# Class 12 Maths NCERT PDF

## RELATIONS AND FUNCTIONS

Recall that the notion of relations and functions, domains, co-domains, and categories is introduced in Class XI with various real-valued functions and their graphs. The concept of the word ‘relation’ in mathematics is derived from the meaning of relations in the English language, according to which two objects or quantities are related when there is a recognizable relationship or link between two objects or quantities.

## INVERSE TRIGONOMETRIC FUNCTIONS

In Chapter 1 we have studied that the inverse of the function f represented by f – 1 exists if f is unicellular and overlapping. There are many functions that are not one-to-one, secret, or both and hence we cannot talk about their inverse.

In eleventh grade, we read that trigonometric functions are not homogeneous and occur on their natural domains and complexes and hence their inversions are not present.

In this chapter, we will study the restrictions on the domains and categories of trigonometric functions that ensure the existence of their inversions and observe their behavior through graphical representation. And In addition, some primary properties will also be discussed.

## MATRICES

Knowledge of Matrix is required for various branches of Mathematics. The matrix is one of the most powerful tools of mathematics. This mathematical tool simplifies our task to a great extent compared to other simpler methods. class 12 maths ncert pdf.

The development of the concept of the matrix is the result of an attempt to derive compact and simple methods to solve a system of linear equations.

In this chapter, we will find it interesting to be familiar with the Basics of Matrix and Matrix Algebra.

## DETERMINANTS

In the previous chapter, we have studied the algebra of matrices and matrices. We have also learned that bodies of algebraic equations can be expressed as matrices.

## CONTINUITY AND DIFFERENTIABILITY

This chapter is essentially a continuation of our study of the differentiation of functions in the eleventh grade. We learned to distinguish some functions such as polynomial functions and trigonometric functions. In this chapter, we introduce the very important concepts of continuity, differentiation, and the relationship between them.

We will also learn about inverse trigonometric functions. In addition, we introduce a new class of functions called exponential and logarithmic functions. These tasks lead to powerful techniques of differentiation. NCERT Class 12 maths book pdf. We describe some geometrically explicit positions through differential calculus. In this process, we learn about some fundamental theorems in this area.

## APPLICATION OF DERIVATIVES

In Chapter 5, we learned how the derivative of mixed functions, inverse trigonometric functions, implicit functions, exponential functions, and logarithmic functions are determined.

In this chapter, we will study derivative applications in various disciplines such as engineering, science, social science, and many other fields.

For example, we will learn how a derivative can be used (i) to determine the rate of change of quantities, (ii) to find tangents and general equations of a curve at a point, (iii) a Finding the graph bend of the function will help us find the points at which the function has the largest or smallest value (locally).

We will also use the derivative to find the intervals at which a function is increasing or decreasing. Finally, we use derivatives to find the approximate value of some quantities.

## INTEGRALS

Differential calculus focuses on the concept of derivatives. the basic motivation for the derivative was the problem of defining tangent lines to the graphs of the functions and calculating the slope of such lines.

## APPLICATION OF INTEGRALS

In geometry, we have learned formulas for calculating the areas of various geometric figures, including triangles, rectangles, trapezes, and circles. Such formulas are fundamental in applications of mathematics to many real-life problems.

Formulas for elementary geometry allow us to calculate the areas of many simple shapes. However, they are inadequate for calculating areas bounded by curves. For that, we will need some concepts of integral calculus.

## DIFFERENTIAL EQUATIONS

NCERT Class 12 Maths pdf In Class XI and Chapter 5 of the present book, we discussed how to separate a given function f with respect to an independent variable, that is, f (x) for a given function f for each x in its domain.

## VECTOR ALGEBRA

We face many questions in our daily life such as – What is your height? How should a football player hit the ball to pass it to another player on their team? Note that the possible answer to the first query may be 1.6 m, a quantity that has only one value (magnitude) that is a real number. Such zodiac signs are called scalar zodiacs. NCERT Class 12 Maths pdf.

However, the answer to the second question is a quantity (called force) that includes the strength (magnitude) and direction of the muscle (in which the second player is located). Such quantities are called vectors.

## THREE DIMENSIONAL GEOMETRY

In the eleventh grade, studying analytic geometry in two dimensions, and introducing three-dimensional geometry, we limited it to Cartesian methods only. In the last chapter of this book, we have studied some basic concepts of vectors. Now we will use vector algebra for three-dimensional geometry. The purpose of this approach to 3-dimensional geometry is that it makes the study simple and elegant *.

In this chapter, we will study the square-cosine and squares of a line joining two points and the equations of lines and planes in space under different conditions at an angle between two lines, two planes, one line, and one plane. . Will also discuss. The minimum distance between two oblique lines and the distance of a point from a plane.

## LINEAR PROGRAMMING

class 12 maths ncert pdf. In previous classes, we have discussed systems of linear equations and their applications in day-to-day problems. In class XI, we have studied systems of linear inequalities and linear inequalities in two variables and their solutions by the graphical method.

### PROBABILITY

In previous classes, we have studied probability in a randomized experiment as a measure of the uncertainty of events. We have found the Russian mathematician A.N. Discussed the axiomatic approach formulated by Kolmogorov (1903–1987) and treated probability as a function of the results of the experiment.

We have also established an analogy between axiomatic theory and classical theory of probability in terms of equally likely outcomes. Based on this relationship, we derived the probabilities of events associated with discrete sample spaces. We have also studied the sum law of probability.

In this chapter, we will discuss the important concept of the conditional probability of an event that occurred in another event, which will be helpful in understanding the Bayes theorem, the multiplication law of probability, and the independence of events.

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