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NCERT Maths 12th 2023 ( Maths Ncert Solutions class 12th )
Every Class 12 Board student understands the immense importance of the Class 12 Maths NCERT Solutions. It is well known that CBSE and other state boards prepare CBSE question papers primarily based on the NCERT Textbooks. If you are searching for complete NCERT Solutions, your search ends here. We at Shiksha provide the best Class 12th Math Solutions for Mathematics. Shiksha's NCERT solutions help students get all the questions with a strong conceptual understanding.
Why should you refer to Shiksha for Class 12 Math Solutions? Well, Shiksha offers error-free and well-structured solutions with a free downloadable PDF for offline study. You can use CBSE 12th Maths Chapter-wise Answers for multiple purposes. Shiksha also offers NCERT Notes for CBSE classes 11 and 12 for all subjects. Students can practice, make notes, resolve doubts, and revise effectively. Class 12 Maths includes several important topics, notably some topics such as Calculus, Matrices & Determinants, and Probability have significant weightage in Class 12 CBSE Board exams. You can cover these topics in detail through our Maths Class 12 Notes.
Class 12 NCERT Solutions for Mathematics are significant for CBSE Boards as well as Competitive Exams like JEE Main, MHT CET, and others. Shiksha’s 12th Maths NCERT Book Solutions are aligned with the latest CBSE 2026 syllabus. We offer accurate, to-the-point, and step-by-step explained solutions in a similar format to that provided in NCERT Textbooks. These Solutions include every exercise, question and formula, and concept required to get a good score in CBSE Board Exams.
Students appearing in competitive exams should refer to CBSE Class 12 NCERT Notes. These notes will help solve the Class 12 NCERT Maths, along with the NCERT Class 11 Maths Solutions, for better performance.
Shiksha covers all the Class 12 Maths Chapters, including important units like Calculus, Geometry and Algebra. We include all the problems with detailed and accurate solutions for all Class 12 Maths. Students should access the Class 12 Maths NCERT solutions PDF of all chapters for free. Check more information below;
| Important Related Links |
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|---|---|
- Download Chapter-wise Class 12 Math NCERT Solution PDF
- Download Chapter-wise Class 12 Math NCERT Solution PDF
- Class 12 Math NCERT solution: Chapters, Key Topics & More
- Class 12 Math NCERT Solution: unit-wise weightage
- Class 12 Mathematics NCERT Solutions FAQs
Download Chapter-wise Class 12 Math NCERT Solution PDF
In Class 12 Math Solutions, we have provided step-by-step explanations on our pages for all exercises, helping students understand concepts thoroughly. Students can access Chapter-wise NCERT Solutions for Class 12 Mathematics to make exam preparation easier. Students can access and Download Chapter-wise Class 12 Math Solution PDF for free by clicking on the respective links of the chapters below.
- 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
Download Chapter-wise Class 12 Math NCERT Solution PDF
In Class 12 Math Solutions, we have provided step-by-step explanations on our pages for all exercises, helping students understand concepts thoroughly. Students can access Chapter-wise NCERT Solutions for Class 12 Mathematics to make exam preparation easier. Students can access and Download Chapter-wise Class 12 Math Solution PDF for free by clicking on the respective links of the chapters below.
- 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 Math NCERT solution: Chapters, Key Topics & More
Students can check weightage, topics covered and related information for all chapters in class 12th mathematics below;
Class 12 Maths Chapter 1 Relations and Functions
This chapter lays the foundation for the whole algebra unit, along with calculus. Chapter 1 of Class 1 Maths deals with Relations and Functions, their definition, domain, range, and other properties important for board exams. The Relations and Functions have a weightage of around 8-10 marks in the CBSE 12th Boards. All these topics are covered in the NCERT Relations and Functions Solutions, check exercises and subtopics below;
Class 12 Relations And Functions Exercise-wise Topics
Check the topics covered as per the exercises included in the chapter.
| Exercises | Topics Covered |
|---|---|
| Exercise 1.1 | Type of Relations: Reflexive, Symmetric, Transitive, and Equivalence Relations. |
| Exercise 1.2 | Types of Functions: Many-one, One-one, Onto (Surjective), into, Bijective Functions. |
| Exercise 1.3 (Old NCERT) | Invertibility, Composite Functions, Binary Operations of Functions |
| Miscellaneous Exercise | Type of Relations, Functions, Invertible Functions, and Composition of Functions |
Students can also download Class 12 Relations and Functions Solutions PDF for free to practice at their speed, despite low or no internet. Click below to download;
Class 12 Math Chapter 1 Relation and Function Exercise-wise Solution PDF
Class 12 Maths Chapter 2 Inverse Trigonometric Functions
Inverse Trigonometric Functions carry around 6 marks in the class 12 Board Exams. Inverse trigonometric functions applications are important for other mathematics chapters, such as Calculus, Matrices, and others. Class 12 Math Chapter 2 focuses on the fundamental concepts of inverse trigonometric functions, their properties, domains, ranges, and principal values. This chapter also covers important identities of inverse trigonometric functions and their behavior through graphical representations. That's why Inverse Trigonometric Functions NCERT Solutions are also important for aspirants preparing for competitive exams like JEE, NDA.
Chapter 2 Inverse Trigonometric Functions Topics: Exercise-wise
| Exercises | Topics Covered |
|---|---|
| Exercise 2.1 | Definition of inverse trigonometric functions; Domain and Range, Principal Value, Principal value branches of ITFs (sin⁻¹x, cos⁻¹x, tan⁻¹x, cot⁻¹x, sec⁻¹x, and cosec⁻¹x), and Evaluation of ITF using principal Values |
| Exercise 2.2 | Properties, Use of Identitites, Simplification of ITF expressions, Solving ITF Equations |
| Miscellaneous | All the topics covered |
We offer free downloadable Class 12 Maths Chapter 2 ITF Solutions PDF, Students can access the PDF for offline study.
Class 12 Math Chapter 2 Inverse Trigonometric Function Exercise-wise Solution PDF
Class 12 Maths Chapter 3 Matrices
Chapter 3 Matrices is a very important topic as per its weightage in CBSE boards around 4-6 marks. Fundamental concepts of Matrices form the basis for various advanced concepts in algebra and calculus. Chapter 3 Matrices covers the definition and types of matrices, algebraic operations such as addition, subtraction, and multiplication, as well as key properties of matrix operations. Class 12 Matrices Solutions also discuss the transpose, determinant, and inverse of a matrix, along with elementary transformations. A matrix can be defined as an ordered rectangular array of numbers or functions. Matrices and Determinant combined are also significant for competitive exam such as JEE, NDA and others. Check key topics below;
Class 12 Chapter 2 Matrices Topics: Exercise-wise
| Exercise | Topics Covered |
|---|---|
| Exercise 3.1 | Introduction to Matrices, Types of Matrices |
| Exercise 3.2 | Operations on Matrices: Addition, Subtraction, Scalar Multiplication |
| Exercise 3.3 | Multiplication of Matrices, Properties of Matrix Multiplication |
| Exercise 3.4 | Transpose of a Matrix, Symmetric and Skew-Symmetric Matrices |
| Exercise 3.5 | Invertible Matrices and Proofs of Properties |
| Miscellaneous Exercise | All Topics of the Chapter |
Download the Matrices NCERT Solutions PDF through the below given link below, Students can use this PDF for study offline and clear their doubts whenever needed.
Class 12 Matrices Exercise-wise NCERT Solutions PDF
Class 12 Mathematics NCERT Solutions Chapter 4 - Determinants
A determinant is a scalar value that can be calculated from the elements of a square matrix. Students can use the NCERT Solutions for Determinants to understand the exercises thoroughly. They are advised to practice the NCERT Solutions Maths Class 12 to improve their speed of solving problems. We have provided the accurate solutions to all the exercises in this chapter.
Class 12 Chapter 4 Determinants: Exercise-wise Topics
| Exercise | Topics Covered |
|---|---|
| Exercise 4.1 | Introduction to Determinants, Determinant of a Square Matrix |
| Exercise 4.2 | Properties of Determinants |
| Exercise 4.3 | Area of a Triangle using Determinants |
| Exercise 4.4 | Minors, Cofactors, and Adjoint of a Matrix |
| Exercise 4.5 | Inverse of a Matrix using Adjoint Method |
| Exercise 4.6 | Solving System of Linear Equations using Matrix Method |
| Miscellaneous Exercise | All concepts of the chapter |
Candidates can access the free downloadable PDF. This PDF can be used in many ways, like practicing, resolving doubts, and others. Download by clicking on the link below;
Class 12 Determinants Exercise-wise NCERT Solutions PDF
Class 12 Maths NCERT solutions Chapter 5 - Continuity and Differentiability
In this chapter students will learn the important concepts of continuity, differentiability, relations between them, differentiation of inverse trigonometric functions, and exponential and logarithmic functions. The NCERT Solutions for Continuity and Differentiability of Class 12 Maths have been prepared as per the latest update on latest CBSE 2025 Syllabus. Students can use these solutions to strengthen their basics.
Class 12 Chapter 5 Continuity and Differentiability: Exercise-wise Topics
| Exercise | Topics Covered |
|---|---|
| Exercise 5.1 | Continuity of Functions at a Point and over an Interval |
| Exercise 5.2 | Differentiability of Functions and Relationship between Continuity and Differentiability |
| Exercise 5.3 | Derivatives of Composite Functions, Chain Rule |
| Exercise 5.4 | Derivatives of Inverse Trigonometric Functions |
| Exercise 5.5 | Exponential and Logarithmic Functions Differentiation |
| Exercise 5.6 | Logarithmic Differentiation |
| Exercise 5.7 | Derivatives of Functions in Parametric Form |
| Exercise 5.8 | Second Order Derivatives |
| Exercise 5.9 | Mean Value Theorem and Rolle's Theorem |
| Miscellaneous Exercise | Mixed problems covering all concepts from the chapter |
The NCERT Solutions PDF for Class 12 Maths Continuity and Differentiability chapter is available below, Aspirants can access the PDF for offline study.
Class 12 Continuity and Differentiability Exercise-wise NCERT Solutions PDF
Class 12 Maths NCERT solutions Chapter 6 - Application of Derivatives
Application of derivatives explains how the derivative can be used to find rate of change of quantities, finding the equations of tangent and normal to a curve at a point, to find turning points on the graph of a function which in turn will help us to locate points at which largest or smallest value (locally) of a function occurs. NCERT Solutions For Chapter 6 Application of Derivatives also discusses how to find intervals on which a function is increasing or decreasing and how to determine the approximate value of certain quantities. We have provided accurate solutions of the exercises of the chapter Application of derivatives.
Class 12 Chapter 6 Application of Derivatives: Exercise-wise Topics
| Exercise | Topics Covered |
|---|---|
| Exercise 6.1 | Rate of Change of Quantities |
| Exercise 6.2 | Increasing and Decreasing Functions |
| Exercise 6.3 | Tangents and Normals to Curves |
| Exercise 6.4 | Approximations using Differentials |
| Exercise 6.5 | Maxima and Minima of Functions |
| Miscellaneous Exercise | Application-based problems involving all concepts from the chapter |
Students can check the AOD Solutions in PDF format to
Class 12 Application of Derivatives Exercise-wise NCERT Solutions PDF
Class 12 Maths NCERT solutions Chapter 7 - Integrals
Chapter 7 Integrals, explains some indefinite and definite integrals and their elementary properties, including some techniques of integration. Integration is the calculation of an integral. There are so many formulas in this chapter that students have to learn thoroughly. Integration is a process that is the inverse of differentiation. Students should understand the basics of integrals and learn them thoroughly. Class 12 Integrals NCERT solutions will help students to understand the chapter.
Chapter 7 Integrals: Exercise-wise Topics
| Exercise | Topics Covered |
|---|---|
| Exercise 7.1 | Integration as Inverse Process of Differentiation |
| Exercise 7.2 | Methods of Integration: Substitution, Partial Fractions, and by Parts |
| Exercise 7.3 | Integration of Trigonometric Functions |
| Exercise 7.4 | Definite Integrals and their Properties |
| Exercise 7.5 | Evaluation of Definite Integrals using Substitution |
| Exercise 7.6 | Application of Definite Integrals in Calculating Area under Curves |
| Miscellaneous Exercise | Comprehensive problems covering all integration techniques |
Class 12 Integrals Solutions PDF is a very beneficial document for the students, providing possibility of offline study and doubt resolutions for all the NCERT problems.
Class 12 Integrals Exercise-wise NCERT Solutions PDF
Class 12 Maths NCERT solutions Chapter 8 - Application of Integrals
Application of Integrals explains how to determine the area under simple curves, area between lines and arcs of circles, parabolas and ellipses (standard forms), and the area bounded by the curves. This is a chapter of great importance for the Class 12 board exam. Students can expect 2-3 questions from this chapter for entrance exams too. We have provided detailed solutions of this chapter for free.
Exercise-wise Topics of Application of Integrals
| Exercise | Topics Covered |
|---|---|
| Exercise 8.1 | Area under Simple Curves |
| Exercise 8.2 | Area between Two Curves |
| Miscellaneous Exercise | Application-based problems involving area calculations using integrals |
The PDF Solutions for this chapter are available below, Students can access and download the PDF to practice and revise the chapter.
Class 12 Application of Integrals Exercise-wise NCERT Solutions PDF
Class 12 Maths NCERT solutions Chapter 9 - Differential Equations
An equation having derivatives of the dependent variable concerning the independent variables (variables) is known as a differential equation. In the chapter Differential Equations, students will learn some basic concepts related to differential equations, formation of differential equations, general and particular solutions of a differential equation, methods to solve a first-order - first-degree differential equation, and some applications of differential equations in different areas. NCERT Differential Equations Solutions includes five exercises and one miscellaneous exercise in this chapter.
| Exercise | Topics Covered |
|---|---|
| Exercise 9.1 | Basic Concepts of Differential Equations: Order and Degree |
| Exercise 9.2 | General and Particular Solutions of a Differential Equation |
| Exercise 9.3 | Formation of Differential Equations |
| Exercise 9.4 | Methods of Solving First-Order, Second- Order Differential Equations |
| Exercise 9.5 | Applications of Differential Equations in Real-life Problems |
| Miscellaneous Exercise | Mixed problems covering all concepts from the chapter |
Class 12 Differential Equations Exercise-wise NCERT Solution PDF
Class 12 Maths NCERT solutions Chapter 10 - Vectors Algebra
In this chapter, students will learn some of the basic concepts about vectors, various operations on vectors, and their algebraic and geometric properties. Vector algebra and 3D geometry have a weightage of 14 marks in the Class 12 board exam. This chapter has four exercises and one miscellaneous exercise. These NCERT Solutions for Vector Algebra Students have to learn this chapter thoroughly to score high marks in board exams and entrance exams.
Chapter 10 Vector Algebra: Exercise-wise Topics Covered
| Exercise | Topics Covered |
|---|---|
| Exercise 10.1 | Introduction to Vectors, Types of Vectors |
| Exercise 10.2 | Addition of Vectors, Multiplication of a Vector by a Scalar |
| Exercise 10.3 | Scalar (Dot) Product of Vectors |
| Exercise 10.4 | Vector (Cross) Product of Vectors |
| Miscellaneous Exercise | Comprehensive problems involving all vector operations |
Class 12 Math Vector Algebra NCERT Solutions PDF
Class 12 Mathematics NCERT solutions Chapter 11 - Three-Dimensional Geometry
In 3D Geometry, students will learn the direction cosines and direction ratios of a line joining two points, equations of lines and planes in space under different conditions, angle between two lines, two planes, a line and a plane, shortest distance between two skew lines and distance of a point from a plane. These NCERT Solutions for Chapter 11 3D Geometry include two exercises and one miscellaneous exercise in this chapter. We provide complete solutions of Three Dimensional Geometry which are prepared by experts.
Class 12 Maths 3D Geometry: Exercise-wise Topics
| Exercise | Topics Covered |
|---|---|
| Exercise 11.1 | Direction Cosines and Direction Ratios of a Line |
| Exercise 11.2 | Equation of a Line in Space |
| Exercise 11.3 | Angle between Two Lines, Shortest Distance between Two Lines |
| Exercise 11.4 | Equation of a Plane, Angle between Two Planes |
| Exercise 11.5 | Distance of a Point from a Plane |
| Miscellaneous Exercise | Application-based problems involving lines and planes in space |
Class 12 Three-Dimensional Geometry Solutions PDF
Class 12 Mathematics NCERT solutions Chapter 12 - Linear Programming
In this chapter, students will learn some linear programming problems and their solutions by the graphical method only. Linear programming has a weightage of 5 marks for the Class 12 board exam. We provide accurate solutions of this chapter in a detailed manner which are prepared by expert teachers. Students can refer to Linear Programming Class 12 Solutions of NCERT exercises to ensure getting 5 marks ofthis chapter in the exam.
Class 12 Maths Chapter 12 Linear Programming: Exercise-wise Topics
| Exercise | Topics Covered |
|---|---|
| Exercise 12.1 | Introduction to Linear Programming Problems (LPP) |
| Exercise 12.2 | Mathematical Formulation of LPP |
| Exercise 12.3 | Graphical Method of Solving LPP |
| Miscellaneous Exercise | Application-based problems involving optimization using LPP |
Class 12 Linear Programming NCERT Solutions PDF
Class 12 Mathematics NCERT solutions Chapter 13 - Probability
Probability can be defined as the likelihood of an event occurring. Probability is an important chapter that has a weightage of 8 marks for the Class 12 board exam. In chapter Probability, students will learn the important concept of conditional probability of an event given that another event has occurred, which will be helpful in understanding the Bayes' theorem, multiplication rule of probability and independence of events. This chapter also covers the concept of a random variable and its probability distribution, mean and variance of a probability distribution and the Binomial distribution. Probability class 12 NCERT solutions covers the following topics.
Class 12 Chapter 13 Probability: Exercise-wise Topics
| Exercise | Topics Covered |
|---|---|
| Exercise 13.1 | Conditional Probability |
| Exercise 13.2 | Multiplication Theorem on Probability |
| Exercise 13.3 | Independent Events |
| Exercise 13.4 | Bayes' Theorem |
| Exercise 13.5 | Random Variables and its Probability Distribution |
| Exercise 13.6 | Mean and Variance of a Random Variable |
| Miscellaneous Exercise | Comprehensive problems covering all concepts from the chapter |
Probability is one of the high-scoring topics, and most of the CBSE questions related to Probability are direct and formula-based. Students can download the below given Probability Solutions PDF and practice to get full marks.
Class 12 Math NCERT Solution: unit-wise weightage
Students must know the weightage of individual chapters of class 12 Maths in CBSE Boards and other competitive exams. Students can prioritize the revision and learning of concepts per the chapters' weightage out of 80 marks and the rest 20 marks are provided through the internal assessment. Students can check the check the weightage below fo each chapter;
| Unit | Chapter Name | Weightage (Marks) |
|---|---|---|
| Unit 1 Relations and Functions | Relations and Functions | 6-8 |
| Inverse Trigonometric Functions | 6-8 | |
| Unit 2 Algebra | Matrices | 8-10 |
| Determinants | 8-10 | |
| Unit 3 Calculus | Continuity and Differentiability | 6-8 |
| Applications of Derivatives | 8-10 | |
| Integrals | 12-14 | |
| Applications of Integrals | 4-6 | |
| Differential Equations | 4-6 | |
| Unit 4 Vectors and 3D Geometry | Vectors | 6-8 |
| Three-dimensional Geometry | 6-8 | |
| Unit 5 Linear Programming | Linear Programming | 4-6 |
| Unit 6 Probability | Probability | 8-10 |
| Total | 80 |
Class 12 Mathematics NCERT Solutions FAQs
Q 1. Which are the best books for CBSE Class 12 Maths board exam and JEE exam preparation?
A 1. NCERT books are the best books for CBSE board exams and JEE exam preparation. Students should learn the concepts using the NCERT books. Once they are thorough with the concepts in NCERT books, they can refer to other books available in the market. Students have to select the reference books wisely. To prepare for competitive exams like JEE Main, JEE Advanced etc., students must refer to other books also. Some of the recommended reference books for Class 12 Maths are Problems Plus in IIT Mathematics by A Das Gupta, 36 Years’ Chapter-wise Solved Papers by Arihant, IIT Mathematics by M.L. Khanna, and Class 11th & Class 12th Mathematics by R.D. Sharma. Course in Mathematics for IIT JEE by Tata McGraw Hill publications is another reference book.
Q 2. Which are the chapters covered in Class 12 Maths?
A 2. There are 6 chapters in NCERT Class 12 Maths Part 1. These include Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, and Application of Derivatives. NCERT Class 12 Maths Part 2 consists of Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Linear Programming, and Probability. Students have to thoroughly learn these chapters to achieve better results for the board exams as well as the entrance exams.
Q 3. Where can I find NCERT Class 12 Maths solutions?
A 3. We have provided NCERT Class 12 Maths solutions chapter-wise on this page. Students can click the links given on this page and check the Class 12 NCERT Maths solutions of the required chapters. The NCERT Class 12 Maths solutions are prepared by expert teachers. These solutions are given with explanations of each step. This will help students to understand the NCERT Maths Class 12 problems easily.
Q 4. How to score high marks in Class 12 Maths Board exam?
A 4. Maths is a subject which students have to give more attention to as compared to other subjects. Students should learn NCERT Class 12 Maths carefully to score high marks in the board exam. They should write and practice the Class 12 Maths problems. This will help students to avoid mistakes while appearing for the annual exam. It will also help them to improve their problem solving skills. They are advised to make short notes of Maths formulas and theorems. They can use these notes to have a quick revision before the exam. Revision is very important to score high marks.
Q 5. What is the weightage of the units in NCERT Class 12 Maths?
A 5. The individual weightage of units in NCERT Class 12 Maths are given below.
- Relations and Functions - 8 marks
- Algebra - 10 marks
- Calculus - 35 marks
- Vectors and Three Dimensional Geometry - 14 marks
- Linear Programming - 5 marks
- Probability - 8 marks
Students have to learn the NCERT Class 12 Maths Solutions thoroughly so as to score high marks in the board exams.
Q 6. Which unit has the maximum weightage in NCERT Class 12 Maths for CBSE board exam?
A 6. As per the course structure of 2024-25, the unit III - Calculus has the maximum weightage of marks. It has a weightage of 35 marks. There are 5 chapters under Calculus. They are Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, and Differential Equations. Students can expect high weightage questions from these chapters for JEE exams too.
Q 7. What is the marks distribution of Maths Class 12 for CBSE Theory exam and internal assessment?
A 7. According to the CBSE Maths Syllabus for Class 12, the theory exam is of 80 marks. Internal assessment carries 20 marks. The total marks for CBSE Class 12 Maths exam is 100. Students can score full marks in the Class 12 Maths exam by regular learning and hard work. They are recommended to learn and revise the NCERT solutions Maths Class 12.
Q 8. Which are the topics covered in Class 12 Maths Vector algebra?
A 8. Vector Algebra is an important chapter for the Class 12 Maths CBSE annual exam. It covers topics like Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector, Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, and multiplication of a vector by a scalar are covered in this chapter. Position vector of a point dividing a line segment in a given ratio, definition, geometrical interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors are also included in the chapter Vectors. Students can definitely expect questions from this chapter for entrance exams like JEE.
Q 9. Is it necessary to learn the exercises given in the NCERT Class 12 Maths textbook?
A 9. Yes, it is necessary to solve the examples and learn the exercises given in the NCERT Class 12 Maths textbook. It helps students to make the basics thorough. Practicing these solutions will help students to improve problem-solving skills. All the questions provided are solved by the subject experts in a detailed manner. Students are advised to revise and learn the NCERT Maths Class 12 solutions to score better marks.
Q 10. How to download the NCERT solutions Maths Class 12?
A 10. Students can click on the links given in the table on this page. We have provided chapter-wise solutions prepared by our experts. Students can click on the required links and navigate to the respective pages. They can find the NCERT solutions Maths Class 12 PDF download option on the landing page. Students can download and save the NCERT solutions Maths Class 12.
Q 11. What is the weightage of Probability in Class 12 Maths board exam?
A 11. Probability is an important chapter for Class 12 Maths which has a weightage of 8 marks for the CBSE board exam. Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, and mean of random variable are the topics covered in this chapter. Students can expect 2-3 questions from this chapter for board exams and other competitive exams. They are advised to make use of the solutions provided for Class 12 Maths Probability.
Maths Ncert Solutions class 12th Exam
Student Forum
Anything you would want to ask experts?Answered 2 months ago
The Magnitude of a vector by providing clear, step-by-step explanations using both algebraic formulas and geometric interpretation. For a vector? = xi? + yj? + zk? , the magnitude is calculated as:
Shiksha's NCERT Solutions provides explanation for
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Beginner-Level 5
Answered 2 months ago
NCERT Solutions for Class 12 Vector Algebra are prepared by our experts. Our NCERT SOlutions are fully updated according to the latest CBSE 2025 syllabus. NCERT Vector Algebra solutions cover all the revised textbook exercises, including essential concepts like types of vectors, magnitude and direct
E
Beginner-Level 5
Answered 2 months ago
As per the NCERT Textbooks, An orthogonal triad in vector algebra is a 3D cordinate point system where three vectors that are mutually perpendicular to each other, meaning the angle between each pair of vectors is 90°. These vectors are typically non-zero, linearly independent, and often form the ba
P
Beginner-Level 5
Answered 2 months ago
Students can access and download the NCERT Solutions for Class 12 Vector Algebra in free PDF format from our website Shiksha.com. We provide the NCERT Solutions PDF for free for all the chapter of class 12th including the chapter 10 Vector algebra. Students can visit the below link to download the P
A
Beginner-Level 5
Answered 2 months ago
Shiksha's NCERT Solutions for Class 12 Vector Algebra are designed by expert Math faculties. Our NCERT Vector Algebra Solutions provide step-by-step explanations for all NCERT textbook exercises. These Solutons covers topics of the chapter such as addition, scalar multiplication, and dot/cross produ
C
Beginner-Level 5
Answered 2 months ago
Shiksha provides solutions of class 11th and 12th chapters for all subjects NCERT textbooks. Our NCERT Solutions for Class 12 Differential Equations and other chapter aligne with the latest CBSE 2025 syllabus and exam pattern. We aso provide additional information related to the chapter including i
H
Beginner-Level 5
Answered 2 months ago
Class 12 Maths includes the chapter Differential Equations as a part of calculus unit. As per the formal NCER Definition, A differential equation is an equation that contains one or more derivatives of a dependent variable with respect to one or more independent variables.
For example:
Here,
J
Beginner-Level 5
Answered 2 months ago
Students must understand that a complete understanding of the topic can only come through solving all types of questions of the chapter in other words practice all exercises of the chapter. All exercises cover different types and levels of problems, including general and particular solutions, variab
A
Beginner-Level 5
Answered 2 months ago
We all are aware that all the quesstions asked in the CBSE Class 12 Board Exams are based on NCERT Textbooks. This information tells that if students only cover whole NCERT textbook it will enough for the boards. Shiksha's NCERT Solutions are more than sufficient for CBSE Board Exams as they cover a
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Contributor-Level 10
What kind of questions from Applications of Derivatives come in board exams?