2 1. Relations & functions
3 2. Inverse trigonometric functions
4 3. Matrices
5 4. Determinants
6 5. Continuity & Differentiability
7 6. Application Of derivatives
8 a1. Appendix 1. Proofs in Mathematics
9 a2. Appendix 2. Mathematical Modelling
10 an. Answers & Supplementary Material
NCERT Class 12 Solutions Maths includes all the questions given in NCERT Books for Class 12 Maths Subject. Here are all questions are solved with a full explanation and available for free to download. NCERT Class 12 Solutions Maths are given below for all chapter. Choose chapter name to check NCERT Solution chapter wise. We hope that our NCERT Solutions for Class 12 Maths helped with your studies! If you liked our NCERT Class 12 Solutions Maths, please share this post.
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Chapter 1 - Relations and Functions
The Chapter 1 of CBSE Class 12 deals with the concept of relations and functions, domain, co-domain and range which have already been presented in class 11 syllabus along with several types of specific real-valued functions and their graphs. In Chapter 1, you will be answering a total of four exercise's questions entailing all the primary topics in them.
Chapter 2 - Inverse Trigonometric Functions
There are several functions which are not one, onto or even both and therefore we cannot talk of their inverses. In Class 11 read that trigonometric functions are not one-one and onto over their real domains and ranges and from their inverses don't exist. In CBSE Class 12 Inverse Trigonometric Functions, there are only 2 exercises where you will study concerning the restrictions on ranges and domains of trigonometric functions which allows the visibility of their inverses and observe their ways through graphical representations. Additionally, some elementary features will also be considered. The inverse trigonometric functions include a great value in calculus for they help to define many integrals. Inverse trigonometric functions concepts are applied vastly in engineering and science.
Chapter 3 - Matrix
You need to understand about Matrices as it is instrumental in different branches of mathematics. Matrices are regarded as one of the most powerful weapons in mathematics. It explains our work to a great extent when compared with another method. There is a total of 62 questions in four exercises of this chapter. In this Matrix chapter, you will be delving deeper into the basics of matrix and matrix algebra.
Chapter 4 - Determinants
In chapter 3, matrix and matrix algebra will be explained. Whereas, in this chapter, you will be reading about determinants up to order 3 only with real entries. Also, the 6 exercises are given in a way that you will study many properties of determinants, minors, adjoint and inverse of a square matrix, cofactors and applications of determinants in finding the area of a triangle, consistency and inconsistency of system of linear equations and solution of linear equations in 2 or 3 variables using inverse of a matrix in these practices.
Chapter 5: Continuity and Differentiability
This chapter is the addition of differentiation of functions which you have studied in Class 11. You must have learnt to differentiate some functions such as polynomial functions and trigonometric functions. This chapter describes the very important concepts of continuity, differentiability and relationships between them. You will be reading about the differentiation of inverse trigonometric functions. Moreover, you will be getting introduced to a new class of functions called exponential and logarithmic functions. There is a total of 8 exercises in this chapter so you will have to give some extra time and effort to get well versed with this chapter.
Chapter 6 - Application of Derivatives
In Chapter 5, you would see how to find a derivative of composite functions, exponential functions, inverse trigonometric functions, implicit functions and logarithmic functions. In this chapter, you will study the importance of the derivative in different disciplines such as science, engineering and many other fields. For example, we will study how the derivative can be applied to determine the rate of change of quantities and to get the equations of tangent and normal to a drop at a point and many more way of derivatives. We will also use the derivative to find intervals of decreasing or increasing functions. There are 5 exercises in total where you will get a detailed insight into the Use of Derivatives. Finally, the derivative is used to determine the approximate value of certain quantities.
Chapter 7 - Integrals
Differential Calculus is based on the concept of the derivative. Derivative came into being for the difficulty of defining tangent lines to the graphs of functions and determining the slope of such lines. Integral Calculus raises the problem of determining and calculating the area of the area bounded by the graph of the functions. With a total of 11 exercises in total, you will have to read every topic and their related questions with absolute concentration.
Chapter 8: Application of Integrals
In this chapter, you will read some specific application of integrals to get the area provided under the simple curves, also, area between lines and arcs of circles, parabolas and ellipses. There are 2 exercises in this chapter in which you will also deal with getting the area bounded by the above-said curves.
Chapter 9 - Differential Equations
In this Chapter 9 Differential Equations, you will be reading some fundamental concepts related to the differential equation, formation of differential equations, general and particular solutions of a differential equation, number of ways to solve a question based on first order - first-degree differential equation and some applications of differential equations in different regions. There is a total of 6 exercises in this chapter 9 Differential Equations for the students. Differential equations are implemented in a plethora of uses in all the other subjects and fields. Hence, if you read the Differential equations chapter in a detailed way, it will help you to obtain a detailed insight into all current scientific investigations.
Chapter 10 - Vector Algebra
Did you know that quantity that involves only one value (magnitude), which is a real number is call scalars? Whereas, quantities that include magnitude and direction are called Vectors. In chapter 10 Vector Algebra, you will be studying about some basic topics of vectors, various operations on vectors, and they are algebraic as well as geometric properties.
Chapter 11 - Three Dimensional Geometry
The chapter 11 Three Dimensional Geometry will take you into the study of the place cosines and direction ratios of a line connecting two points and also about the equating of lines and planes in space under various conditions. Along with that, you will additionally get to know about the angle between two lines, a line and a plane, two planes, the shortest distance between 2 skew lines and range of a point from a plane.
Chapter 12 - Linear Programming
This chapter 12 Linear Programming has only 2 exercises in which you will study some linear programming problems and also their solutions by graphical method, though there are various other methods also available to answer such problems.
Chapter 13 - Probability
In this chapter 13 Probability will take you through the necessary concepts of the conditional probability of an event provided that another event has happened, which will, in turn, clarify the Baye theorem, multiplication rule of probability and independence of events. With a total of 5 exercises, you will also read an important concept of the random variable and its probability number and the mean and variation of a probability distribution.
Class 12 is an essential milestone in your life as you take any serious decisions about your future study on your performance. Indeed, Maths forms a vital part of Class 12 as well as every competitive exams syllabus. Whether you select to be a doctor or engineer, you will have to deal with Maths in every area. Making the concepts of class 12 concrete can immensely help you in obtaining good marks in the CBSE Class 12 board examination as well as in different competitive exams. NCERT Solution for Class 12 Maths plays an important role in your exam preparation as it has shown chapter wise solutions for all topics. First, you should imprint this in your mind that NCERT books are the most important tool that you can have to get well-versed with the basics.
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