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NCERT Solutions for Mathematics [English] Class 12

CBSE, Karnataka Board PUC Class 12 Maths Solutions Guide

Shaalaa.com provides the CBSE, Karnataka Board PUC Class 12 Maths Solutions Digest. Shaalaa is undoubtedly a site that most of your classmates are using to perform well in exams.

You can solve the Class 12 Maths Book Solutions CBSE, Karnataka Board PUC textbook questions by using Shaalaa.com to verify your answers, which will help you practise better and become more confident.


CBSE, Karnataka Board PUC Class 12 Maths Textbook Solutions

Questions and answers for the Class 12 Maths Textbook are on this page. NCERT Solutions for Class 12 Maths Digest CBSE, Karnataka Board PUC will help students understand the concepts better.


NCERT Solutions for Class 12 Maths Chapterwise List | Class 12 Maths Digest

The answers to the NCERT books are the best study material for students. Listed below are the chapter-wise NCERT Maths Class 12 Solutions CBSE, Karnataka Board PUC.


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NCERT Solutions for Mathematics [English] Class 12 - Shaalaa.com
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NCERT Class 12 solutions for other subjects

We also provide solutions for other subjects to help you top the exams. These NCERT solutions are curated with respect to the exam pattern and old papers. Find the best questions and solutions here. Click now to access it.

Chapters covered in NCERT Solutions for Mathematics [English] Class 12

NCERT Solutions for Class 12 Mathematics 1: Relations and Functions

Concepts covered in Relations and Functions are Composition of Functions and Invertible Function, Concept of Binary Operations, Introduction of Relations and Functions, Inverse of a Function, Types of Functions, Types of Relations.

NCERT Class 12 Mathematics 1: Relations and Functions exercises

ExerciseNo. of questionsPages
Exercise 1.1295 to 7
Exercise 1.21710 to 11
Exercise 1.31718 to 19
Exercise 1.42224 to 26
Exercise 1.52029 to 31

NCERT Solutions for Class 12 Mathematics 2: Inverse Trigonometric Functions

Concepts covered in Inverse Trigonometric Functions are Graphs of Inverse Trigonometric Functions, Inverse Trigonometric Functions, Inverse Trigonometric Functions - Principal Value Branch, Inverse Trigonometric Functions (Simplification and Examples), Properties of Inverse Trigonometric Functions.

NCERT Class 12 Mathematics 2: Inverse Trigonometric Functions exercises

ExerciseNo. of questionsPages
Exercise 2.11441 to 42
Exercise 2.22047 to 48
Exercise 2.31751 to 52

NCERT Solutions for Class 12 Mathematics 3: Matrices

Concepts covered in Matrices are Addition of Matrices, Elementary Transformations, Equality of Matrices, Introduction of Matrices, Introduction of Operations on Matrices, Inverse of a Matrix by Elementary Transformation, Invertible Matrices, Matrices Notation, Multiplication of a Matrix by a Scalar, Multiplication of Matrices, Multiplication of Two Matrices, Negative of Matrix, Order of a Matrix, Proof of the Uniqueness of Inverse, Properties of Matrix Addition, Properties of Multiplication of Matrices, Properties of Scalar Multiplication of a Matrix, Properties of Transpose of the Matrices, Subtraction of Matrices, Symmetric and Skew Symmetric Matrices, Transpose of a Matrix, Types of Matrices.

NCERT Class 12 Mathematics 3: Matrices exercises

ExerciseNo. of questionsPages
Exercise 3.11764 to 65
Exercise 3.23780 to 83
Exercise 3.32388 to 90
Exercise 3.42297 to 100
Exercise 3.513100 to 101

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NCERT Solutions for Class 12 Mathematics 4: Determinants

Concepts covered in Determinants are Applications of Determinants and Matrices, Area of a Triangle, Determinant of a Matrix of Order 3 × 3, Determinant of a Square Matrix, Determinants of Matrix of Order One and Two, Elementary Transformations, Introduction of Determinant, Inverse of a Square Matrix by the Adjoint Method, Minors and Co-factors, Properties of Determinants, Rule A=KB.

NCERT Class 12 Mathematics 4: Determinants exercises

ExerciseNo. of questionsPages
Exercise 4.113108 to 109
Exercise 4.219119 to 121
Exercise 4.39122 to 123
Exercise 4.47126
Exercise 4.518131 to 132
Exercise 4.616136 to 137
Exercise 4.719141 to 143

NCERT Solutions for Class 12 Mathematics 5: Continuity and Differentiability

Concepts covered in Continuity and Differentiability are Algebra of Continuous Functions, Concept of Continuity, Concept of Differentiability, Continuous Function of Point, Derivative - Exponential and Log, Derivatives of Composite Functions - Chain Rule, Derivatives of Functions in Parametric Forms, Derivatives of Implicit Functions, Derivatives of Inverse Trigonometric Functions, Exponential and Logarithmic Functions, Higher Order Derivative, Infinite Series, Logarithmic Differentiation, Mean Value Theorem, Proof Derivative X^n Sin Cos Tan, Second Order Derivative.

NCERT Class 12 Mathematics 5: Continuity and Differentiability exercises

ExerciseNo. of questionsPages
Exercise 5.137159 to 161
Exercise 5.29166
Exercise 5.315169
Exercise 5.410147 to 174
Exercise 5.518178 to 179
Exercise 5.611181
Exercise 5.717183 to 184
Exercise 5.88186
Exercise 5.923191 to 192

NCERT Solutions for Class 12 Mathematics 6: Application of Derivatives

Concepts covered in Application of Derivatives are Approximations, Graph of Maxima and Minima, Increasing and Decreasing Functions, Introduction to Applications of Derivatives, Maxima and Minima, Maximum and Minimum Values of a Function in a Closed Interval, Rate of Change of Bodies or Quantities, Simple Problems on Applications of Derivatives, Tangents and Normals.

NCERT Class 12 Mathematics 6: Application of Derivatives exercises

ExerciseNo. of questionsPages
Exercise 6.119197 to 199
Exercise 6.222205 to 206
Exercise 6.332211 to 213
Exercise 6.423216 to 2016
Exercise 6.548231 to 234
Exercise 6.625242 to 244

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NCERT Solutions for Class 12 Mathematics 7: Integrals

Concepts covered in Integrals are Comparison Between Differentiation and Integration, Definite Integral as the Limit of a Sum, Definite Integrals, Evaluation of Definite Integrals by Substitution, Evaluation of Simple Integrals of the Following Types and Problems, Fundamental Theorem of Calculus, Geometrical Interpretation of Indefinite Integrals, Indefinite Integral by Inspection, Indefinite Integral Problems, Integrals of Some Particular Functions, Integration as an Inverse Process of Differentiation, Integration Using Trigonometric Identities, Introduction of Integrals, Methods of Integration: Integration by Parts, Methods of Integration: Integration by Substitution, Methods of Integration: Integration Using Partial Fractions, Properties of Definite Integrals, Some Properties of Indefinite Integral.

NCERT Class 12 Mathematics 7: Integrals exercises

ExerciseNo. of questionsPages
Exercise 7.122299
Exercise 7.240304 to 305
Exercise 7.324307
Exercise 7.425315 to 316
Exercise 7.523322 to 323
Exercise 7.624327 to 328
Exercise 7.712330
Exercise 7.86334
Exercise 7.924338 to 340
Exercise 7.108340
Exercise 7.1121347
Exercise 7.1244352 to 354

NCERT Solutions for Class 12 Mathematics 8: Application of Integrals

Concepts covered in Application of Integrals are Area Between Two Curves, Area of the Region Bounded by a Curve and a Line, Area Under Simple Curves.

NCERT Class 12 Mathematics 8: Application of Integrals exercises

ExerciseNo. of questionsPages
Exercise 8.113365 to 366
Exercise 8.27371 to 372
Exercise 8.320375 to 376

NCERT Solutions for Class 12 Mathematics 9: Differential Equations

Concepts covered in Differential Equations are Differential Equations, Differential Equations with Variables Separable Method, Formation of a Differential Equation Whose General Solution is Given, General and Particular Solutions of a Differential Equation, Homogeneous Differential Equations, Linear Differential Equations, Order and Degree of a Differential Equation, Procedure to Form a Differential Equation that Will Represent a Given Family of Curves, Solutions of Linear Differential Equation.

NCERT Class 12 Mathematics 9: Differential Equations exercises

ExerciseNo. of questionsPages
Exercise 9.112382 to 383
Exercise 9.212385
Exercise 9.312391
Exercise 9.423395 to 397
Exercise 9.517406 to 407
Exercise 9.619413 to 414
Exercise 9.723419 to 421

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NCERT Solutions for Class 12 Mathematics 10: Vector Algebra

Concepts covered in Vector Algebra are Addition of Vectors, Basic Concepts of Vector Algebra, Components of Vector, Direction Cosines, Geometrical Interpretation of Scalar, Introduction of Product of Two Vectors, Introduction of Vector, Magnitude and Direction of a Vector, Multiplication of a Vector by a Scalar, Position Vector of a Point Dividing a Line Segment in a Given Ratio, Projection of a Vector on a Line, Properties of Vector Addition, Scalar (Or Dot) Product of Two Vectors, Scalar Triple Product of Vectors, Section Formula, Vector Joining Two Points, Vector (Or Cross) Product of Two Vectors, Vectors and Their Types, Vectors Examples and Solutions.

NCERT Class 12 Mathematics 10: Vector Algebra exercises

ExerciseNo. of questionsPages
Exercise 10.119428
Exercise 10.219440 to 441
Exercise 10.318447 to 448
Exercise 10.412454 to 455
Exercise 10.519458 to 459

NCERT Solutions for Class 12 Mathematics 11: Three Dimensional Geometry

Concepts covered in Three Dimensional Geometry are Angle Between Line and a Plane, Angle Between Two Lines, Angle Between Two Planes, Coplanarity of Two Lines, Direction Cosines and Direction Ratios of a Line, Distance of a Point from a Plane, Equation of a Line in Space, Equation of a Plane in Normal Form, Equation of a Plane Passing Through Three Non Collinear Points, Equation of a Plane Perpendicular to a Given Vector and Passing Through a Given Point, Intercept Form of the Equation of a Plane, Introduction of Three Dimensional Geometry, Plane Passing Through the Intersection of Two Given Planes, Relation Between Direction Ratio and Direction Cosines, Shortest Distance Between Two Lines, Three - Dimensional Geometry Examples and Solutions, Vector and Cartesian Equation of a Plane.

NCERT Class 12 Mathematics 11: Three Dimensional Geometry exercises

ExerciseNo. of questionsPages
Exercise 11.111467 to 478
Exercise 11.213477 to 478
Exercise 11.331493 to 494
Exercise 11.423497 to 499

NCERT Solutions for Class 12 Mathematics 12: Linear Programming

Concepts covered in Linear Programming are Different Types of Linear Programming Problems, Graphical Method of Solving Linear Programming Problems, Introduction of Linear Programming, Linear Programming Problem and Its Mathematical Formulation, Mathematical Formulation of Linear Programming Problem.

NCERT Class 12 Mathematics 12: Linear Programming exercises

ExerciseNo. of questionsPages
Exercise 12.110513 to 514
Exercise 12.214519 to 526
Exercise 12.38526 to 582

NCERT Solutions for Class 12 Mathematics 13: Probability

Concepts covered in Probability are Bayes’ Theorem, Bernoulli Trials and Binomial Distribution, Conditional Probability, Independent Events, Introduction of Probability, Mean of a Random Variable, Multiplication Theorem on Probability, Probability Examples and Solutions, Properties of Conditional Probability, Random Variables and Its Probability Distributions, Variance of a Random Variable.

NCERT Class 12 Mathematics 13: Probability exercises

ExerciseNo. of questionsPages
Exercise 13.124538 to 540
Exercise 13.222546 to 548
Exercise 13.314555 to 557
Exercise 13.421569 to 571
Exercise 13.515576 to 578
Exercise 13.621582 to 584

NCERT solutions of class 12th maths

If you're seeking the most up-to-date NCERT Solutions for Class 12 Mathematics, Shaalaa.com is the place to go. It's free to download in PDF format. You may be aware that The National Council of Education Research and Training (NCERT) sets the curriculum for all schools in the country that follow the Central Board of Secondary Education (CBSE). Our Mathematics specialists provide NCERT Solutions for Class 12 Maths based on the CBSE syllabus to help students tackle the tasks in the textbooks.

Understanding mathematics's fundamental formulae and ideas would help you do better in your Class 12 maths test. NCERT Solutions for Class 12 Mathematics are available in PDF format for all students.

NCERT Class 12 Maths Solutions gives a sound conceptual foundation for all topics covered in the CBSE Class 12 Maths Syllabus. It includes extensive explanations of all major theorems and equations to help students gain a better conceptual understanding. NCERT Solutions for Class 12 Maths would assist students in studying for undergraduate engineering entrance exams such as JEE Mains, BITSAT, VITEEE, etc.,

Shaalaa gives you NCERT Solutions Class 12 Maths, created by our subject specialists, to help you comprehend topics more clearly. NCERT Solutions for Class 12 provide extensive step-by-step explanations of issues found in the textbooks. Shaalaa also gives Class 12 Maths notes, answered sample problems, and previous year's exams, in addition to solutions for each chapter of CBSE Class 12 Maths and solved exemplar problems

12 Class Maths NCERT Solutions are a critical resource for students preparing for exams and homework. Maths is essential for students' performance in Class 12 boards and competitive tests. These NCERT Class 12 maths solutions may be an excellent educational resource for preparing for board exams. It's tough to get a good grade in Mathematics only by remembering equations. Students in Class 12 would benefit much from studying Shaalaa NCERT answers, as they can extract conceptual meaning from any issue. NCERT Maths Solutions for CBSE Class 12th offers comprehensive solutions to all the questions given in the syllabus. All the chapters listed above are equally significant and may be learned via persistent practice and strenuous effort. 

Key Features of CBSE Class 12 Maths NCERT Solutions

  • These solutions make it simple for students to practice and review subjects.
  • It helps you save time by logically presenting all the relevant ideas and equations.
  • These CBSE Class 12 Maths NCERT Solutions include helpful hints for correctly solving common questions.
  • These options are beneficial for short modifications during exams.

Mathematics is a subject that many students dislike due to its complications and puzzling sums and equations, and finding the correct reference sums and straightforward explanations can be challenging to come by. This can become all the more challenging, especially when you are getting ready for your standard 12 examinations, as finding the right sort of study material for your major board examination can decide how successfully you can solve and ace your exam. Finding suitable and reliable study material, such as NCERT Class 12 Maths, will ensure you can find solutions and clarifications for your doubts and difficulties. 

Download NCERT Books to read it. CBSE class 12 prescribes these books. 

NCERT Solutions for Mathematics [English] Class 12

Class 12 NCERT solutions answers all the questions given in the NCERT textbooks in a step-by-step process. Our Maths tutors have helped us put together this for our Class 12 Students. The solutions on Shaalaa will help you solve all the NCERT Class 12 Maths questions without any problems. Every chapter has been broken down systematically for the students, which gives fast learning and easy retention.

Shaalaa provides free NCERT solutions for Mathematics [English] Class 12. Shaalaa has carefully crafted NCERT solutions for Class 12 Maths that can help you understand the concepts and learn how to answer properly in your board exams. You can also share our link for free Class 12 Maths NCERT solutions with your classmates.

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Frequently asked questions about NCERT Solutions for Mathematics [English] Class 12

How can Class 12 Maths NCERT Solutions help you?

One of the most challenging exams you will ever appear for is your class 12 board exam. Ensuring that you have access to the best study material, such as Maths NCERT Class 12 Solutions for those challenging subjects, will ensure that you can put your doubts and confusions at ease. Good study material, especially for a complex subject such as Mathematics, requires students to constantly practice and find sums and equations that vary while ensuring that the exact numbers are not repeated.

How to effectively use NCERT 12 Maths Solution?

Unlike other subjects, such as language history and even science, that require one to study, read and memorise answers, mathematics requires a student to constantly practice and practice getting a thorough understanding of how to solve complicated and challenging equations, which can come only through repeated practice and therefore, the answer to acing your mathematics exam is through referring to various NCERT solutions of class 12th maths books and mathematics equations, to ensure that you are constantly solving new sums and equations, which will help you stay in touch with the complicated subject.

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Every exam has time limitations, something that many students fail to take into consideration while preparing for a subject such as mathematics, and the best and most effective way to do the same is to practice and refer to Class 12 Maths Solutions constantly, and to refer to previous year question papers, to ensure that you make the best use of the available time. Try to appear for the mock exams from home and time yourself as you would be timed at an examination hall. Set a timer and build discipline to ensure you take these mock exams seriously. By doing so, with the help of Class 12 Maths Solutions by your side, you will help yourself prepare most effectively and ensure that you will not feel nervous come exam time. You will be looking forward to the same.

How can Class 12 Maths NCERT Solutions help you gain an edge?

Your 12th standard examination can help shape and decide your future and career, and it needs to be taken; not only will all the seriousness possible, but it also must be tackled most effectively. It is a known fact that a good source of study material such as Class 12 Maths NCERT Solutions cannot just help you gain a competitive edge over the competition but will also ensure that you get prepared for the crucial board examination most effectively and efficiently, one which will ensure that you tap into your potential and score the maximum marks possible.

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How do NCERT Solutions help the student prepare for competitive exams?

Maths NCERT 12 Solutions helps students to prepare for undergraduate-level engineering entrance exams like JEE mains, BITSAT, VITEEE, etc. Many previous year's question papers and mock tests help students cover the syllabus and increase confidence levels and performance. When the student is confident that he has prepared well, his performance is bound to be good.

Do the Solutions cover the whole syllabus?

Maths is all about practice and precision. NCERT Solutions of Mathematics of Class 12 provides plenty of practice questions. It is helpful to the student to see all the questions solved so that they can perfect the methods employed. NCERT 12 Mathematics Solutions also gives Solutions to all the textbook problems.

NCERT Solutions for Class 12 Maths CBSE, Karnataka Board PUC

Class 12 NCERT Solutions answer all the questions in the NCERT textbooks in a step-by-step process. Our Maths tutors helped us assemble this for our Class 12 students. The solutions on Shaalaa will help you solve all the NCERT Class 12 Maths questions without any problems. Every chapter has been broken down systematically for the students, which gives them fast learning and easy retention.

Shaalaa provides a free NCERT answer guide for Maths Class 12, CBSE, Karnataka Board PUC. Shaalaa has carefully crafted NCERT solutions for the Class 12 Maths to help you understand the concepts and adequately answer questions in your board exams.

If you have any doubts while going through our Class 12 Maths NCERT solutions, you can go through our Video Tutorials for Maths. The tutorials help you better understand the concepts.

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NCERT Class 12 Maths Guide Book Back Answers

The following CBSE, Karnataka Board PUC NCERT Class 12 Maths Book Answers Solutions Guide PDF Free Download in English Medium will be helpful to you. Answer material is developed per the latest exam pattern and is part of NCERT Class 12 Books Solutions. You will be aware of all topics or concepts discussed in the book and gain more conceptual knowledge from the study material. If you have any questions about the CBSE, Karnataka Board PUC New Syllabus Class 12 Maths Guide PDF of Text Book Back Questions and Answers, Notes, Chapter Wise Important Questions, Model Questions, etc., please get in touch with us.

Comprehensive NCERT Solutions for CBSE, Karnataka Board PUC Maths Class 12 Guide

The NCERT Maths Class 12 CBSE, Karnataka Board PUC solutions are essential as they can offer a good improvement guideline. You must push the boundaries and take things to the next level to improve. That certainly helps a lot and can bring tremendous benefits every time. It takes the experience to the next level, and the payoff alone can be extraordinary.

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Our NCERT Maths Answer Guide for the Class 12 CBSE, Karnataka Board PUC covers all 13 chapters. As a result, you will be able to fully prepare for the exam without worrying about missing anything. You rarely get such a benefit, which makes the Maths Class 12 CBSE, Karnataka Board PUC NCERT solutions provided here such an extraordinary advantage that you can always rely on. Consider giving it a try for yourself, and you will find it very comprehensive, professional, and convenient at the same time.

Our CBSE, Karnataka Board PUC NCERT solutions for Maths Class 12 cover everything from Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Linear Programming, Probability and the other topics.

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