answering the questions in exams. Keeping in mind the exam pattern and most coverage from NCERT books, these solutions are well formulated to provide excellent exam results. They promote impactful learning to top board exams. Each exercise in these solutions is well-explained to provide in-detailed knowledge for strategic learning to help students. It serves as an efficient way to optimize learning for better exam results. By practicing the exercises and reasoning provided in solutions, students attain a step by step clear conceptual understanding of topics required for good exam preparation.

## Importance of NCERT Solutions for Competitive exams

NCERT Class 12 solutions can be used as a resourceful guide for various competitive exams including Math Olympiad, JEE, NTSE, etc. These solutions are based on the CBSE syllabus to cover all the basics and fundamentals of each and every topic in detail. Providing step by step solutions to each and every question to help students clear all necessary concepts, these solutions are a perfect guide for building a strong mathematical foundation. Created in a very simple and easy to understand language these are helpful in grasping various concepts easily.

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• If the online learning program provides proper coverage of all the topics in a child's school syllabus.

• If the tutors are well qualified and trained according to the requirement.

• If the basic structure and content of the program are designed to maximize the child’s potential.

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