{"id":6597,"date":"2019-09-26T21:20:58","date_gmt":"2019-09-26T15:50:58","guid":{"rendered":"https:\/\/www.cbselabs.com\/?page_id=6597"},"modified":"2021-09-18T15:32:35","modified_gmt":"2021-09-18T10:02:35","slug":"ncert-solutions-class-12-maths","status":"publish","type":"page","link":"https:\/\/www.cbselabs.com\/ncert-solutions-class-12-maths\/","title":{"rendered":"NCERT Solutions for Class 12 Maths"},"content":{"rendered":"<p><strong>NCERT Solutions for Class 12 Maths<\/strong> has been written to help 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 Class 12 Maths NCERT textbook. There are 13 important chapters from the NCERT textbook. Both problems and their detailed solutions are provided. The solutions have been devised by India\u2019s best teachers to help students grasp basic concepts better and faster.<\/p>\n<h2>NCERT Solutions for Class 12 Maths All Chapters<\/h2>\n<p>NCERT Maths Class 12 Solutions are given below for all chapter. Select chapter number to view Class 12 Maths NCERT chapter wise solutions.<\/p>\n<div class=\"featured-snippet\">\n<ul>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12-maths-relations-and-functions\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 1 Relations and Functions<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12-maths-inverse-trigonometric-functions\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 2 Inverse Trigonometric Functions<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12th-maths-chapter-3-matrices\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 3 Matrices<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12th-maths-chapter-4-determinants\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 4 Determinants<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12-maths-continuity-and-differentiability\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 5 Continuity and Differentiability<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12-maths-application-of-derivatives\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 6 Application of Derivatives<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12-maths-integrals\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 7 Integrals<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12th-maths-chapter-8-application-of-integrals\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 8 Application of Integrals<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12-maths-differential-equations\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 9 Differential Equations<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12th-maths-chapter-10-vector-algebra\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 10 Vector Algebra<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12th-maths-chapter-11-three-dimensional-geometry\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 11 Three Dimensional Geometry<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12th-maths-chapter-12-linear-programming\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 12 Linear Programming<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-12-maths-probability\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 13 Probability<\/a><\/strong><\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"size-full wp-image-93065 aligncenter\" src=\"https:\/\/i2.wp.com\/www.cbselabs.com\/wp-content\/uploads\/2019\/09\/Class-12-Maths-NCERT-Solutions.png?resize=600%2C400&#038;ssl=1\" alt=\"Class 12 Maths NCERT Solutions\" width=\"600\" height=\"400\" srcset=\"https:\/\/i2.wp.com\/www.cbselabs.com\/wp-content\/uploads\/2019\/09\/Class-12-Maths-NCERT-Solutions.png?w=600&amp;ssl=1 600w, https:\/\/i2.wp.com\/www.cbselabs.com\/wp-content\/uploads\/2019\/09\/Class-12-Maths-NCERT-Solutions.png?resize=300%2C200&amp;ssl=1 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" data-recalc-dims=\"1\" \/><\/p>\n<\/div>\n<p>If you are looking for Class 12 Maths NCERT Solutions, there is no better place to be than right here. We provide Maths NCERT solutions class 12 that are precise, to the point and absolutely error free. With NCERT reputed to be the best textbooks for school education, we make the solutions that are at par with the excellent textbooks.<\/p>\n<h3>Important Questions for Class 12 Maths Chapter wise<\/h3>\n<p><strong>Relations and Functions<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-cbse-class-12-maths-concept-of-relation-and-functions\/\" target=\"_blank\" rel=\"noopener noreferrer\">Concept of Relations and Functions<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-binary-operations\/\" target=\"_blank\" rel=\"noopener noreferrer\">Binary Operations<\/a><\/strong><\/li>\n<\/ul>\n<p><strong>\u00a0<a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-inverse-trigonometric-functions\/\" target=\"_blank\" rel=\"noopener noreferrer\">Inverse Trigonometric Functions<\/a><\/strong><\/p>\n<p><strong>Matrices<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-matrix-and-operations-of-matrices\/\" target=\"_blank\" rel=\"noopener noreferrer\">Matrix and Operations of Matrices<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-transpose-of-a-matrix-and-symmetric-matrix\/\" target=\"_blank\" rel=\"noopener noreferrer\">Transpose of a Matrix and Symmetric Matrix<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-inverse-of-a-matrix-by-elementry-operations\/\" target=\"_blank\" rel=\"noopener noreferrer\">Inverse of a Matrix by Elementary Operations<\/a><\/strong><\/li>\n<\/ul>\n<p><strong>Determinants<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-cbse-class-12-maths-expansion-of-determinants\/\" target=\"_blank\" rel=\"noopener noreferrer\">Expansion of Determinants<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-properties-of-determinants\/\" target=\"_blank\" rel=\"noopener noreferrer\">Properties of Determinants<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-inverse-of-a-matrix-and-application-of-determinants-and-matrix\/\" target=\"_blank\" rel=\"noopener noreferrer\">Inverse of a Matrix and Application of Determinants and Matrix<\/a><\/strong><\/li>\n<\/ul>\n<p><strong>Continuity and Differentiability<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-cbse-maths-continuity\/\" target=\"_blank\" rel=\"noopener noreferrer\">Continuity<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-cbse-maths-differntiability\/\" target=\"_blank\" rel=\"noopener noreferrer\">Differentiability<\/a><\/strong><\/li>\n<\/ul>\n<p><strong>Application of Derivatives<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-rate-measure-approximations-and-increasing-decreasing-functions\/\" target=\"_blank\" rel=\"noopener noreferrer\">Rate Measure Approximations and Increasing-Decreasing Functions<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-rate-tangents-and-normals\/\" target=\"_blank\" rel=\"noopener noreferrer\">Tangents and Normals<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-rate-maxima-and-minima\/\" target=\"_blank\" rel=\"noopener noreferrer\">Maxima and Minima<\/a><\/strong><\/li>\n<\/ul>\n<p><strong>Integrals<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-cbse-maths-types-of-integrals\/\" target=\"_blank\" rel=\"noopener noreferrer\">Types of Integrals<\/a><\/strong><\/li>\n<\/ul>\n<p><strong>Differential Equation<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-cbse-formation-of-differential-equations\/\" target=\"_blank\" rel=\"noopener noreferrer\">Formation of Differential Equations<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-cbse-maths-solution-of-different-types-of-differential-equations\/\" target=\"_blank\" rel=\"noopener noreferrer\">Solution of Different Types of Differential Equations<\/a><\/strong><\/li>\n<\/ul>\n<p><strong>Vector Algebra<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-cbse-maths-algebra-of-vectors\/\" target=\"_blank\" rel=\"noopener noreferrer\">Algebra of Vectors<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-cbse-maths-dot-and-cross-products-of-two-vectors\/\" target=\"_blank\" rel=\"noopener noreferrer\">Dot and Cross Products of Two Vectors<\/a><\/strong><\/li>\n<\/ul>\n<p><strong>Three Dimensional Geometry<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-cbse-maths-direction-cosines-and-lines\/\" target=\"_blank\" rel=\"noopener noreferrer\">Direction Cosines and Lines<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-cbse-class-12-maths-plane\/\" target=\"_blank\" rel=\"noopener noreferrer\">Plane<\/a><\/strong><\/li>\n<\/ul>\n<p><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-linear-programming\/\" target=\"_blank\" rel=\"noopener noreferrer\">Linear Programming<\/a><\/strong><\/p>\n<p><strong>Probability<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-conditional-probability-and-independent-events\/\" target=\"_blank\" rel=\"noopener noreferrer\">Conditional Probability and Independent Events<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/www.cbselabs.com\/important-questions-for-class-12-maths-cbse-bayes-theorem-and-probability-distribution\/\" target=\"_blank\" rel=\"noopener noreferrer\">Baye\u2019s Theorem and Probability Distribution<\/a><\/strong><\/li>\n<\/ul>\n<h3>NCERT Exemplar Class 12 Maths<\/h3>\n<ul>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-relations-functions\/\">Chapter 1 Relations and Functions<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-inverse-trigonometric-functions\/\">Chapter 2 Inverse Trigonometric Functions<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-matrices\/\">Chapter 3\u00a0Matrices<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-determinants\/\">Chapter 4 Determinants<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-continuity-differentiability\/\">Chapter 5\u00a0Continuity and Differentiability<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-application-derivatives\/\">Chapter 6\u00a0Application of Derivatives<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-integrals\/\">Chapter 7\u00a0Integrals<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-applications-integrals\/\">Chapter 8\u00a0Applications of Integrals<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-differential-equations\/\">Chapter 9\u00a0Differential Equations<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-vector-algebra\/\">Chapter 10\u00a0Vector Algebra<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-three-dimensional-geometry\/\">Chapter 11\u00a0Three Dimensional Geometry<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-linear-programming\/\">Chapter 12\u00a0Linear Programming<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-exemplar-problems-class-12-mathematics-probability\/\">Chapter 13\u00a0Probability<\/a><\/li>\n<\/ul>\n<p><a href=\"https:\/\/www.cbselabs.com\/rd-sharma-class-12-solutions-free-online\/\">RD Sharma Class 12 Maths Solutions<\/a><\/p>\n<h3>Class 12 Maths NCERT Solutions<\/h3>\n<p>Class 12 Maths is key in the preparation for boards as well as JEE Main and Advance, and our solutions are made keeping in mind the very same thing. The solutions are concise, and also discuss alternative methods to solve some problems. We make it a point to provide the students the best help they can get, and the solutions reflect just that.<\/p>\n<p>The\u00a0National Council of Educational Research and Training (<a href=\"http:\/\/ncert.nic.in\/\" rel=\"nofollow\">NCERT<\/a>) is an autonomous organization of the Government of India that was established in 1961 as a literary, scientific and charitable society under the Societies\u2019 Registration Act (Act XXI of 1860). Its headquarters are located at Sri Aurobindo Marg in New Delhi. It sets the curriculum for all schools that follow the Central Board of Secondary Education (CBSE) across the country. Class 12 Maths NCERT Solutions is the perfect guide to help you prepare for CBSE exams as well as engineering entrances like the JEE.<\/p>\n<p>Your performance in the board exams will play a role in determining your admission into a good college or even your dream college! That will undoubtedly induce a lot of pressure upon you and you may tend to get demotivated or stressed out. To help you overcome such situations, LearnCBSE is a platform all the way helps you to crack your target. if you have any queries leave in the comments box.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-59918 size-full\" src=\"https:\/\/i0.wp.com\/www.cbselabs.com\/wp-content\/uploads\/2019\/03\/NCERT-Solutions-for-Class-12-Maths.png?resize=560%2C315&#038;ssl=1\" alt=\"NCERT Solutions for Class 12 Maths\" width=\"560\" height=\"315\" srcset=\"https:\/\/i0.wp.com\/www.cbselabs.com\/wp-content\/uploads\/2019\/03\/NCERT-Solutions-for-Class-12-Maths.png?w=560&amp;ssl=1 560w, https:\/\/i0.wp.com\/www.cbselabs.com\/wp-content\/uploads\/2019\/03\/NCERT-Solutions-for-Class-12-Maths.png?resize=300%2C169&amp;ssl=1 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" data-recalc-dims=\"1\" \/><\/p>\n<h3>NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions<\/h3>\n<p>The chapter builds up on the concepts of relations, functions, domain and codomain introduced in Class 11. The students explore several real valued functions, and their graphs. The chapter comprises of four exercises that consolidate the concepts explained in the chapter.<\/p>\n<h3>NCERT Solutions for\u00a0Class 12 Maths Chapter 2 Inverse Trigonometric Functions<\/h3>\n<p>This chapter plays in the restricted range of trigonometric functions that enables them to be one on one, and hence makes inverse of the functions visible. This chapter explores the inverse trigonometric through two exercises that teach the students the behavior of the functions, their graphical representations, and the elementary properties. These prove to be of more value in integration later.<\/p>\n<h3>NCERT Solutions for\u00a0Class 12 Maths Chapter 3 Matrix<\/h3>\n<p>This chapter takes you through the properties of one of the most important tools of Mathematics, namely Matrices. The students learn the basics of Matrices and Matrix Algebra..<\/p>\n<h3>NCERT Solutions for\u00a0Class 12 Maths Chapter 4 Determinants<\/h3>\n<p>Correctly preceded by Matrix, this chapter deals with an important part of Matrices, namely Determinants. The chapter deals with determinants of orders upto 3, and their cofactors and inverses.This chapter also talks about the applications of determinants, like calculation of area of triangles, adjoint of matrices, consistency of a set of linear equations.<\/p>\n<h3>NCERT Solutions for\u00a0Class 12 Maths Chapter 5 Continuity and Differentiability<\/h3>\n<p>This chapter picks up after the Differentiation of Functions introduced in Class 11. The chapter explores the important concepts of Continuity, Differentiability and establishes the relationship between them. It also deals with the continuity and differentiability of Inverse Trigonometric Functions. It also introduces exponential and logarithmic functions.<\/p>\n<h3>NCERT Solutions for\u00a0Class 12 Maths Chapter 6 Application of Derivatives<\/h3>\n<p>With Continuity and Differentiability marking the start of Calculus, this chapter deals with the differentiability of functions, and introduction to derivatives. It delves 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 talks about increasing and decreasing functions.<\/p>\n<h3>NCERT Solutions for\u00a0Class 12 Maths Chapter 7 Integrals<\/h3>\n<p>This is one of the most important and time consuming chapters in the whole Class 12 Mathematics. This chapter deals with integration of functions, and its applications in terms of calculation of areas. This marks the introduction to Integral Calculus. There are a total of 11 exercises in this chapter, making it a very practice driven part of the syllabus.<\/p>\n<h3>NCERT Solutions for\u00a0Class 12 Maths Chapter 8 Application of Integrals<\/h3>\n<p>This chapter deals with the applications of integrals in calculating areas under simple curve, lines, parabolas and ellipses. The two exercises provide enough questions for practicing the area calculations.<\/p>\n<h3>NCERT Solutions for\u00a0Class 12 Maths Chapter 9 Differential Equations<\/h3>\n<p>This chapter introduces the concept of Differential equations, the general and particular solutions, and the order and degree of an equation. This also talks about the applications of differential equations in the six exercises.<\/p>\n<h3>NCERT Solutions for\u00a0Class 12 Maths Chapter 10 Vector Equations<\/h3>\n<p>This chapter deals with the vector quantities, that is, the quantities with both magnitude and direction. The Vector algebra summarises the rules of addition of vector quantities, and other important properties. Vector Algebra plays a big role in Physics.<\/p>\n<h3>Class 12 Maths Chapter 11 Three Dimensional Geometry<\/h3>\n<p>This chapter utilises 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 introduces the concept of direction cosines<\/p>\n<h3>Class 12 Maths Chapter 12 Linear Programming<\/h3>\n<p>This chapter explores the concept of linear programming problems, and their solutions using graphical method only.<\/p>\n<h3>Class 12 Maths Probability<\/h3>\n<p>This chapter deals with the concept of Conditional Probability and the encounters of the same in our daily lives. This explores Bayes\u2019 Theorem, the multiplication rule, and the independence of events. This chapter is best understood by practicing as many questions as possible.<\/p>\n<h4><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-2\/\">NCERT Solution<\/a><\/h4>\n<p>We hope you will have great learning experience while using the solutions. You can download the solutions by clicking on the links above in the description.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 12 Maths has been written to help 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 Class 12 Maths NCERT textbook. There are 13 important chapters from the NCERT &hellip;<\/p>\n","protected":false},"author":1,"featured_media":93065,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","meta":{"spay_email":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.2 (Yoast SEO v17.2) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 12 Maths (Updated for 2020-21)<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 12 Maths solved by subject experts from latest edition books and as per NCERT (CBSE) guidelines.Class 12 Maths NCERT Solutions and Extra Questions with Solutions to help you to revise complete Syllabus and Score More marks.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.cbselabs.com\/ncert-solutions-class-12-maths\/\" \/>\n<meta property=\"og:locale\" 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