NCERT Class 12 Maths Solutions PDF Download, Chapter-Wise Solutions

NCERT Class 12 Maths Solutions: NCERT Solutions for Class 12 Maths include all the topics from the CBSE class 12 Mathematics syllabus and it helps to build a conceptual understanding for all the topics. Students who are looking for NCERT Class 12 Maths Solutions PDFs can check this article. Students can download free Maths Solutions PDFs in the article below. NCERT Class 12 Maths Solutions include important explanations and theorems to enhance students’ understanding. Students who are willing to appear in competitive exams such as JEE, CUET, BITSAT, etc can refer to NCERT Class 12 Maths Solutions by Physics Wallah for better preparation.  

Check Out: CBSE Class 12th Books

NCERT Class 12 Maths Solutions PDF Download

Students can download class 12 Maths NCERT Solutions for each chapter in the table below

Class 12 Maths NCERT Solutions

NCERT Class 12 Maths Solutions helps the students to prepare well for the board exam as well as for the entrance examinations. Students can check the chapter-wise solutions below

Chapter 1 Relations and Functions

NCERT Class 12 Maths Solutions for Chapter 1 Relations and Functions deals with the types of relations, types of functions, the composition of functions and invertible functions, binary operations, etc. This topic covers Types of relations: Reflexive, symmetric, transitive and equivalence relations. One-to-one and onto functions, composite functions, the inverse of a function. Binary operations. Candidates can check the exercise in the table below

Check out: Class 12th Question Banks

Chapter 2 Inverse Trigonometric Functions

Inverse Trigonometric Functions are explained very well through the examples given in the PDF. This topic deals with the basic concepts of inverse trigonometric functions, properties of inverse trigonometric functions, and miscellaneous examples. Inverse Trigonometric Functions cover topics such as Definition, range, domain, principal value branches, Graphs of inverse trigonometric functions, and Elementary properties of inverse trigonometric functions.

Chapter 3 Matrices

NCERT Class 12 Maths Chapter 3 Matrices deals with the definition of matrices, equality of matrices, types of matrices, addition and multiplication of matrices, properties of matrices, etc. This topic is very important and easy to understand for the students. The chapter matrices cover topics such as Concept, notation, order, equality, types of matrices, zero matrices, transpose of a matrix, symmetric and skew-symmetric matrices. Addition, multiplication, and scalar multiplication of matrices, simple properties of addition, multiplication, and scalar multiplication. Candidates can check the exercise in the table below.

Chapter 4 Determinants 

Chapter 4 of class 12 Maths NCERT solution includes the topic Determinants. In this chapter, students learn about the meaning and definition of determinants, properties of determinants, Order of determinants, remarks, finding the area of a triangle using determinants, determinants of a square matrix, minors and cofactors of determinants, adjoint of a matrix, inverse of a matrix, applications of determinants and matrices, and miscellaneous examples. Candidates can check the NCERT Class 12 Maths Solutions for determinants in the table below

Chapter 5 Continuity and Differentiability

NCERT Chapter 5 Continuity and Differentiability is one of the most important topics in class 12 maths. This chapter deals with the definition of Continuity, algebra of continuous function, definition and meaning of differentiability, derivative of implicit functions, derivatives of composite functions, derivative of inverse trigonometric functions, logarithmic differentiation, Concept of exponential and logarithmic functions, derivatives of functions in parametric forms, exponential and logarithmic functions, second order derivatives, mean value theorem, etc. Candidates can check the exercises for Continuity and Differentiability below

Check out: Class 12th Sample Papers

Chapter 6 Applications of Derivatives

NCERT Class 12 Maths Solution for Applications of Derivatives covers the definition of derivatives, rate of change of quantities, tangents and normal, increasing and decreasing functions, derivative of composite functions, derivatives of inverse trigonometric functions, a derivative of an implicit function, etc. Candidates need to practice a lot to have a complete understanding of the Applications of Derivatives. Candidates can check the NCERT solutions class 12 Maths in the table below.

Chapter 7 Integrals

NCERT Class 12 Maths Chapter 7 Integral is the process of finding the integral of any function. Integrals help to calculate volumes, areas, and other quantities. According to the fundamental theorem of calculus, integration and differentiation are inverse operations which means the original function is equal to the integral of the derivative of a function. This chapter includes integration by substitution, integration using partial fractions, integration by parts, integration using trigonometric identities, integration of some integral functions, definition and meaning of definite integrals, definite integral as the limit of a sum, fundamental theorem of calculus, etc. Candidates can check the NCERT Class 12 Maths Solutions Chapter 7 below

Chapter 8 Applications of Integrals

Candidates may refer to the NCERT Class 12 Maths Solution PDF for Applications of Integral for the questions and solutions. This topic covers the definition of Integrals, circles/ parabolas/ellipses, especially lines, area between two curves, area under simple curves, etc. 

Check out: Class 12 Mathematics Question & Concept Bank

Chapter 9 Differential Equations

Students will be able to understand the definition and the application of Differential Equations from NCERT Class 12 Maths Solution PDF for Differential Equations. This chapter covers topics such as the degree of a differential equation, order of a differential equation, general and particular solutions of a differential equation, homogeneous differential equations, linear differential equations, etc. Check the type of linear differential equations below

dy/dx + Py = Q, where P and Q are functions of x

Chapter 10 Vector Algebra

NCERT Class 12 Maths Solution PDF for Vector Algebra helps students understand the introduction of Vector Algebra, some basic concepts related to vector algebra, and position vectors. This chapter covers topics such as direction cosines, types of vectors such as zero vector, unit vector, collinear vector, equal vector, negative of a vector, addition of vectors, properties of vector addition, multiplication of a vector by a scalar, components of a vector, vector joining two points, section formula, product of two vectors, scalar or dot product of two vectors, properties of scalar product, projection of a vector on a line, etc. Candidates can refer to the PDF above for NCERT Class 12 Solutions for Maths for Vector Algebra.

Chapter 11 Three-Dimensional Geometry

Candidates need to understand the basic concepts of Three-Dimensional Geometry to solve the problems related to this chapter. In this chapter, candidates will be able to learn the properties of a line, the equation of a line through a given point and parallel direction cosines of a line passing through two points, the relation between the direction cosines of a line, equation of a line in space, a plane passing through the intersection of two given planes, the angle between two planes, co-planarity of two lines, etc. Candidates can download NCERT Class 12 Maths Solution PDF for Three-Dimensional Geometry here. 

Chapter 12 Linear Programming

In this chapter, students will learn about the mathematical formulation of the problem, different types of linear programming problems graphical feasible and infeasible method solutions. This chapter includes topics such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, etc. Candidates can download NCERT Class 12 Maths Solution PDF for Linear Programming here.

Chapter 13 Probability

Students will learn about the concept of random variables and their probability in this chapter. More and more practice can make this chapter look easy. This chapter includes Conditional probability, independent events, total probability, Baye’s theorem. Random variable and its probability distribution, mean and variance of haphazard variable, etc. Candidates can download NCERT Class 12 Maths Solution PDF for Probability here.

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NCERT Solutions Class 12 Maths: Unit-wise Weightage

Students who are studying in class 12 can check the unit-wise weightage of CBSE class 12 Mathematics topics. Students must prepare according to the weightage.

NCERT Solutions for Class 12 Maths: Key Features

Students can check the key features of NCERT Solutions for Class 12 Maths in below

• These solutions help the students to practice and revise the concepts.

• These solutions include all the necessary concepts and formulae in proper sequence which saves time.

• NCERT Class 12 Maths Solutions helps the students to follow a logical approach. 

• These solutions are very helpful in quick revision during the exam. 

Class 12 Maths NCERT Solutions FAQs

Q1. How many chapters are there in NCERT Solutions for Class 12 Maths?

Ans. There are a total of 13 chapters in CBSE class 12 Maths syllabus - Matrices, Inverse Trigonometric Functions, Relations and Functions, Determinants, Applications of Derivatives, Continuity and Differentiability, Applications of Integrals, Vector Algebra, Differential Equations, Three Dimensional Geometry, Probability and Linear Programming.

Q2. What is the resource for NCERT Class 12 Maths Solutions?

Ans. Physics Wallah provides NCERT Class 12 Maths Solutions PDF for each subject. 

Q3. What are the features of NCERT Class 12 Maths Solutions?

Ans. The features of NCERT Class 12 Maths Solutions are These solutions help the students to practice and revise the concepts, These solutions include all the necessary concepts and formulae in proper sequence which saves time, Class 12 Maths Solutions helps the students to follow a logical approach, These solutions are very helpful in quick revision during the exam. 

Q4. Which chapter has the highest weightage in CBSE Class 12 Maths?

Ans. Linear Programming has the highest weightage in CBSE Class 12 Maths.