Categories: NCERT Solutions

### Chapter 13 Probability

NCERT Solutions for Class 12 Maths has been written to help 12th Class students like you who are appearing for different board exams as well as the JEE. It provides sound knowledge and understanding of all important concepts covered in each chapter in the NCERT plus Two Maths Textbook. There are 13 Important Chapters from the NCERT Inter Maths textbook. Both problems and their detailed solutions are provided. The solutions have been devised by India’s best teachers to help students grasp basic concepts better and faster. It is the perfect guide to help you prepare for CBSE 12 Maths exams as well as engineering entrances like the JEE.

#### Class 12 Maths Chapter 1 Relations and Functions

The first chapter in CBSE Class 12 deals with the notions related to functions and relations. Some of the topics like range, domain, and co-domain are already discussed in class 11 Solution of Maths. It was introduced along with real-valued functions and their respective graphs. There are a total of 4 exercises that you will be solved in this Mathematics Chapters.

#### Class 12 Maths Chapter 2 Inverse Trigonometric Functions

Many functions are not onto, one-one or even both. Thus, we cannot talk about the inverses of these types of functions. This is possible and you will study it in inverse trigonometry. There are two exercises in this Maths Class 12 chapter where you will study about the restrictions on ranges and domain of trigonometric functions. This helps in enabling the visibility of inverses and thus their behavior can be observed using graphical representation. Along with there are some elementary properties also which will be discussed in Maths Class 12.

#### Class 12 Maths Chapter 3 Matrix

Matrices are one of the fundamentals in the branch of Mathematics Class 12. That is why they are considered as one of the powerful tools in maths Soln. When you compare with other methods, using matrices simplifies our work. There are a total of 4 exercises and in that 62 questions in this NCERT 12th Maths chapter. You will be delving into the fundamentals of the matrix in this chapter.

#### Class 12 Maths Chapter 4 Determinants

In this NCERT 12 Maths chapter, you will be studying determinants up to three real entries. Furthermore, there are six exercises in this chapter that can provide you enough opportunities for practice. You will study various properties of cofactors, determinants and their applications in this Class 12 Math chapter. You will use these properties to find the are of minors, adjoint, triangle, and the inverse of a square matrix. There are also topics related to consistency and inconsistency of the system.

#### Class 12 Maths Chapter 5 Continuity and Differentiability

In class 11 Mathematics Chapters, you must have studied the differentiation of functions and this chapter is an extension to it. In that chapter, you must have learned about differentiating different types of functions like trigonometric functions and polynomial functions. Also, this Class 12 Maths chapter helps you understand important concepts related to differentiability, continuity, and relations between both. Furthermore, you will also learn about differentiation of inverse trigonometric functions in 12 Class Maths. There are a total of 8 practice exercises which you can solve to understand the concepts better.

#### Class 12 Chapter 6 Application of Derivatives

In 12 Mathematics chapter 5, you got to learn how to find out derivatives of implicit functions, composite functions, exponential functions, logarithmic functions, and inverse trigonometric functions. While in this 12th Maths chapter, you will get to learn about the applications of derivatives in various fields like science, engineering, and other fields. For example, you will get to learn how derivatives are used to find the equations of tangent and rate of change of quantities. Furthermore, you will also learn about finding the intervals of various increasing and decreasing functions. There are a total of 5 exercises for 12th Standard Maths students to practice in this chapter.

#### Class 12 Maths Chapter 7 Integrals

The idea of the derivative is behind differential calculus. Thus, derivative came into the picture for typical problems of defining the tangent lines. This is also used to calculate the slope lines. Integral calculus helps in calculating the area and define the problem of the region beyond the graph. There are a total of 11 exercises in this Class 12 Maths NCERT chapter. In these exercises, you will learn each and every topic and the questions related to the Plus Two Maths chapter with the utmost attention.

#### Class 12 Maths Chapter 8 Application of Integrals

Under this NCERT 12 Maths chapter, you will be able to learn some specific applications for integers. You will also learn to find the area given under curves. Along with this, you will learn to find the areas of lines and arcs of parabolas, circles, and ellipses. There are 2 exercises in this mathematics chapter and you will be required to find the area bounded by the curves mentioned above.

#### Class 12 Maths Chapter 9 Differential Equations

In this NCERT Solutions for Class 12 Maths chapter, you will study some basic concepts related to differential equations. Furthermore, you will be required to find the particular and general solutions of differential equations. You will also have to find the formation of differential equations different methods to solve a question that is based on first order. There are a total of 6 exercises for this Maths Class 12 NCERT chapter for your practice.

#### Class 12 Maths Chapter 10 Vector Algebra

When the quantities include only one value or magnitude than they are called scalars. Whereas if the quantity has multiple directions and magnitude than they are called vectors. So, in vector algebra, ou will get to know basic concepts of vectors, different operations in vectors along with the algebraic and geometric properties.

#### Class 12 Maths Chapter 11 Three-dimensional Geometry

This NCERT Solutions Maths chapter will go through the study of different directions of ratios and cosines. There are also different ratios of a line joining two points and about the equations of planes and lines in ice but in different conditions. Furthermore, you will have an opportunity to get to know the angles between two different lines, two planes, a line and a plane, distance from a point to a plane, and shortest distance between 2 skew lines.

#### Class 12 Maths Chapter 12 Linear Programming

There are only two exercises in the entire NCERT Solutions for Class 12 Maths chapter. You will get to know more about problems in linear programming and their solutions. This solution will be possible through the graphical method only. Although there are many various methods to solve these types of problems.

#### Class 12 Maths Chapter 13 Probability

This Mathematics Class 12 chapter will take you through fundamental concepts of conditional probability for an event where another event has already occurred. This in will be clarified by Bayes’ theorem, independence of events, and multiplication rule of probability. There are a total of 5 exercises in this NCERT Math chapter and you will get to learn important concepts for random variables and it’s a probability distribution.

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