# NCERT Solutions for Class 12 Maths

## NCERT Solutions for Class 12 Maths

Performance of students in the board exams plays an important role to determine their future so that they can take admission into a good college. Here we are providing NCERT Solutions for Class 12 Maths to help students who are appearing for board exams as well as the JEE Main and other competitive exams like BITSAT, VITEEE etc. In CBSE class 12 maths there are 13 chapters which cover important theorems and formulas. NCERT Solutions for Class 12 Maths, prepared and solved by subject experts to facilitate easy and smooth understanding of concepts. These NCERT solutions have a detailed step-by-step explanation of textbook questions.

## Here we will cover NCERT Solutions for Class 12 Maths in detail. In these mathematics, the following are the chapters:-

Chapter-1 Relations and Functions

Chapter-2 Inverse Trigonometric Functions

Chapter-3 Matrices

Chapter-4.Determinants

Chapter-5 Continuity and Differentiability

Chapter-6 Application of Derivatives

Chapter-7 Integrals

Chapter-8 Application of Integrals

Chapter-9 Differential Equations

Chapter-10 Vector Algebra

Chapter-11 Three Dimensional Geometry

Chapter-12 Linear Programming

Chapter-13 Probability

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## CBSE Class 12 Weightage Distribution Of Mathematics-

 Units Marks Relations & Functions 10 Algebra 13 Calculus 44 Vector & 3-Dimensional Geometry 17 Linear Programming 6 Probability 10 Total 100

## Now we are going to analyze every single chapter:-

Chapter-1 Relations and Functions- The first chapter of NCERT class 12 Maths deals with the concepts of relations and functions, range, domain and codomain which have already introduced in NCERT class 11 maths book. In this chapter, there are 4 exercises.

Chapter-2 Inverse Trigonometric Functions- This chapter deals inverse of trigonometric functions in restricted range and properties of inverse trigonometric functions. In class 11 we already learn that trigonometric functions are not one-one and onto in their natural ranges. We restrict domains and ranges of trigonometric functions to enable their inverse one-one and onto This chapter contains 2 exercises with 35 questions.

Chapter-3 Matrices- In this chapter, we are going to study the properties of matrices which is one of the most powerful tools of mathematics. This tool simplifies our work when we compared with other straight forward methods. In Chapter 3 Matrices there are 4 exercises with 62 questions.

Chapter-4 Determinants- In this chapter, we will learn about determinants which is an important part of matrices and also learn their properties. In this, we deal with determinants of order up to three only. In this chapter, there are 6 exercises.

Chapter-5  Continuity and Differentiability- In this chapter, NCERT introduces important concepts of continuity, differentiability and also relations between them. In this chapter, we will also learn about differentiation of inverse trigonometric functions. In this chapter, there is a total of eight exercises.

Chapter-6  Application of Derivatives- In Chapter 5, we already learnt how to find the derivative of implicit functions, composite functions, exponential functions, inverse trigonometric functions and logarithmic functions. In this chapter, we are going to study the applications of derivatives in various fields like science, social science, engineering, and many other fields. In NCERT Chapter Application of Derivatives, there are five exercises.

Chapter-7 Integrals- This is the most time-consuming chapter in class 12 mathematics. In this chapter, we will learn about the integrals of various functions and also discuss its application like calculation of areas under the graphs. There are 11 exercises in this chapter.

Chapter-8 Application of Integrals- In this chapter, we will study a specific application of integrals to find the area between the lines and arcs of circles, ellipses and parabolas and area under simple curves. The two exercises of this chapter deal with finding the area bounded by the above-mentioned curves.

Chapter-9 Differential Equations- In this chapter, we are going to learn some basic concepts related to differential equation, particular and general solutions of a differential equation, to solve a first order - first degree differential equation we learn some methods for this,  also learn formation of differential equations, and discuss some applications of differential equations in different areas.

Chapter-10 Vector Algebra- This chapter deals with the vector quantities. Quantity with both magnitude and direction is termed as a vector quantity. In this chapter, we will learn about some basic concepts of vectors, their algebraic properties like addition etc and also learn their geometric properties.

Chapter-11 Three Dimensional Geometry- In NCERT Chapter Three Dimensional Geometry we will study the direction ratio and direction cosines of a line joining two points, equations of planes and lines in space under different conditions, the angle between two planes, two lines, a plane and a line and other important concepts.

Chapter-12 Linear Programming- There are two exercises in Chapter 12 Linear programming.  In this chapter, we deal with some problems on linear programming and their solutions by the graphical method only, also there are many other methods to solve such problems.

Chapter-13 Probability- In this chapter, we will learn the important concept of the conditional probability of an event given that another event has occurred, which will be helpful in understanding multiplication rule of probability, Bayes' theorem and independence of events. In this chapter, we will also study an important concept of the random variable and its probability distribution and also the mean and variance of a probability distribution.

Here we are going to provide step-by-step NCERT Solutions for Class 12 Maths which will help students in the preparation of CBSE board exam as well as in JEE Main. The NCERT Solutions for Class 12 Maths prepared by subject experts to facilitate easy understanding and smooth of concepts.