Class 12 Math NCERT Solutions: The topics covered in the CBSE Class 12 Maths Syllabus are discussed in depth by NCERT Class 12 Maths Solutions. To help students obtain a deeper conceptual understanding, it contains thorough explanations of all significant theorems and equations. With NCERT Solutions for Class 12 Maths, students will be able to prepare for undergraduate engineering admission examinations in 2022-2023, such as JEE Mains, BITSAT, VITEEE, etc.
Subject experts have produced NCERT Solutions for Class 12 Maths to assist students in understanding concepts more clearly. NCERT Solutions for Class 12 provide in-depth, step-by-step explanations of topics covered in the textbooks. Infinity Learn offers Class 12 Maths notes, solved sample problems, previous year question papers, worksheets as study aids for students preparing for their board examinations, and solutions for each Chapter of CBSE Class 12 Maths.
Chapters list for NCERT Class 12 Maths:
- Chapter 1 Relations and Functions
- Chapter 2 Inverse Trigonometric Functions
- Chapter 3 Matrices
- Chapter 4 Determinants
- Chapter 5 Continuity and Differentiability
- Chapter 6 Applications of Derivatives
- Chapter 7 Integrals
- Chapter 8 Applications of Integrals
- Chapter 9 Differential Equations
- Chapter 10 Vector Algebra
- Chapter 11 Three-dimensional Geometry
- Chapter 12 Linear Programming
- Chapter 13 Probability
It may be difficult for pupils to understand what is taught in class. Students should look up information online to clear their doubts about dealing with this issue. Regular practice of concepts in which they are weak will enhance their confidence in terms of the exam. Students should study the Chapter from the NCERT textbook and answer the exercise problems to gain a sound conceptual understanding. Students’ problem-solving and analytical thinking skills will be improved if they use the NCERT Solutions available at Infinity Learn to react to the challenges.
Go for Infinity Learn NCERT Solutions for Class 12 Maths to begin your board exam preparations.
NCERT Solutions Class 12 Maths
It is important to study NCERT Solutions Class 12 Maths for board exams and competitive examinations. According to the CBSE syllabus and test structure, the solutions are presented in simple language to aid students. Every Chapter in the most recent NCERT textbook is covered in the solutions. The solutions explain various fundamental concepts to provide accurate information to the students.
NCERT Solutions Class 12 Mathematics Chapter Details and Exercises
Chapter 1 of the NCERT textbook covers relations and functions, kinds of relations, types of functions, the composition of functions and invertible functions, binary operations, and miscellaneous examples. The links to the exercise solutions for the topics covered in this Chapter may be found here.
Reflexive, symmetric, transitive, and equivalence relations are examples of relations. One-to-one and onto functions, composite functions, and the inverse of a function are all examples of functions.
|Maths Class 12 NCERT Solutions Chapter 1 Exercise|
|Exercise 1.1 Class 12 Maths|
|Exercise 1.2 Class 12 Maths|
|Exercise 1.3 Class 12 Maths|
|Exercise 1.4 Class 12 Maths|
|Miscellaneous Exercise on Chapter 1 Class 12|
The NCERT Class 12 Maths Chapter 2, Inverse Trigonometric Functions, covers many topics, including notes on basic inverse trigonometric function concepts, inverse trigonometric function features, and various examples. These concepts are well-explained and supported by examples. This is where you’ll find the answers to this Chapter’s activities.
Definition, range, domain, and major value branch are all terms that can describe anything. Inverse trigonometric function graphs Inverse trigonometric functions have several basic features.
|Maths Class 12 NCERT Solutions Chapter 2 Exercises|
|Exercise 2.1 Class 12 Maths Solutions|
|Exercise 2.2 Class 12 Maths|
|Miscellaneous Exercise on Chapter 2 Class 12|
Concept, notation, order, equality, types of matrices, zero and identity matrices, transpose of a matrix, symmetric and skew-symmetric matrices, and symmetric and skew-symmetric matrices are all covered. Matrix manipulation: Multiplication with a scalar and addition and multiplication. The presence of non-zero matrices whose product equals the zero matrices and on commutativity of matrices multiplication (restrict to square matrices of order 2). Row and column operations in their most basic form. Invertible matrices and confirmation of the inverse’s uniqueness, if one exists; (Here, all matrices will have real entries).
|Maths Class 12 NCERT Solutions Chapter 3 Exercises|
|Exercise 3.1 Class 12 Maths|
|Exercise 3.2 Class 12 Maths|
|Exercise 3.3 Class 12 Maths|
|Exercise 3.4 Class 12 Maths|
|Miscellaneous Exercise on Chapter 3 Class 12|
Determinants are discussed in Chapter 4 of the NCERT Maths Solution for Class 12. The definition and meaning of determinants, remarks based on determinant order, properties of determinants, finding the Area of a triangle using determinants, minors and cofactors of determinants, adjoint of a matrix, the inverse of a matrix, applications of determinants, and matrices, and miscellaneous examples will be covered. In this Chapter, we’ve included links to each exercise solution.
Determinant of a square matrix (up to 3 x 3 matrices), determinant properties, minors, cofactors, and determinant applications in calculating the Area of a triangle. A square matrix’s adjoint and inverse. Using examples, students will learn about consistency, inconsistency, the number of solutions to a system of linear equations, and how to solve a system of linear equations in two or three variables (with a unique solution) using the inverse of a matrix.
The fifth Chapter of the NCERT textbook is dedicated to the definition of continuity. The concepts include continuity and differentiability, composite function derivatives, chain rule, inverse trigonometric function derivatives, implicit function derivatives, and Exponential and logarithmic functions.
Logarithmic and exponential functions have derivatives. The derivative of functions expressed in parametric forms is called logarithmic differentiation. Second-order derivatives are a type of derivative—the geometric interpretation of Rolle’s and Lagrange’s Mean Value Theorems (without proof).
In Chapter 6 of the NCERT textbook, students learn about derivatives, rate of change of quantities, rising and decreasing functions, tangents and normals, approximations, maxima and minima, first derivative test, maximum and minimum values of a part in a closed interval, and other topics. Students can find exercises here that clearly illustrate these concepts.
Rate of change of bodies, increasing/decreasing functions, tangents, normals, and derivatives usage in approximation, maxima, and minima are all examples of derivative applications (the first derivative test is motivated geometrically and the second derivative test given given given given as a provable tool). Simple issues (that illustrate basic principles and understanding of the subject and real-life situations).
|Maths Class 12 NCERT Solutions Chapter 6 Exercises|
|Exercise 6.1 Class 12 Maths|
|Exercise 6.2 Class 12 Maths|
|Exercise 6.3 Class 12 Maths|
|Exercise 6.4 Class 12 Maths|
|Exercise 6.5 Class 12 Maths|
|Miscellaneous Exercise on Chapter 6 Class 12|
Integration as an inverse process of differentiation, geometrical interpretation of indefinite integral, properties of indefinite integral, differentiation vs integration, integration by substitution, integration using partial fractions, integration by parts, integration using trigonometric identities, integration of some integral functions, the definition of indefinite integral We’ve given exercises with solutions based on the topics covered in the Chapter.
Integration can be thought of as the inverse of differentiation. Substitution, partial fractions, and parts are used to integrate a number of functions. Simple integrals of the rational functions and problems dependent on them are evaluated.
Fundamental Theorem of Calculus, Definite Integrals as a Limit of a Sum (without proof). Evaluation of definite integrals and basic properties of definite integrals.
In Chapter 8 of the NCERT textbook, we continue our treatment of integrals with definitions, the Area under simple curves, the Area of the region encompassed by a curve and a line, the Area between two curves, and other examples. By clicking on the links below, students can obtain activities with solutions that explain the concepts from this Chapter.
|Maths Class 12 NCERT Solutions Chapter 8 Exercises|
|Exercise 8.1 Class 12 Maths|
|Exercise 8.2 Class 12 Maths|
|Miscellaneous Exercise on Chapter 8 Class 12|
The definition of differential equations, basic concepts related to differential equations, degree of a differential equation, order of a differential equation, general and particular solutions of a differential equation, formation of a differential equation whose general solution is known, and procedure to form a differential equation that will represent a given family of curves, methods of solving first order, first-degree differentiable equations, and mechanistic ways of solving first order, first-degree differentiable equations are all covered. This is where you’ll find the answers to this Chapter’s activities.
A differential equation’s definition, order, and degree are general and special solutions. The formation of a differential equation with a given general solution. Solutions of homogeneous differential equations of the first order and first degree and solutions of differential equations using the separation of variables approach. Linear differential equation solutions of the type:
This Chapter introduces students to vector algebra. The magnitude and direction of a vector and vectors and scalars. A vector’s direction cosines and direction ratios. The position vector of a point, the negative of a vector, the components of a vector, the addition of vectors, the multiplication of a vector by a scalar, and the position vector of a point splitting a line segment in a specific ratio are all examples of vectors. Scalar (dot) product of vectors, vector (cross) product of vectors, and scalar triple product of vectors: definition, geometrical interpretation, properties, and applications.
|Maths Class 12 NCERT Solutions Chapter 10 Exercises|
|Exercise 10.1 Class 12 Maths|
|Exercise 10.2 Class 12 Maths|
|Exercise 10.3 Class 12 Maths|
|Exercise 10.4 Class 12 Maths|
|Miscellaneous Exercise on Chapter 10 Class 12|
Three-dimensional geometry, line direction cosines and ratios, the relation between line direction cosines, direction cosines of a line passing through two points, equation of a line in space, equation of a line through a given point, and parallel to a given vector are all topics covered in NCERT Chapter 11 and Class 12 Maths.
Derivation of cartesian form from vector form, the angle between two lines, the shortest distance between two lines, the distance between two skew lines, the distance between two parallel lines, the plane in cartesian form, equation of a plane in a normal form, equation of a plane perpendicular to a given vector and passing through a given point, equation of a plane passing through three non-collinear points, intercede In this section, we’ve added links to the solutions to the exercises given in the Chapter.
A line connecting two places has direction cosines and direction ratios. Coplanar and skew lines, the shortest distance between two lines, Cartesian equation and vector equation of a line A plane’s Cartesian and vector equations. The angle is formed by two lines, two planes, or a line and a plane. A point’s distance from a plane.
|Maths Class 12 NCERT Solutions Chapter 11 Exercises|
|Exercise 11.1 Class 12 Maths|
|Exercise 11.2 Class 12 Maths|
|Exercise 11.3 Class 12 Maths|
|Miscellaneous Exercise on Chapter 11 Class 12|
This Chapter introduces students to linear programming. Linear programming problems and their mathematical formulations, mathematical formulations of problems, graphical techniques of addressing linear programming problems, and various types of linear programming problems with examples are covered in this Chapter. Students can find exercises that clearly explain and solve these problems.
|Maths Class 12 NCERT Solutions Chapter 12 Exercises|
|Exercise 12.1 Class 12 Maths|
|Exercise 12.2 Class 12 Maths|
|Miscellaneous Exercise on Chapter 12 Class 12|
Random variable and its probability distribution, mean and variance of a random variable, conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, and Probability distribution with a binomial distribution.
|Maths Class 12 NCERT Solutions Chapter 13 Exercises|
|Exercise 13.1 Class 12 Maths|
|Exercise 13.2 Class 12 Maths|
|Exercise 13.3 Class 12 Maths|
|Exercise 13.4 Class 12 Maths|
|Exercise 13.5 Class 12 Maths|
|Miscellaneous Exercise on Chapter 13 Class 12|
CBSE Marking Scheme 2022-23
A student will take the board exams twice in their lives. One is in Class 10, and the other is in Class 12. Students can use their Class 10 scores to understand better the topics in which they excel, and their Class 12 grades can help them plan their future. The CBSE board has divided the entire syllabus into two terms to make it easier for students to study all concepts. After studying the CBSE board’s revised course structure, students can comprehend the chapters worth more marks and practice them effectively.
The 12th grade is a critical year in a student’s life. To help students understand all of the concepts quickly, the CBSE board has divided the entire course into two terms of equal marks. The chapters are divided into divisions based on their importance in the board exam and their weight in terms of marks. The mission is to provide Class 12 students with a high-quality education and support them in reaching their long-term goals.
The term I and Term II: CBSE Class 12 Maths Syllabus Course Structure 2022-23
|I||Relations and Functions||8|
|IV||Vectors and Three–Dimensional Geometry||14|
Class 12 Maths NCERT Solutions
NCERT Solutions for Class 12 PDF Math is a crucial tool for students to employ in their exam and assignment preparation. Students’ performance in Class 12 boards and competitive assessments depends on their ability to solve problems in math. These Class 12 answers PDFs could be the most valuable educational resource for preparing for the board exam. It’s difficult to achieve a good grade in Mathematics solely by memorizing formulae.
Learn Infinite Students in Class 12 will benefit from NCERT Solutions’ assistance in extracting conceptual meaning from any problem. NCERT Maths Solutions for CBSE Class 12th provides comprehensive answers to all the problems covered in the curriculum. Probability, calculus, coordinate geometry, and trigonometry are straightforward topics that students can quickly master with enough practice.
Why Do Toppers Prefer Infinity Learn NCERT Solutions?
According to many students, Infinity Learn’s NCERT Solutions are the most user-friendly solutions available on the internet. Most CBSE students prefer our solutions due to their reliability and precision. Using Infinity Learn’s solutions, students may quickly finish the NCERT Class 12 Maths Syllabus. Some of the most crucial elements of the NCERT Solutions we provide are listed below.
- It is possible to access it at any time and from any location.
The 12th-grade exam is a watershed moment in a student’s academic career. Thus, finding study materials that meet their needs is of utmost importance. Infinity Learn has devised strategies to help students establish confidence in their ability to answer difficult questions in board exam preparation easily. Infinity Learn provides free solutions to textbook practice problems that can be used anywhere and anytime.
Benefits of Maths NCERT Solutions Class 12
- Teachers with a lot of experience did the study and produced the solutions.
- There are new value-based questions with solutions in each Chapter.
- Jargon-free and easy-to-understand language.
- The content is based on the CBSE curriculum for 2022-23.
- There is a lot of coverage of important concepts.
- The most beneficial information for CBSE board examinations preparation.
NCERT Solutions for Class 12 Maths: A Comprehensive Analysis
NCERT Textbooks are known for their clarity and straightforward explanations of concepts. For CBSE Class 12 students, these texts are good. It is made up of multiple-choice questions that evaluate their conceptual understanding.
The Maths NCERT Solutions Class 12 provides all the necessary content and fundamental ideas to help students prepare for medical entrance exams like the NEET.
Frequently Asked Questions on NCERT Solutions for Class 12 Maths
What role does NCERT Class 12 Maths Solutions have in exam preparation?
NCERT textbook questions can be really useful in ensuring that you study effectively and do well in exams and evaluations. Students can start learning NCERT Solutions Class 12 Maths right away, improving their academic performance in the future.
How can I get NCERT Maths Solutions for Class 12?
All of these principles are covered in full in the solutions we give.
What are the benefits of using the Infinity Learn NCERT Maths Solutions for Class 12?
The following are some of the benefits of using the Infinity Learn NCERT Solutions for Class 12 Maths: In-depth answers are given to logical thinking issues. Numericals are solved step by step according to the CBSE syllabus's mark weightage. Concise and to-the-point responses are supplied for theoretical questions. Top-tier subject experts create the solutions to the needs of the pupils.
Do Infinity Learn NCERT Solutions for Class 12 Maths have better quality?
Subject matter experts write NCERT Solutions for Class 12 Maths with years of expertise. They curate the solutions by sticking to the most recent CBSE board syllabus and guidelines.
Do Infinity Learn NCERT Solutions for Class 12 Maths help students get full marks in their board exams?
Subject-specific and chapter-specific solutions are available to students who have difficulty answering textbook questions. Aside from the board, students will receive assistance with their board exams.