Study MaterialsNCERT SolutionsNCERT Solutions for Class 12Class 12 Math NCERT Solutions – NCERT Solutions for Class 12 Maths

Class 12 Math NCERT Solutions – NCERT Solutions for Class 12 Maths

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. NCERT Solutions for Class 12 Maths will help students prepare for undergraduate engineering admission exams in 2021-2022, 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.

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    class 12 math ncert solutions

    The following Chapters are explained in NCERT Class 12 Maths :

    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

    NCERT Solutions Class 12 Maths is important not only for board exams but also for competitive testing. Faculty have developed solutions to help students learn more topics regardless of their I.Q. Level. 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. Students can also access the NCERT Solutions Class 12 Maths and other online and offline study materials.

    NCERT Solutions Class 12 Mathematics Chapter Details and Exercises

    NCERT Solutions for Class 12 Maths Chapter 1

    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.

    The following topics were covered:

    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

    Class 12 Maths Chapter 2

    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.

    The following topics were covered:

    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

    NCERT Solutions for Class 12 Maths Chapter 3

    The definition of a matrix, types of matrices, equality of matrices, operations on matrices such as matrix addition and scalar multiplication, properties of matrix addition and scalar multiplication, multiplication of matrices, properties of multiplication of matrices, transpose of a matrix, properties of the transpose of the matrix, symmetric and skew-symmetric matrices, and elementary operations on matrices are all covered. You’ll find links to the exercise solutions for the topics covered in this Chapter.

    NCERT Solutions for Class 12 Maths

    The following topics were covered:

    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. In addition, multiplication and scalar multiplication have simple features. 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

    NCERT Solutions for Class 12 Maths Chapter 4

    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.

    The following topics were covered:

    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.

    Maths Class 12 NCERT Solutions Chapter 4 Exercises
    Exercise 4.1 Class 12 Maths
    Exercise 4.2 Class 12 Maths
    Exercise 4.3 Class 12 Maths
    Exercise 4.4 Class 12 Maths
    Exercise 4.5 Class 12 Maths
    Exercise 4.6 Class 12 Maths
    Miscellaneous Exercise on Chapter 4 Class 12

    NCERT Solutions for Class 12 Maths Chapter 5

    The fifth Chapter of the NCERT textbook is dedicated to the definition of continuity. Students are then taught through a variety of examples about continuity, algebra of continuous functions, definition and meaning of differentiability, derivatives of composite functions, implicit functions, inverse trigonometric functions, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivatives, and the mean value theorem. Students can find challenges here that appropriately explain and solve these concepts.

    The following topics were covered:

    The concepts include continuity and differentiability, composite function derivatives, chain rule, inverse trigonometric function derivatives, implicit function derivatives, 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).

    Maths Class 12 NCERT Solutions Chapter 5 Exercises
    Exercise 5.1 Class 12 Maths
    Exercise 5.2 Class 12 Maths
    Exercise 5.3 Class 12 Maths
    Exercise 5.4 Class 12 Maths
    Exercise 5.5 Class 12 Maths
    Exercise 5.6 Class 12 Maths
    Exercise 5.7 Class 12 Maths
    Exercise 5.8 Class 12 Maths
    Miscellaneous Exercise on Chapter 5 Class 12

    NCERT Solutions for Class 12 Maths Chapter 6

    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 function in a closed interval, and other topics. Students can find exercises here that clearly illustrate these concepts.

    The following subjects were discussed:

    Rate of change of bodies, increasing/decreasing functions, tangents, normals, and derivatives usage in approximation, maxima, and minima are all examples of derivative applications (first derivative test motivated geometrically and 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

    NCERT Solutions for Class 12 Maths Chapter 7

    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.

    The following subjects were discussed:

    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.

    Maths Class 12 NCERT Solutions Chapter 7 Exercises
    Exercise 7.1 Class 12 Maths
    Exercise 7.2 Class 12 Maths
    Exercise 7.3 Class 12 Maths
    Exercise 7.4 Class 12 Maths
    Exercise 7.5 Class 12 Maths
    Exercise 7.6 Class 12 Maths
    Exercise 7.7 Class 12 Maths
    Exercise 7.8 Class 12 Maths
    Exercise 7.9 Class 12 Maths
    Exercise 7.10 Class 12 Maths
    Exercise 7.11 Class 12 Maths
    Miscellaneous Exercise on Chapter 7 Class 12

    NCERT Solutions for Class 12 Maths Chapter 8

    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.

    The following subjects were discussed:

    I am finding the Area under simple curves, such as lines, circles, parabolas, and ellipses (in standard form only), Area between any of the above curves (the region should be identifiable).

    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

    NCERT Solutions for Class 12 Maths Chapter 9

    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.

    The following subjects were discussed:

    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:

    Where and are functions of or constants.

    Where and are functions of or constants.

    Maths Class 12 NCERT Solutions Chapter 9 Exercises
    Exercise 9.1 Class 12 Maths
    Exercise 9.2 Class 12 Maths
    Exercise 9.3 Class 12 Maths
    Exercise 9.4 Class 12 Maths
    Exercise 9.5 Class 12 Maths
    Exercise 9.6 Class 12 Maths
    Miscellaneous Exercise on Chapter 9 Class 12

    NCERT Solutions for Class 12 Maths Chapter 10

    This chapter introduces students to vector algebra. This chapter covers how to find a position vector, 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, a product of two vectors, scalar or dot product of two vectors, properties of scalar product, a product of two vectors, By clicking on the links below, students can obtain activities with solutions that explain the concepts from this Chapter.

    The following topics were covered:

    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, negative of a vector, components of a vector, the addition of vectors, 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

    NCERT Solutions for Class 12 Maths Chapter 11

    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.

    The following topics were covered:

    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

    NCERT Solutions for Class 12 Maths Chapter 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.

    The following subjects were discussed:

    Different forms of linear programming (L.P.) problems, mathematical formulation of L.P. issues, and related terms such as constraints, objective function, and optimization of viable and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions, the graphical technique of solution for problems in two variables (up to three non-trivial constraints).

    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

    NCERT Solutions for Class 12 Maths Chapter 13

    The topic of this Chapter is probability. In this chapter, we’ll review the basic facts and formulae from Class 11 as well as the advanced concepts mentioned, such as conditional probability, properties of conditional probability, multiplication theorem on probability, multiplication rule of possibility for more than two events, independent events, Bayes’ theorem, the partition of a sample space, total probability theorem, random variables, and their probability dist Here are the answers to the activities from this Chapter that have effectively explained the topic.

    The following subjects were discussed:

    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

    Because Infinity Learn is a learning organization, we understand the significance of study materials and how they influence academic performance. Each Chapter of the NCERT Class 12 textbook has many concepts that may stress students. As a result, it’s critical to first master the tricks and techniques for remembering everything. NCERT Class 12 Books can be downloaded from this page. As a result, we developed Class 12 NCERT Solutions, a learning resource aimed at helping students study and achieve their objectives.

    CBSE Marking Scheme 2021-22

    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. It also provides a strong foundation in core topics important for board exams.

    Term I and Term II: CBSE Class 12 Maths Syllabus Course Structure 2021-22

    No. Units Marks
    I Relations and Functions 8
    II Algebra 10
    III Calculus 35
    IV Vectors and Three–Dimensional Geometry 14
    V Linear Programming 5
    VI Probability 8
    Total Theory 80
    Internal Assessment 20
    Total 100

    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. Instead, the most effective way to achieve success is to practice.

    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. The preceding chapters are equally important and maybe learned with consistent practice and effort. 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. Because of the reliability and precision of our solutions, we are the preferred option for most CBSE students. Using Infinity Learn’s solutions, students may now quickly finish the NCERT Class 12 Maths Syllabus. Some of the most crucial elements of the NCERT Solutions we provide are listed below.

    • Teachers with a lot of experience come up with the answers.

    Math is a subject that covers a wide range of concepts with practical applications. To master these concepts, students must reference the best online study material available. We at Infinity Learn to curate the solutions with the comprehension ability of Class 12 students in mind. As a result, they are dependable and correct because the solutions are based on the CBSE board’s exam timetable.

    • There are a variety of problems to practice with.

    When it comes to final exam preparation, practice is the only way to earn a good grade. As a result, Infinity Learn has developed chapter-by-chapter solutions that students can access online and offline. Because the solutions are authentic, students can rely on them to help them prepare for their board exams.

    • 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. As a result, finding the ideal study material that meets all of their needs is crucial. Infinity Learn has devised strategies to help students establish confidence in their ability to easily answer difficult questions in board exam preparation. When solving the textbook’s practice problems, Infinity Learn gives free solutions that can be utilized 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 2021-22.
    • 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. As a result, a solid understanding of the syllabus would emerge.

    How can I get NCERT Maths Solutions for Class 12?

    Go to the Infinity Learn website and select NCERT Solutions, then select class 12 and subject to get the solutions. 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's syllabus and guidelines. The NCERT textbook questions are thoroughly handled so that students can grasp the concepts quickly.

    Do Infinity Learn NCERT Solutions for Class 12 Maths help students get full marks in their board exams?

    Of course, NCERT Solutions for Class 12 Maths is one of the most popular online study materials. When textbook questions stump students, they can turn to subject-specific and chapter-specific solutions for help. It also improves their ability to react to more complicated questions on board exams. Aside from the board, students will receive assistance with their board exams.

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