Class 12th mathematics has a total of 13 chapters and each chapter has various exercises. For a student like you are required to solve each exercise in order to gain a good understanding in this subject. However, sometimes a few questions look very difficult to answer and that is why our math experts have prepared chapter wise mathematics solutions for class 12th.
These solutions are in the downloadable format that facilitate you to start your practice anytime you want. While practising the maths questions, you may need formulas and short notes. The solutions are quite enough to give you access to them as well and that is why you should download the PDF of NCERT Solutions to give a boost in your preparation and learnings together.
Class 12th mathematics contains a total of 13 chapters and each chapter comprises various exercises. In order to score good marks in mathematics you will need to comprehend all the topics and subtopics of maths chapters. Therefore, here we have given the chapter wise solutions to all the chapters and its exercises.
Chapter 1 Relations & Functions which is given in the term 1 syllabus of class 12th contains a total of 4 exercises. All those 4 exercises are based on the various topics that have been discussed in this chapter. Topics such as relations and functions, domain, co-domain, symmetric, transitive have been explained and the questions are asked to assess student’s understanding.
There are miscellaneous exercises in this chapter too that contain a mix of questions of all the topics and exercises. Given Class 12 Maths NCERT Solutions chapter 1 will help you to tackle the questions very easily.
There are two exercises and a Miscellaneous exercise in this chapter that deals with various topics such as properties of inverse trigonometric functions. Chapter 2nd of 12th mathematics assists students to learn about inverse trigonometric functions in detail. You can refer to the solutions book to comprehend this chapter more precisely and easily.
This chapter deals with types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices, etc. Chapter 3 matrices is considered as one of the best methods in mathematics that simplifies our work of calculations such as addition, multiplications and more. It contains a total of 62 questions that are given in the 4 exercises.
Students should definitely refer to this in order to learn fundamentals of matrix & matrix algebra.
6 Exercises of Chapter 4 Determinants are fully focused on informing students about properties of determinants, applications of determinants, adjoint of a matrix, inverse of matrix, and more. The six exercises are distributed in a way that helps students to cover each topic in a systematic manner. There is one miscellaneous exercise too that facilitates students with a variety of questions to practice and learn the methodology to tackle questions of Determinants.
Here 12th standard students can access the solutions of 8 exercises and one miscellaneous exercise of Chapter 5 Continuity and Differentiability. Topics such as derivatives of composite functions, derivatives of implicit functions, derivatives of inverse trigonometric functions, Concept of exponential and logarithmic functions, and more are explained explicitly. To gain deeper knowledge in these given topics you will need to solve all the given 8 exercises.
Taking help of the solutions book will aid you in knowing the many essential processes to answer them in your board exams.
Class 12 maths chapter 6 Applications of Derivatives contains 5 exercises and one miscellaneous exercise that precisely explains this topic in detail. Our solutions helps students to learn about Finding Rate of Change of a Quantity, Approximation Value, Finding the equation of a Tangent and Normal To a Curve, Maxima and Minima, and Point of Inflection, and more.
Integrals are a part of calculus and the process of finding the integrals is known as integration. The topics that have been discussed in this chapter are Definite Integral, Fundamental Theorem of Calculus, properties of integrals, and more. There are 11 exercises and a miscellaneous exercise that is focused on helping students to learn about the integrals in a bit of detail.
Chapter 8 Application of Integrals mostly deals with the shape such as finding the area of a bounded region by a curve or line, simple curves, area between curves and more. The implementation of Integrals allow us to easily find the area of a shape enclosed by curves. The concepts explained in this chapter ease the students to find out the areas of such objects or shapes that are enclosed by a curve. There are 2 exercises that assist students to practice the questions based on the application of integrals.
Chapter 9 has six exercises that comprise the questions based on the basic concepts related to differential equations, degree of a differential equation, order of a differential equation, and more. The application of differential equations can be used in Physics, Chemistry, Biology, Anthropology, Geology, Economics etc. So, in-depth understanding in this chapter is important for students.
In chapter 10 Vector Algebra there are two topics which have been discussed; Scalar and Vector. A magnitude without direction is known as scalar while magnitude with direction is known as vector. Vector is a very interesting topic in mathematics and it has a very good implementation in physics as well. Scalar quantity can be recognised when we see only one value such as mass, time, distance, speed, area, volume. However, vectors can be recognised when we see force, weight, momentum, it has magnitude and direction as well.
Three dimensional geometry is a chapter that helps you to use the vectors. In this chapter you will study about the direction cosines and direction ratios of a line joining two points. It also discussed the equation of lines and planes. There are 3 exercises in this chapter that deal with the whole topics and allow students to examine their understanding in the given topics.
There are various methods to solve the problems based on Linear Programming. However, in this class the chapter 12 is fully focused on graphical methods to solve linear programming. There are various applications of linear programming in day to day life and that is why it is very important for students to focus on this chapter and practice the questions as much as possible. However, 2 exercises that are given in this chapter are good enough to understand the fundamental use of graphical methods to solve linear programming.
This chapter will allow you to learn about the conditional probability of an event that will help in understanding the Bayes' theorem, multiplication rule of probability and independence of events. Binomial distribution has been also explained in this lesson. It comprises a total of 5 exercises and one miscellaneous exercise to enable students to learn core and advanced level of probability questions. Probability is an extremely important topic and vast too that is very helpful in determining the various events along with that it is quite useful in making Advanced intelligence programs.