NCERT Solutions Class 12 Maths provides a solid conceptual base for all the topics included in CBSE Class 12 Maths Syllabus. It covers all the important theorems and formulae with detailed explanations to promote a better conceptual understanding in students. NCERT Maths Solutions for Class 12 will help students in the preparation of undergraduate level Engineering entrance exams like JEE Mains, BITSAT, VITEEE, etc, to be conducted this year, in 2020.
BYJUâ€™S brings you NCERT Solutions Class 12, designed by our subject experts to facilitate smooth and precise understanding of concepts. These CBSE Class 12 Solutions of NCERT have detailed step-by-step explanations of problems given in the textbooks. Apart from solutions for each chapter of CBSE Class 12 Maths, BYJUâ€™S also provides Class 12 Maths notes, solved exemplar problems and previous year questions papers, along with worksheets as study materials for students who are preparing for their Class 12 board exams.
NCERT Solutions for Class 12 Maths Chapter-wise PDF
- 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
Class 12 Maths NCERT SolutionsÂ Exercises
Students can download PDF of Maths NCERT Solutions for Class 12, chapter-wise from the links given below.
Chapter 1 Relations and Functions
Chapter 1 of NCERT textbook deals with relations and functions, types of relation, types of functions, composition of functions and invertible function, binary operations and miscellaneous examples. Here, you can find the exercise solution links for the topics covered in this chapter.
Chapter 1 Exercises |
---|
Exercise 1.1 |
Exercise 1.2 |
Exercise 1.3 |
Exercise 1.4 |
Miscellaneous Exercise |
Chapter 2 Inverse Trigonometric Functions
Chapter 2, Inverse Trigonometric Functions of NCERT Class 12 Maths, gives an account of various topics such as the remarks based on basic concepts of inverse trigonometric functions, properties of inverse trigonometric functions and miscellaneous examples. These concepts are explained very well through examples. Solutions to the exercises from the chapter can be accessed from here.
Chapter 2 Exercises |
---|
Exercise 2.1 |
Exercise 2.2 |
Miscellaneous Exercise |
Chapter 3 Matrices
In Chapter 3 of NCERT textbook, we shall see the definition of a matrix, types of matrices, equality of matrices, operations on matrices such as addition of matrices and multiplication of a matrix by a scalar, properties of matrix addition, properties of scalar multiplication, multiplication of matrices, properties of multiplication of matrices, transpose of a matrix, properties of transpose of the matrix, symmetric and skew symmetric matrices, elementary operation or transformation of a matrix, inverse of a matrix by elementary operations and miscellaneous examples. Here, you can find the exercise solution links for the topics covered in this chapter.
Chapter 3 Exercises |
---|
Exercise 3.1 |
Exercise 3.2 |
Exercise 3.3 |
Exercise 3.4 |
Miscellaneous-Exercise |
Chapter 4 Determinants
Chapter 4 of NCERT Solutions Maths discusses the topic of determinants. Students will get to learn about the definition and meaning of determinants, remarks based on order of determinants, properties of determinants, finding area of triangle using determinants, minors and cofactors of determinants, adjoint of a matrix, inverse of matrix, applications of determinants and matrices and miscellaneous examples. Below we have links provided to each exercise solution covered in this chapter.
Chapter 4 Exercises |
---|
Exercise 4.1 |
Exercise 4.2 |
Exercise 4.3 |
Exercise 4.4 |
Exercise 4.5 |
Exercise 4.6 |
Miscellaneous Exercise |
Chapter 5 Continuity and Differentiability
Chapter 5 of NCERT textbook starts with the definition of continuity. Students go on to learn about continuity, algebra of continuous function, definition and meaning of differentiability, derivatives of composite functions, derivative of implicit functions, derivative of inverse trigonometric functions, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second order derivatives, mean value theorem via miscellaneous examples. Here, students can find the exercises explaining these concepts properly with solutions.
Chapter 5 Exercises |
---|
Exercise 5.1 |
Exercise 5.2 |
Exercise 5.3 |
Exercise 5.4 |
Exercise 5.5 |
Exercise 5.6 |
Exercise 5.7 |
Exercise 5.8 |
Miscellaneous Exercise |
Chapter 6 Applications of Derivatives
Chapter 6 of NCERT textbook, provides definition of derivatives, rate of change of quantities, increasing 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 miscellaneous examples. Here, students can find the exercises explaining these concepts properly.
Chapter 6 Exercises |
---|
Exercise 6.1 |
Exercise 6.2 |
Exercise 6.3 |
Exercise 6.4 |
Exercise 6.5 |
Miscellaneous Exercise |
Chapter 7 Integrals
In Chapter 7, Integrals we shall see the definition of indefinite integral, integration as an inverse process of differentiation, geometrical interpretation of indefinite integral, properties of indefinite integral, comparison between differentiation and integration, methods of integration such as 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, evaluation of definite integrals by substitution, some properties of definite integrals and miscellaneous examples. Here, we have given exercises with solutions based on these topics from the chapter.
Chapter 7 Exercises |
---|
Exercise 7.1 |
Exercise 7.2 |
Exercise 7.3 |
Exercise 7.4 |
Exercise 7.5 |
Exercise 7.6 |
Exercise 7.7 |
Exercise 7.8 |
Exercise 7.9 |
Exercise 7.10 |
Exercise 7.11 |
Miscellaneous Exercise |
Chapter 8 Applications of Integrals
In Chapter 8 of NCERT textbook, we continue the discussions about integrals starting with definition, area under simple curves, area of the region bounded by a curve and a line, area between two curves and miscellaneous examples. From the below given links, students can access the exercises with solutions explaining the concepts from this chapter.
Chapter 8 Exercises |
---|
Exercise 8.1 |
Exercise 8.2 |
Miscellaneous Exercise |
Chapter 9 Differential Equations
In this chapter, students concentrate on 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 given, procedure to form a differential equation that will represent a given family of curves, methods of solving first order, first degree differential equations, differential equations with variable separable, homogeneous differential equations, linear differential equations, procedure involved to solve first order linear differential equations and miscellaneous examples. Solutions to the exercises from the chapter can be accessed from here.
Chapter 9 Exercises |
---|
Exercise 9.1 |
Exercise 9.2 |
Exercise 9.3 |
Exercise 9.4 |
Exercise 9.5 |
Exercise 9.6 |
Miscellaneous Exercise |
Chapter 10 Vector Algebra
In this chapter, students are introduced to the vector algebra. The concepts in this chapter cover how to find position vector, some basic concepts related to vector algebra, 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, vector or cross product of two vectors and miscellaneous examples. From the below given links, students can access the exercises with solutions explaining the concepts from this chapter.
Chapter 10 Exercises |
---|
Exercise 10.1 |
Exercise 10.2 |
Exercise 10.3 |
Exercise 10.4 |
Miscellaneous Exercise |
Chapter 11 Three dimensional Geometry
Chapter 11 of NCERT Class 12 Maths constitutes topics related to three dimensional geometry, direction cosines and direction ratios of a line, relation between the direction cosines of a line, 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, derivation of cartesian form from vector form, equation of a line passing through two given points, angle between two lines, shortest distance between two lines, distance between two skew lines, distance between two parallel lines, 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, intercept form of the equation of a plane, plane passing through the intersection of two given planes, coplanarity of two lines, angle between two planes, distance of a point from a plane, angle between a line and a plane and miscellaneous examples. Below we have listed links to the solutions for the exercises from this chapter.
Chapter 11 Exercises |
---|
Exercise 11.1 |
Exercise 11.2 |
Exercise 11.3 |
Miscellaneous Exercise |
Chapter 12 Linear Programming
In this chapter, students are introduced to linear programming. The concepts covered in this chapter are linear programming problem and its mathematical formulation, mathematical formulation of the problem, graphical method of solving linear programming problems, different types of linear programming problems with miscellaneous examples. students can find the exercises explaining these concepts properly with solutions.
Chapter 12 Exercises |
---|
Exercise 12.1 |
Exercise 12.2 |
Miscellaneous Exercise |
Chapter 13 Probability
This chapter deals with probability. By reviewing the basic facts and formulae studied earlier in Class 11, we shall implement those formulas again in this chapter along with the advance concepts mentioned i.e. conditional probability, properties of conditional probability, multiplication theorem on probability, multiplication rule of probability for more than two events, independent events, Bayeâ€™s theorem, partition of a sample space, theorem on total probability, random variables and its probability distributions, probability distribution of random variable, mean of random variable, variance of random variable, Bernoulli trials and binomial distribution with miscellaneous examples. We have compiled here the solutions to exercises from this chapter, which have explained the concept thoroughly.
Chapter 13 Exercises |
---|
Exercise 13.1 |
Exercise 13.2 |
Exercise 13.3 |
Exercise 13.4 |
Exercise 13.5 |
Miscellaneous Exercise |
CBSE Class 12 Maths Exam Pattern 2020
CBSE Class 12 Maths Exam Pattern 2020 is based on the revised guidelines of Central Board of Secondary Education. CBSE Class 12 marking scheme is the guide that is used for allocating the marks to the students. In class 12 Maths, the board exam will be conducted for 100 marks, with three sections that is very short answer type, short answer type and long answer type of questions. Students who are appearing for the exam must go through the Marking Scheme 2020 after solving the CBSE Class 12 CBSE Sample Papers and previous year question paper. This also helps to attend the competitive exams as it gives more importance to very short answer type. Here you can find the CBSE Class 12 Maths Exam pattern.
CBSE Class 12 Maths (Basic and Standard Paper) Marking Scheme |
|||
Sections |
No. of Questions |
Marks per Question |
Total Marks |
Section A |
10 Qs |
1 Mark |
10 |
Section B |
12 Qs |
4 Marks |
48 |
Section C |
7 Qs |
6 Marks |
42 |
Total |
40 Qs |
100 |
CBSE Class 12 Chapter-wise marks weightage
The marking scheme for the exam 2020 is released by the CBSE on the official site. Here you can find the CBSE Class 12 Chapter-wise marks weightage according to the previous year question papers.
Unit |
Marks |
1. (a) Relations and Functions (b) Inverse trigonometric Functions |
10 |
2. (a) Matrices (b) Determinants |
13 |
3. (a) Continuity and Differentiability (b) Applications of Derivatives (c) Integrals (d) Applications of Integrals (e) Differential Equations |
44 |
4. (a) Vectors (b) 3 â€“ dimensional Geometry |
17 |
5. Linear Programming |
06 |
6. Probability |
10 |
Total Marks |
100 |
NCERT Solutions Class 12 Maths Chapter 1 to 13
NCERT Solutions acts as a vital tool for students in their exam preparation and home assignments. Maths plays a vital role in the success of students in Class 12 boards and competitive exams. These NCERT Class 12 maths solutions can be your best education support for board exam preparations. Itâ€™s difficult to score in Mathematics simply by reading and memorizing the formulae. Instead, practice is the perfect method to succeed. Learning from BYJUâ€™S NCERT solutions will help students of Class 12 to squeeze conceptual meaning out of every problem quite effectively.
CBSE class 12 Maths solutions provide in-depth answers to all the problems covered in the syllabus. All the above-mentioned chapters are equally important and can be mastered with consistent practice and hard work. The topics like probability, calculus, coordinate geometry, trigonometry are easy and with proper practice, students can easily score good marks from these units. We have also provided solved examples at the end of every chapter to make concepts clear to our readers.
Key Features of CBSE Class 12 Maths NCERT Solutions
- Students can easily practice and revise concepts by referring to these solutions.
- It saves your time by providing all the necessary concepts and formulae in a proper sequence.
- These CBSE Class 12 Maths solutions contain important tips, useful for answering typical questions accurately.
- These solutions are extremely helpful for quick revisions during examinations.
Students are advised to follow the NCERT Class 12 books and solutions on a regular basis to get in-depth knowledge about all the concepts covered in the syllabus.
Frequently Asked Questions on NCERT Class 12 Maths Solutions
Which book is best for Class 12 Maths?
The most trusted book for Class 12 board exam is NCERT Book. Students must build up their concepts through NCERT Class 12 Maths book by solving the examples and exercise problems. After that, they can practice questions from other reference books like RD Sharma and RS Aggarwal. But firstly they are recommended to solve the NCERT book as this book follows the CBSE syllabus and pattern.
Is NCERT enough for Class 12 board Maths?
Yes, NCERT books are enough for board exams. Students can easily grasp the concepts from NCERT books by solving the examples and exercise problems. For practising more questions, they can refer to other books also.
Is Class 12 NCERT Maths difficult?
The class 12 NCERT Maths is not at all difficult. If students have understood the concept and gone through the solved examples then they can easily solve the questions related to it. For this, they have to practice the questions daily. Practice is the only way through which students can master the subject.
How many chapters are there in NCERT Maths Class 12?
The NCERT Class 12 Maths book has 2 parts. Part 1 contains chapters 1 to 6 and part 2 contains chapters 7 to 13. Therefore, there is a total of 13 chapters in NCERT Maths Class 12. Viz, Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Applications of Derivatives, Integrals, Applications of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Linear Programming and Probability.
Where can I get NCERT Class 12 Maths Solutions with Miscellaneous Exercise?
The NCERT Class 12 Maths Solutions are provided on the BYJUâ€™S site. These solutions are prepared by our subject experts. The questions are solved in the simplest method so that students can easily understand them. Also, the solutions for miscellaneous exercises are provided.
Do Miscellaneous Exercise questions come in board exam?
Questions may be asked from the miscellaneous exercise in the board exam. So, to be on the safer side, students must solve the miscellaneous exercise. Also, the level of these exercises is quite high so it will be good practice for students.