Chapter-wise Class 12 maths NCERT solutions for students

To provide you with a sound understanding of the concepts we are bringing you the Class 12 maths NCERT solutions. A good understanding of the solutions is important both for the boards and for the JEE Mains and Advanced as it will equip you with the information related to class 12 Maths. The class 12th Maths includes 13 important chapters that you must be well-versed with. So, to make your board exams easy we have provided solutions that are not just concise but also provide alternative ways to solve some questions. In this article, we will reflect on some of the ways to get solutions to your problems of class 12th boards and JEE exam. 

The CBSE schools follow the curriculum provided by the NCERTs and hence to aid you with the class 12 maths NCERT solutions this is the best place to be. 

Why is familiarizing with the Class 12 maths NCERT solutions crucial? 

Your score on the boards or in the JEE exam is a deciding factor in the college you get admission to. Be it the 12th board or the JEE exam, clearing both of these is not an easy task. Thus, you have to bend over backward to get a good percentage in both. And Math being one of the most hard going subjects requires a little extra effort.

Therefore, familiarizing yourself with the Class 12 maths NCERT solutions will help you beat the exam. 

Chapter-wise Class 12 maths NCERT solutions

Relations and functions

This chapter deals with concepts of relations, functions, domains, and codomains introduced in Class 11. Students are taught about several real-valued functions and their graphs. This chapter includes 4 exercises that focus on strengthening the concepts explained in the chapter. 

Inverse Trigonometric Functions

This chapter involves a constricted array of trigonometric functions that empowers them to be one on one and thus makes the inverse of the functions clear. This chapter digs into inverse trigonometry through its two exercises that acknowledge the students about the behavior of the functions, their graphical representations, and the elementary properties. This later provides great help in integers later.

Matrix

This chapter fills you in on the most important aspect of mathematics, i.e, Matrices. It gives an insight into matrices and Matrix algebra. 

Determinants

After a good intro with the matrixes in chapter 3, chapter 4 proceeds with another important Class 12 maths NCERT solutions which are Determinants. This chapter digs into the determinants of orders up to 3, and their cofactors and inverses. It further involves the applications of determinants, like calculation of the area of triangles, adjoint of matrices, and consistency of a set of linear equations.

Continuity and Differentiability

This chapter proceeds after the  Differentiation of Functions taught in Class 11. This chapter carries on with the important concepts of  Continuity, and Differentiability and puts in place the relation between them. 

Along with this, the chapter involves the continuity and differentiability of Inverse Trigonometric Functions. Students are also introduced to exponential and logarithmic functions through this chapter. 

Application of Derivatives

Continuity and Differentiability give way to the beginning of calculus. This chapter approaches the differentiability of functions and introduction to derivatives. This chapter dwells into the derivatives of specific functions, and their applications, namely the tangents and normal to curves, and the rate of change in some quantities. It also focuses on the increasing and decreasing of the function. 

Integrals

This is one of the pivotal chapters of class 12th Mathematics and questions related to it require more time to be solved. This chapter covers the integration of functions, and their applications in terms of the calculation of areas and introduces integral calculus. This chapter provides a total of 11 exercises making it part of the chapter that requires ample practice. 

Application of Integrals

This chapter deals with the applications of integrals in calculating areas under simple curves, lines, parabolas, and ellipses. This chapter provides 2 exercises that are enough for the practice of the area of calculus. 

Differential Equations

This chapter instigates the concept of Differential equations, the general and particular solutions, and the order and degree of an equation. It will also provide sound knowledge to the students about the applications of differential equations in the six exercises. 

Vector Equations

Concepts like vector quantities, that is, the quantities with both magnitude and direction are covered in this chapter. It focuses on vector algebra that encapsulates rules of addition of vector quantities and other important properties. Vector Algebra plays a crucial role in Physics. 

Three-Dimensional Geometry

This chapter emphasizes the utilization of vectors to calculate the distance between lines, a point, and a line, and a line and a plane, along with the angles between them. It also familiarizes with the concepts of direction cosines.

Linear Programming

This chapter deals with the concepts of linear programming problems, and their solutions with the help of graphical methods only.

Probability

This chapter explores the concept of Conditional Probability and its use in our daily lives. It covers the multiplication rule and the independence of events.

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