NCERT Solutions for Class 12 Maths

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These solutions consist of error-free answers to all the questions given in NCERT Maths Textbooks. If you want to understand the maths questions in an easy and quick manner then get Class 12 Maths NCERT Solutions for chapter-wise exercises, examples, miscellaneous problems, and Intext Questions. The whole NCERT Solutions For Class 12 Maths are explained in an easy to understand manner. It helps in having a precise and step by step answer to the questions mentioned in the NCERT Class 12 Maths Textbook.

Follow the below-given tables to find out the class 12 maths NCERT solutions as per your requirement. It is free to download and can be accessed in a PDF file.

Because every question and their answers are explained very briefly so, it saves students time and energy to find out the correct steps of maths solutions. It is considered a very helpful study material for standard XII students but that is not its limit. Any students who are keen to prepare for the National level competitions or entrance exams such as JEE, BITSAT, VITEEE, etc, that are conducted every year can use the solutions that are provided herein chapter wise, term wise, exercise-wise. 

These are provided by the Selfstudy’s maths experts. Hence, it is free and error-free too. You can download all these NCERT Maths Solutions for class 12th from this page.

Class 12 Maths NCERT Solutions PDF for Chapter Wise

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NCERT Solutions For Class 12 Maths Term Wise is available here. It is provided in term wise format because recently the CBSE Board has updated its curriculum and as per the new CBSE Class 12th Maths Syllabus the chapters will be divided into two parts. Half part, meaning 50% syllabus of the maths book will be used to assess the students in term 1 exam while 50% syllabus in term 2 exams. 

Therefore, to excel and get good marks in the board exams students will have to prepare for the exams accordingly. For that reason, the NCERT Solutions For Class 12 Maths Term Wise for all the chapters is given here. It consists of problems and detailed solutions to give students immersive and smooth learning experiences. Any student looking for a resource that can help them to boost their maths exam preparation can use the NCERT Solutions for Class 12 Maths PDF; Below given table contains the Solutions.

NCERT Solutions Class 12 Maths Chapter Wise
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

NCERT Solutions For Class 12 Maths Chapter Wise (Term 1)

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The Term 1 Chapter Wise Maths solutions include the exercises from chapters 1 to 6. These are the following chapters of CBSE Mathematics term 1: Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Applications of Derivatives. All of these are essential to get good marks in the Term first exam of mathematics. Class 12 Maths NCERT Book Solution PDF for these chapters can be downloaded from the below-given table and its links.

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

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The first chapter of NCERT Class 12th Maths is relations and functions. It teaches the students about types of relations, types of functions, the composition of functions and invertible functions, binary operations along with miscellaneous examples. Here, you can find the links for the topics covered in this chapter.

The topics that are covered in the first chapters of mathematics for the first term exam are reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.

Most Important Formulas for NCERT Solutions Class 12 Maths Chapter 1 Relations and Functions

  • – A = (–1)A

  • A – B = A + (–1) B
  • A + B = B + A
  • (A + B) + C = A + (B + C)
  • k(A + B) = kA + kB

where A, B and C are matrices.

Other study materials For Chapter 1 Relations and Functions

NCERT & Other study materials For Chapter 1 are given here. There are various study resources for students that can help them to grasp the knowledge of chapter 1 Relations and Functions.

  1. Online MCQ Test Chapter 1 Relations and Functions
  2. MCQs PDF Chapter 1 Relations and Functions
  3. NCERT Books For Chapter 1 Relations and Functions
  4. NCERT Exemplar Solutions For Chapter 1 Relations and Functions
  5. NCERT Exemplar Books For Chapter 1 Relations and Functions
  6. Revision Notes For Chapter 1 Relations and Functions
  7. RD Sharma Solutions For Chapter 1 (Relations & Functions)
  8. RS Aggarwal Solutions For Chapter 1 (Relations & Functions)
  9. HOTS Questions For Chapter 1

NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

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Inverse trigonometry can be simply defined as the inverse functions of basic trigonometry functions. It is used to measure the angles of any trigonometry ratio. This is the chapter that will be used to examine the student's mathematical knowledge on the basis of finding angles. 

Every single concept of this chapter has been explained in very simple yet extremely detailed. The solutions for this chapter 2 Inverse trigonometry Functions are given here to download for free in PDF.

Most Important Formulas for NCERT Class 12 Maths Solutions Chapter 2 Inverse Trigonometric Functions

  • sin–1 (–x) = – sin–1 x

  • tan–1 x + cot–1 x = π/2
  • sin–1 x + cos–1 x = π/2
  • cos–1 (–x) = π – cos–1 x
  • cot–1 (–x) = π – cot–1 x

Class 12 Maths Chapter 2 Inverse Trigonometric Functions

Topics contained in this chapter are Identifying the domain and finding the value of inverse trigonometric functions at a particular point, in addition to that, simplifying trigonometric expressions using the properties of inverse trigonometry are quite important and all of these have been covered under Class 12 Maths NCERT Solutions

Total Number of Questions: Class 12 maths chapter 2 inverse trigonometric functions contains a total of 52 questions out of which 20 are very simple to solve because they are formula-based sums, 18 are of a moderate level and 14 are tough questions.

Other study materials For Chapter 2

NCERT & Other study materials For Chapter 2 are given here. There are various study resources for students that can help them to grasp the knowledge of chapter 2.

  1. Online MCQ Test Chapter 2 Inverse Trigonometric Functions
  2. MCQs PDF Chapter 2 Inverse Trigonometric Functions
  3. NCERT Books For Chapter 2 Inverse Trigonometric Functions
  4. NCERT Exemplar Solutions For Chapter 2 Inverse Trigonometric Functions
  5. NCERT Exemplar Books For Chapter 2 Inverse Trigonometric Functions
  6. Revision Notes For Chapter 2 Inverse Trigonometric Functions
  7. RD Sharma Solutions For Chapter 2 Inverse Trigonometric Functions
  8. RS Aggarwal Solutions For Chapter 2 Inverse Trigonometric Functions
  9. HOTS Questions For Chapter 2 Inverse Trigonometric Functions

NCERT Solutions for Class 12 Maths Chapter 3 Matrices

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Class 12th maths chapter 3 Matrices is one of the most important chapters for class 12th board exams. It is very simple and interesting to study. It is related to the calculations of matrices in the form of addition, subtractions, multiplications, etc. This chapter requires a very focused mind, in order to solve questions you will need to read them thoroughly and then give special attention while solving the questions. 

However the solutions of matrices that we are giving here are very easy to understand, it will ease your process to comprehend the complex calculations.

Class 12 Maths Chapter 3 Matrices

Class 12 Maths NCERT Solutions comprises numerous interesting topics such as types of matrices, finding unknown quantities using equivalent matrices, and more, furthermore how to transpose matrices and subsequently find the inverse using various methods have been also explained.

Total No. of Questions: There are 78 questions in Class 12 maths chapter 3 matrices in which 36 are complex to answer, 14 are easy and 28 are intermediate problems.

Other study materials For Chapter 3

NCERT & Other study materials For Chapter 3 are given here. There are various study resources for students that can help them to grasp the knowledge of chapter 3.

  1. Online MCQ Test Chapter 3 Matrices
  2. MCQs PDF Chapter 3 Matrices
  3. NCERT Books For Chapter 3 Matrices
  4. NCERT Exemplar Solutions For Chapter 3 Matrices
  5. NCERT Exemplar Books For Chapter 3 Matrices
  6. Revision Notes For Chapter 3 Matrices
  7. RD Sharma Solutions For Chapter 3 Matrices
  8. RS Aggarwal Solutions For Chapter 3 Matrices
  9. HOTS Questions For Chapter 3 Matrices

Class 12 Maths NCERT Solutions Chapter 4 Determinants

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NCERT Class 12th Maths Chapter 4 Determinants solutions aid in solving the given 4 exercises and the questions of this chapter. Determinants are a scalar value that is a function of the square matrix. In this lesson, you will get to know about the definitions and meaning of determinants, their properties, application of determinants, etc.

The Solutions that we are providing here for the Determinants are extremely helpful to solve the questions mentioned in the NCERT Books of Class 12.

Details Of Class 12 Maths Chapter 4 Determinants

This chapter includes the following topics: Evaluating the determinants, proving expressions using the properties of determinants, finding the inverse of a matrix using minors, cofactors, and the adjoint of that matrix. Moreover finding the solution of a linear system of equations using matrices are topics that are covered under Class 12 Maths NCERT Solutions that are important from the board exam perspective.

Number of Questions in this chapter: Class 12 maths chapter 4 determinants have a total of 87 fabulous questions. 17 questions are pretty simple to answer because they are property-based, 30 are moderately difficult, and 40 are based on conceptual understanding that is meant to challenge a student’s thinking capability.

Other study materials For Chapter 4

NCERT & Other study materials For Chapter 4 are given here. There are various study resources for students that can help them to grasp the knowledge of chapter 4.

  1. Online MCQ Test Chapter 4 Determinants
  2. MCQs PDF Chapter 4 Determinants
  3. NCERT Books For Chapter 4 Determinants
  4. NCERT Exemplar Solutions For Chapter 4 Determinants
  5. NCERT Exemplar Books For Chapter 4 Determinants
  6. Revision Notes For Chapter 4 Determinants
  7. RD Sharma Solutions For Chapter 4 Determinants
  8. RS Aggarwal Solutions For Chapter 4 Determinants
  9. HOTS Questions For Chapter 4 Determinants

Class 12 Maths NCERT Solutions Chapter 5 Continuity and Differentiability

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Chapter 5 of NCERT Maths Textbooks starts with the introduction of the topic and the definition of continuity and differentiability. This chapter is the continuous study of differentiation of function which was in class XI. In this chapter, students get to know about the algebra of continuous function, definition and meaning of differentiability, derivatives of composite functions, derivative of implicit functions, the derivative of inverse trigonometric functions, exponential and logarithmic functions, etc.

It has a few concepts that are very difficult to solve but our NCERT Solutions For Class 12 Maths Chapter 5 can help you to solve them very easily. 

Important Formulas for NCERT Solutions Class 12 Maths Chapter 5

  • Chain Rule: df/dv = (dt/dx) * (dt/dx)

  • d/dx (sin-1x) = 1/√(1 - x2)
  • d/dx (cos-1x) = - 1/√(1 - x2)
  • d/dx (tan-1x) = 1/(1 + x2)
  • d/dx (cot-1x) = 1/(1 + x2)
  • d/dx (sec-1x) = 1/x √(1 - x2)

Class 12 Maths Chapter 5 Continuity and Differentiability

Topics Include: Proving the continuity of a function, and performing algebraic operations on continuous functions, are topics covered under Class 12 Maths NCERT Solutions. Other similar topics that are very important for exams: Finding the derivatives of composite, implicit, trigonometric, exponential, and logarithmic functions, differentiation of functions in parametric form, second-order derivatives, mean value theorem, etc.

Total No. of Questions in Class 12 maths chapter 5 continuity and differentiability has 144 that are spread among the given exercises. 80 are easy to solve because of formula-based sums, 35 are a bit more complicated, and 29 are difficult problems that require the great problem-solving skills of a student.

Other study materials For Chapter 5

NCERT & Other study materials For Chapter 5 are given here. There are various study resources for students that can help them to grasp the knowledge of chapter 5.

  1. Online MCQ Test Chapter 5 Continuity and Differentiability
  2. MCQs PDF Chapter 5 Continuity and Differentiability
  3. NCERT Books For Chapter 5 Continuity and Differentiability
  4. NCERT Exemplar Solutions For Chapter 5 Continuity and Differentiability
  5. NCERT Exemplar Books For Chapter 5 Continuity and Differentiability
  6. Revision Notes For Chapter 5 Continuity and Differentiability
  7. RD Sharma Solutions For Chapter 5 (Continuity & Differentiability)
  8. RS Aggarwal Solutions For Chapter 5 Continuity and Differentiability
  9. HOTS Questions For Chapter 5 Continuity and Differentiability

Class 12 Maths NCERT Solutions Chapter 6 Applications of Derivatives

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Chapter 6 Application of Derivatives introduces the learners to Finding the Rate of Change of a Quantity, Finding the Approximation Value, Finding the equation of a Tangent and Normal To a Curve, Finding Maxima and Minima, and Point of Inflection, Determining Increasing and Decreasing Functions, etc. In order to be well versed in these topics, students need to solve their questions. A few of them can be easily solved, but a few can be a little challenging to answer. 

Therefore, the NCERT Solutions for Chapter 6 is available here that will aid in answering those questions properly.

Class 12 Maths Chapter 6 Application of Derivatives

This Chapter Includes Topic: Class 12 Maths NCERT Solutions contains topics such as finding the rate of change of a particular quantity, determining if a function is increasing or decreasing, identifying the slope of a tangent, and using differentiation to approximate a number. Furthermore, this chapter also includes problems based on finding the maxima and minima of a function along with establishing the results of the first and second derivative tests.

The total number of Questions is 126 that are well-researched questions in the Class 12 maths chapter 6 application of derivatives. Out of these, 40 are short answer type simple problems, 75 are of moderate complexity and 11 are tough problems to answer, however, a good understanding of the subject can help students to answer the questions regardless of their difficulty levels.

Other study materials For Chapter 6

NCERT & Other study materials For Chapter 6 are given here. There are various study resources for students that can help them to grasp the knowledge of chapter 6.

  1. Online MCQ Test Chapter 6 Applications of Derivatives
  2. MCQs PDF Chapter 6 Applications of Derivatives
  3. NCERT Books For Chapter 6 Applications of Derivatives
  4. NCERT Exemplar Solutions For Chapter 6 Applications of Derivatives
  5. NCERT Exemplar Books For Chapter 6 Applications of Derivatives
  6. Revision Notes For Chapter 6 Applications of Derivatives
  7. RD Sharma Solutions For Chapter 6 Applications of Derivatives
  8. RS Aggarwal Solutions For Chapter 6 Applications of Derivatives
  9. HOTS Questions For Chapter 6 Applications of Derivatives

NCERT Solutions For Class 12 Maths Chapter Wise (Term 2)

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The term 2 Chapter Wise Solutions of Class 12 consists of Integrals, Application of Integrals, Differential Equations, Vector Algebra, 3D (Three Dimensional Geometry), Linear Programming, Probability. These chapters will be used to assess the students in CBSE Class 12 Term 2 Maths exam 2022. Term 2 will have the questions which students will have to solve manually. It will be short and long answer types of questions hence the candidates need to explain their answers in writing by using the steps-wise approach. 

Therefore, to score good marks in the CBSE Maths term 2 board exam candidates need to give intense practice to all the questions available in NCERT Class 12th Maths Textbooks from Chapters 7 to 13. For ease in practicing the questions, we have provided the NCERT Solutions Class 12 Mathematics for term 2 in a chapter-wise format.

Class 12 Maths NCERT Solutions Chapter 7 Integrals

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Chapter 7 Integrals is a topic of calculus where you can 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, etc. 

We have provided the solutions of integrals for all the questions available in the mathematics book of class 12. 

Class 12 Maths Chapter 7 Integrals

Class 12 Mathematics NCERT Solutions include subject matter such as finding the integral of a function using integration by substitution, partial fractions, parts, and by using trigonometric identities. Definite integrals, their limits, related properties, & the fundamental theorem of calculus are also available in this lesson. All the given topics in chapter 7 help students to uncover their potential of solving maths problems.

Class 12 maths chapter 7 integrals has a total of 271 questions. 115 are based on formulas, 40 are quite easy to solve and 116 are tough problems that can be solved by using the mathematical skills of a student.

Other study materials For Chapter 7

  1. Online MCQ Test Chapter 7 Integrals
  2. MCQs PDF Chapter 7 Integrals
  3. NCERT Books For Chapter 7
  4. NCERT Exemplar Solutions For Chapter 7
  5. NCERT Exemplar Books For Chapter 7
  6. Revision Notes For Chapter 7
  7. RD Sharma Solutions For Chapter 7 (Indefinite & Definite)
  8. RS Aggarwal Solutions For Chapter 7 (Indefinite & Definite)
  9. HOTS Questions For Chapter 7

Class 12 Maths NCERT Solutions Chapter 8 Applications of Integrals

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Chapter 8 of NCERT Class 8 maths textbook is Applications of Integrals. This chapter aids in knowing how to calculate the areas under simple curves, the area between lines, parabolas, etc. It can also be used to calculate the area of an enclosed figure. However, in order to do the above-given things, you have to know the Application of Integrals. To do so, practising the questions is ideal. Also, it plays a crucial role in class 12th mathematics examination so solve these questions as much as possible. 

For your convenience here we have given the download links of Application of Integrals class 12 NCERT solutions. 

Class 12 Maths Chapter 8 Application of Integrals

Class 12 Maths NCERT Solutions explains topics in detail, such as area bound by the curve of a function, area between two curves, and other associated miscellaneous examples.

There are a total of 39 problems in Class 12 maths chapter 8 application of integrals out of which 15 are easy, 8 are of intermediate level and 16 are quite challenging to answer.

Other study materials For Chapter 8

NCERT & Other study materials For Chapter 8 are given here. There are various study resources for students that can help them to grasp the knowledge of chapter 8.

  1. Online MCQ Test Chapter 8
  2. MCQs PDF Chapter 8
  3. NCERT Books For Chapter 8
  4. NCERT Exemplar Solutions For Chapter 8
  5. NCERT Exemplar Books For Chapter 8
  6. Revision Notes For Chapter 8
  7. RD Sharma Solutions For Chapter 8
  8. RS Aggarwal Solutions For Chapter 8
  9. HOTS Questions For Chapter 8

Class 12 Maths NCERT Solutions Chapter 9 Differential Equations

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Chapter 9 Differential Equations is a mathematical equation that relates to one or more functions and their derivatives. Differential equations are considered special because the solution of a differential equation is itself a function instead of a number. In this chapter, you will be able to study the basic concepts related to differential equations, the degree of a differential equation, the order of a differential equation, and many more. 

The solutions for this chapter have been given here to help you out while getting stuck on any question of differential equations in chapter 9 of Class 12 NCERT Maths.

Class 12 Maths Chapter 9 Differential Equations

Determining the order and degree of an equation, verifying the solution of a differential equation, and forming such an equation from the general solution, are the topics that have been covered under the Class 12 Maths NCERT Solutions. Solving a homogeneous and linear differential equation are other topics in this lesson that have the same importance to learn. 

Comprises a total of 113 problems in Class 12 maths chapter 9 differential equations that have varieties in terms of difficulty. 72 are challenging problems, 15 are simple to answer and 26 are of a moderate level.

Other study materials For Chapter 9

NCERT & Other study materials For Chapter 9 are given here. There are various study resources for students that can help them to grasp the knowledge of chapter 9.

  1. Online MCQ Test Chapter 9
  2. MCQs PDF Chapter 9
  3. NCERT Books For Chapter 9
  4. NCERT Exemplar Solutions For Chapter 9
  5. NCERT Exemplar Books For Chapter 9
  6. Revision Notes For Chapter 9
  7. RD Sharma Solutions For Chapter 9
  8. RS Aggarwal Solutions For Chapter 9
  9. HOTS Questions For Chapter 9

Class 12 Maths NCERT Solutions Chapter 10 Vector Algebra

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Vector Algebra is the 10th chapter of NCERT Class 12th Mathematics textbook. This chapter introduces the students to the algebra of vector quantities. It is an essential topic of mathematics, it also impacts the study of Physics. So students must focus on this chapter and solve their questions to get a good grasp on this topic. 

The given solutions will acquaint you with this topic in detail with solutions.

Class 12 Maths Chapter 10 Vector Algebra

Addition, multiplication, and laws of vector operations, section formula, computing the magnitude of vectors, vector projections, as well as dot and cross product, are the very important topics that form the building blocks of the students. Using Class 12 Maths NCERT Solutions can fasten the learning methods of students.

Class 12 maths chapter 10 vector algebra includes 63 sums distributed into 20 straightforward questions, 37 are intermediate level, and 6 are a bit complicated to answer.

Other study materials For Chapter 10

NCERT & Other study materials For Chapter 10 are given here. There are various study resources for students that can help them to grasp the knowledge of chapter 10.

  1. Online MCQ Test Chapter 10
  2. MCQs PDF Chapter 10
  3. NCERT Books For Chapter 10
  4. NCERT Exemplar Solutions For Chapter 10
  5. NCERT Exemplar Books For Chapter 10
  6. Revision Notes For Chapter 10
  7. RD Sharma Solutions For Chapter 10
  8. RS Aggarwal Solutions For Chapter 10
  9. HOTS Questions For Chapter 10

Class 12 Maths NCERT Solutions Chapter 11 Three Dimensional Geometry (3D)

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Chapter 11 Three Dimensional Geometry helps the students to study the direction cosines and direction ratios of a line joining two points, it also discusses the equations of lines and planes in space under different conditions, the angle between two lines, two planes, a line and a plane, the shortest distance between two skew lines and distance of a point from a plane, etc. 

3D has various applications or implementations in the real world and the field of mathematics. Therefore, we have given the NCERT Solutions for 3D. It has a very precise or to-the-point answer. All are explained in detail.

Important Formulas for NCERT Solutions Class 12 Maths Chapter 11

  • Direction cosines of a line joining two points A and B:

          (x2 - x1)/AB,(y2 - y1)/AB,(z2 - z1)/AB

where AB = √[(x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2]

  • cosθ = |[a1a2 + b1b2 + c1c2] / √(a1 + b1 + c1)2√(a2 + b2 + c2)2]|

where a1, b1, c1 and a2, b2, c2 are direction ratios and θ is the acute angle between the two lines.

Class 12 Maths Chapter 11 Three Dimensional Geometry

Topics Covered: Class 12 Maths NCERT Solutions includes topics related to finding the direction cosines of a line, determining the distance and angle between two lines, as well as writing the equation of a plane when different constraints are explained in an easy to understand manner. Moreover, the distance & angle between two planes together with the coplanarity of two lines are also discussed in this chapter lucidly.

Total Questions: Class 12 maths chapter 11 three dimensional geometry has 59 fantastic sums that can be split into 34 easy formula-based problems, 12 complexes, and 13 moderate level questions.

Other study materials For Chapter 11

NCERT & Other study materials For Chapter 11 are given here. There are various study resources for students that can help them to grasp the knowledge of chapter 11.

  1. Online MCQ Test Chapter 11
  2. MCQs PDF Chapter 11
  3. NCERT Books For Chapter 11
  4. NCERT Exemplar Solutions For Chapter 11
  5. NCERT Exemplar Books For Chapter 11
  6. Revision Notes For Chapter 11
  7. RD Sharma Solutions For Chapter 11
  8. RS Aggarwal Solutions For Chapter 11
  9. HOTS Questions For Chapter 11

Class 12 Maths NCERT Solutions Chapter 12 Linear Programming

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In this chapter, students get to know about Linear programming. Linear Programming is also known as L.P is the simplest way to solve complex optimizations in a simple manner. The complex relationship can be depicted through linear programming, and chapter 12 is all about these things. It helps you to understand how to simplify the relationship in simple terms. 

Here on this website, we have given the Linear Programming Solutions for all exercises. It is errorless and available free of cost. 

Class 12 Maths Chapter 12 Linear Programming

The given topics in this chapter aid students in Solving linear programming problems graphically, maximizing and minimizing a given equation, as well as using these concepts for various applications such as diet and manufacturing questions come under the Class 12 Maths NCERT Solutions.

There are a total of 31 questions in class 12 maths chapter 12 that are important for board examinations. Out of the total given questions, 14 are simple, 10 are slightly challenging and 7 are higher-order thinking questions.

Other study materials For Chapter 12

NCERT & Other study materials For Chapter 12 are given here. There are various study resources for students that can help them to grasp the knowledge of chapter 12.

  1. Online MCQ Test Chapter 12
  2. MCQs PDF Chapter 12
  3. NCERT Books For Chapter 12
  4. NCERT Exemplar Solutions For Chapter 12
  5. NCERT Exemplar Books For Chapter 12
  6. Revision Notes For Chapter 12
  7. RD Sharma Solutions For Chapter 12
  8. RS Aggarwal Solutions For Chapter 12
  9. HOTS Questions For Chapter 12

Class 12 Maths NCERT Solutions Chapter 13 Probability

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The probability chapter of class 12th is a little advancement from the class 11th probability lesson. In this chapter, you will be using the information you have acquired in class 11th such as conditional probability, properties of conditional probability, multiplication theorem on probability, multiplication rule of probability for more than two events, independent events, Baye’s theorem, etc. 

We have compiled here the solutions to exercises from the Probability chapter, which have explained the concept thoroughly.

Class 12 Maths Chapter 13 Probability

Class 12 Maths NCERT Solutions covers topics like conditional probability and its properties, applying the multiplication theorem on probability to sums, independent events, Bayes’ theorem, probability distribution, mean and variance of a random variable, Bernoulli trials, along with binomial distribution are covered.

Class 12 maths chapter 13 probability has 100 questions that are precisely curated according to the students' needs. 23 are simple to answer, 37 are of a moderate level and 40 are a bit tricky problems.

Other study materials For Chapter 13

NCERT & Other study materials For Chapter 13 are given here. There are various study resources for students that can help them to grasp the knowledge of chapter 13.

  1. Online MCQ Test Chapter 13
  2. MCQs PDF Chapter 13
  3. NCERT Books For Chapter 13
  4. NCERT Exemplar Solutions For Chapter 13
  5. NCERT Exemplar Books For Chapter 13
  6. Revision Notes For Chapter 13
  7. RD Sharma Solutions For Chapter 13
  8. RS Aggarwal Solutions For Chapter 13
  9. HOTS Questions For Chapter 13

NCERT Solutions

We hope you have learned something from the provided solutions. You can download NCERT Solutions here by clicking on the given links. These solutions are free of cost.

NCERT Exemplar for Class 12 Maths

NCERT Solutions for Class 12 Maths, class 12 maths NCERT solutions, Class 12 Maths NCERT Solutions PDF, NCERT Solutions For Class 12 Maths Chapter Wise, NCERT Class 12 Maths Solutions, ncert solutions for Class 12 maths in hindi, ncert solutions for Class 12 maths pdf, ncert solutions for Class 12 maths in hindi medium, ncert solutions for Class 12 maths hindi medium

NCERT Exemplar Class 12 Maths Solutions is a bit advanced in terms of questions level. Each chapter of class 12th mathematics exemplar consists of questions that challenge students’ learning of maths. Exemplar questions are developed keeping in mind the syllabus, it also enables candidates to practice more questions so that they can easily crack the board exams and competition level of exams.

NCERT Class 12th maths contains an equal number of chapters as available in the NCERT Exemplar Class 12 Maths textbooks. However, with the help of exemplar learners can have access to the quality problems. Those problems not only help in boosting the scores but make students more creative and analytical thinkers.

Unit wise weightage of CBSE Class 12 

NCERT Solutions for Class 12 Maths, class 12 maths NCERT solutions, Class 12 Maths NCERT Solutions PDF, NCERT Solutions For Class 12 Maths Chapter Wise, NCERT Class 12 Maths Solutions, ncert solutions for Class 12 maths in hindi, ncert solutions for Class 12 maths pdf, ncert solutions for Class 12 maths in hindi medium, ncert solutions for Class 12 maths hindi medium

CBSE Class 12th Mathematics has a total of 13 chapters out of which 7 chapters for term 1 exam and 8 chapters for term 2 exams. A good understanding of these chapters is important but knowing about their weightage is also crucial. Therefore, here we have provided the unit wise weightage for both the term examination. Go through the table to understand the marks weightage of each chapter of mathematics.

Unit wise weightage of CBSE Class 12 First Term

NCERT Solutions for Class 12 Maths, class 12 maths NCERT solutions, Class 12 Maths NCERT Solutions PDF, NCERT Solutions For Class 12 Maths Chapter Wise, NCERT Class 12 Maths Solutions, ncert solutions for Class 12 maths in hindi, ncert solutions for Class 12 maths pdf, ncert solutions for Class 12 maths in hindi medium, ncert solutions for Class 12 maths hindi medium

In term 1 exam, questions were asked from 7 chapters all those chapters were taken from 5 units. Below you can check their unit names and mark weightage of those units.

Unit Unit Name Marks
1 Relations and Functions 08
2 Algebra 10
3 Calculus 17
5 Linear Programming 05
  Total 40
  Internal Assessment Marks 10
  Total Marks 50

Unit wise weightage of CBSE Class 12 Second Term

NCERT Solutions for Class 12 Maths, class 12 maths NCERT solutions, Class 12 Maths NCERT Solutions PDF, NCERT Solutions For Class 12 Maths Chapter Wise, NCERT Class 12 Maths Solutions, ncert solutions for Class 12 maths in hindi, ncert solutions for Class 12 maths pdf, ncert solutions for Class 12 maths in hindi medium, ncert solutions for Class 12 maths hindi medium

Calculus, Vectors, 3D, and Probability are the three units for term 2 exams. Questions in the 2nd term examination of CBSE Class 12th will be asked from these units. You can be thorough with their marks weightage from the below-given table.

Unit Unit Name Marks
3 Calculus 18
4 Vectors and Three-Dimensional Geometry 14
6 Probability 08
  Total 40
  Internal Assessment Marks 10
  Total Marks 50

NCERT Solutions For 12 Maths Chapter 1 to 13

NCERT Class 12 Maths Solutions is one of the major study materials for the board candidates and competitive exam aspirants. It enables the learners to develop a deeper understanding in the given topics in maths syllabus of class 12th.

Referring to the Class 12 NCERT Maths Solutions from Chapters 1 to 13 helps the students to cover their whole syllabus of mathematics without facing any issues.

There is a purpose behind giving these NCERT Solutions: to help students to become self-sufficient and successful in their life. So, to score better in the board papers and to learn the various methods to answer a mathematics question, refer to the above-given tables to access your NCERT Class 12 Maths Solutions in chapter wise manner.

Key Features of CBSE 12 NCERT Maths Solutions

  1. These NCERT Maths Solutions of class 12 are extremely helpful for the students wanting to revise their maths syllabus.
  2. It is available for free in PDF format so that you can learn and implement your learning in real life.
  3. It covers all the necessary information and formula related to the 12 Mathematics.

Why Class 12 Maths NCERT Solutions Important?

NCERT Solutions for Class 12 Maths, class 12 maths NCERT solutions, Class 12 Maths NCERT Solutions PDF, NCERT Solutions For Class 12 Maths Chapter Wise, NCERT Class 12 Maths Solutions, ncert solutions for Class 12 maths in hindi, ncert solutions for Class 12 maths pdf, ncert solutions for Class 12 maths in hindi medium, ncert solutions for Class 12 maths hindi medium

Mathematics in class 12th is one of the crucial subjects for students who opted for the science (PCM) stream. They need to solve every single question from each chapter of NCERT Class 12 Maths Book. 

However, because of the complex questions, they face difficulty in answering them. But the NCERT Solutions developed by the maths experts of Selfstudys help students to solve such questions without facing any difficulty.

Furthermore, these NCERT Solutions of class 12th maths aim to guide students to finish their syllabus faster. In addition to that, it assists them to develop a deeper knowledge of the given mathematics concepts. Class 12 Maths NCERT Solutions in Hindi can be referred by those students who have opted for the Hindi medium.

Those who practice maths questions by using the NCERT Maths Book Solutions can practice the important questions to prepare for the board exams so that they can score higher marks.

Scoring higher marks due to the NCERT Maths Solutions not only helps in board exams results but gives them the confidence to prepare for the national level competitive examinations such as JEE, BITSAT, and more.

The Class 12 Solutions prepared by the selfstudys subject experts facilitate the students to cover the whole exercise with answers. It not only helps in comprehending the topics and concepts easier but helps them to reduce their time spent on maths questions while revising. 

Eventually, Referring to the Maths Solutions of class 12 helps students to stay ahead in academics of their fellow students. Therefore, Class 12 Maths NCERT Solutions are considered Important - it help a lot in tackling the competition.

How To Solve NCERT Maths Questions With Ease?

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Including 12 Class Maths Chapters plus NCERT Exemplar Class 12 Maths 13 chapters become a total of 26 chapters to solve.

Solving these 26 chapters is not only important but it is the best to gather a deep knowledge of the advanced level of maths questions.

Since these questions of class 12 maths are of advanced level, students may find it difficult to answer. Therefore, here are the 3 simple yet most effective ways to solve NCERT Maths Questions With Ease:

  • Understand the Question Type

Direct numerical maths questions, Word Problems, and combined types of questions are available in class 12 mathematics. 

Therefore, firstly understand the questions types and try your best to answer them by using the appropriate formulas, law,s or concepts you have studied in NCERT Maths Books.

Having a good understanding of the questions types can ease your mind to initiate the process of finding the right methods to answer them.

  • Solve Them In Simple Steps

Math questions are solved ideally by breaking them down into simple steps. Doing this helps in a better understanding of the problem-solving approach.

It also assists students to plan the next steps they should take to reach accurate answers. 

  • Use NCERT Solutions, If Unable To Solve Maths Questions

Even after applying the above two tips, you might still face difficulty, but using Class 12 Maths NCERT Solutions will surely help you to answer the questions with ease. 

Because it is prepared by the experts who have broken down the questions and their answers into simple steps by applying the appropriate formula, laws, and concepts.

FAQ. On NCERT Solutions For Class 12 Maths

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There are a total of 13 Chapters in NCERT Solutions For Class 12 Maths. Both problems and their detailed solutions are provided in the Selfstudys NCERT Solutions for class 12th.

Getting a good score or high score in class 12th board exams are crucial for the students, because it plays an essential role to the students future career. Therefore, Solving NCERT Solutions for class 12 maths regularly is important. The solutions make sure that there is no doubt left to the students.

You can download the NCERT Solutions for class 12 maths from the Selfstudys website. These solutions are prepared by subject matter experts that ensure to give you a complete knowledge about the chapters and topics that are mentioned in the NCERT Class 12th Mathematics books. The solutions are available for free to download.

Yes, it is easier than class 11 maths. However, to answer the class 12th maths you must have a strong grip on basic and fundamentals of mathematics.

Yes, class 12 NCERT Maths is enough for the CBSE Board exams because the NCERT Class 12 Maths Books are prescribed by the CBSE board.

The best website for NCERT Solutions of class 12 maths is Selfstudys, because the solutions are prepared by our subject matter experts.

Very simple: Practice maths questions from NCERT Maths books, Previous Year Question Papers, and Sample Question Papers. You will be able to develop a good understanding of the exam pattern and the types of questions that are asked in the board exams. It will help you to score 90 or even more than that.

Chapters that come under Calculus are considered as tough chapters in Class 12 Maths. However, you can master this topic if you revise them multiple times and solve relevant questions often.

The very first thing to keep in mind is to pay attention to the prescribed syllabus. Go through all the chapters and solutions to have a better understanding of the subject. Then refer to the question papers to practice the actual board-level problems and solve them as much as possible.

The time you enjoy studying is the best time to study maths. Although, many students think they are more productive and focused in the nighttime. Therefore, try studying both day and night and check what time suits you better.

Yes, NCERT Maths textbooks are important for class 12 boards.

If you want to solve all the mathematics questions given in class 12 maths with ease then yes, NCERT Solution is enough for class 12 maths exam.

Yes, NCERT books are the officially prescribed textbooks and the syllabus is also followed by the NCERT Books and solutions so, yes all questions on board come from Class 12 Maths NCERT Solutions.

13 Chapters are there in NCERT 12 Maths.

None.

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