# NCERT Solutions for Class 12 Maths Pdf 2024-25 Free

These NCERT Solutions for Class 12 Maths serve as an indispensable guide for students navigating the complexities of this crucial academic milestone. NCERT Solutions for Class 12 Maths are Crafted meticulously to meet the curriculum requirements, these Class 12 Maths NCERT Solutions provide comprehensive explanations and step-by-step approaches to tackle every problem with confidence.

Seamlessly aligning with the NCERT Class 12 Mathematics syllabus, these 12 class maths NCERT solutions are tailored to meet the learning needs of students, ensuring a thorough understanding of concepts. Whether it’s delving into calculus, algebra, or geometry, the Class 12 Maths NCERT Solutions act as a beacon of clarity, illuminating the path towards academic excellence.

Dive into the realm of mathematics with the assurance of NCERT solved maths Class 12 solutions, where every query finds resolution and Clear your every concept. NCERT Solutions for Class 12 Maths serve as a roadmap, guiding students through these crucial points with clarity and precision. One such focal point is the thorough coverage of the NCERT Class 12 Mathematics syllabus, ensuring that no concept is left unexplored.

## NCERT Solutions for Class 12 Maths Chapterwise

Chapter Name | View/Download |
---|---|

Chapter 1: Relations and Functions | View/Download |

Chapter 2: Inverse Trigonometric Functions | View/Download |

Chapter 3: Matrices | View/Download |

Chapter 4: Determinants | View/Download |

Chapter 5: Continuity and Differentiability | View/Download |

Chapter 6: Application of Derivatives | View/Download |

Chapter 7: Integrals | View/Download |

Chapter 8: Application of Integrals | View/Download |

Chapter 9: Differential Equations | View/Download |

Chapter 10: Vector Algebra | View/Download |

Chapter 11: Three Dimensional Geometry | View/Download |

Chapter 12: Linear Programming | View/Download |

Chapter 13: Probability | View/Download |

## Key Features of NCERT Solutions for Class 12 Maths

- These solutions are tailored to make learning easy and enjoyable, aligning perfectly with the NCERT Class 12 Mathematics syllabus.
- They are very simple, each concept is explained in a clear and straightforward manner, making even the most complex topics easy to understand.
- Whether it’s calculus, algebra, or geometry, these solutions break down each chapter into bite-sized explanations and step-by-step solutions, ensuring that no concept remains elusive.
- They are easily available in both digital and print formats, students can access these solutions anytime, anywhere, making learning convenient and hassle-free.
- These Solutions are Crafted meticulously to align with the NCERT Class 12 Mathematics syllabus.
- These solutions serve as an invaluable resource for students seeking mastery over the subject.
- Class 12 Maths NCERT Solutions is their thoroughness, addressing every concept with precision and clarity.
- These NCERT Class 12 Maths Solutions increase students confidence among students, empowering them to tackle complex problems independently.

## CBSE Class 12 Mathematics syllabus

Chapter Name | Important Points to Study |
---|---|

Chapter 1: Relations and Functions | – Understand types of relations: reflexive, symmetric, transitive. |

– Learn about composite functions and their properties. | |

– Study types of functions: one-one, onto, and inverse functions. | |

Chapter 2: Inverse Trigonometric Functions | – Understand the properties of inverse trigonometric functions. |

– Learn to find the principal value of inverse trigonometric functions. | |

– Study the properties of trigonometric equations and their solutions. | |

Chapter 3: Matrices | – Learn about different types of matrices: square, symmetric, skew-symmetric. |

– Understand matrix operations: addition, subtraction, multiplication. | |

– Study the properties of determinants and their applications. | |

Chapter 4: Determinants | – Understand the properties of determinants and their applications in solving linear equations. |

– Learn how to find the inverse of a matrix using determinants. | |

– Study the properties of minors and cofactors. | |

Chapter 5: Continuity and Differentiability | – Understand the concepts of continuity and differentiability of functions. |

– Learn about the rules of differentiation: sum, product, quotient, chain rules. | |

– Study the applications of derivatives in finding tangents and normals. | |

Chapter 6: Application of Derivatives | – Understand the applications of derivatives in optimization and rate measures. |

– Learn about increasing and decreasing functions, maxima and minima. | |

– Study the concepts of mean value theorem and Rolle’s theorem. | |

Chapter 7: Integrals | – Understand the concept of integration and its properties. |

– Learn about different integration techniques: substitution, by parts, partial fractions. | |

– Study the applications of integrals in finding areas and volumes. | |

Chapter 8: Application of Integrals | – Understand the applications of integrals in finding areas under curves. |

– Learn about definite integrals and their properties. | |

– Study the concepts of mean value theorem for integrals and their applications. | |

Chapter 9: Differential Equations | – Understand the types of differential equations: ordinary, partial, linear, nonlinear. |

– Learn how to solve differential equations of first order and first degree. | |

– Study the applications of differential equations in various fields. | |

Chapter 10: Vector Algebra | – Understand the concept of vectors and their properties. |

– Learn about scalar and vector products of vectors. | |

– Study the applications of vectors in geometry and physics. | |

Chapter 11: Three Dimensional Geometry | – Understand the concepts of direction cosines, direction ratios, and lines in space. |

– Learn about planes and their equations in three-dimensional space. | |

– Study the concepts of distance and angle between two lines and two planes. | |

Chapter 12: Linear Programming | – Understand the concept of linear programming and its applications. |

– Learn about the graphical method and the simplex method for solving linear programming problems. | |

– Study the applications of linear programming in optimization. | |

Chapter 13: Probability | – Understand the concepts of probability and its axiomatic definition. |

– Learn about conditional probability and independence of events. | |

– Study the concepts of random variables and probability distributions. |

## Detailed Description of Each Chapter

Below is a detailed description of each chapter in the CBSE Class 12 Mathematics syllabus, along with what students learn and the importance of each chapter:

### Chapter 1: Relations and Functions

- Description: This chapter introduces students to the concepts of relations and functions. They learn about different types of relations such as reflexive, symmetric, and transitive relations, as well as various types of functions like one-to-one and onto functions.

- Importance: Understanding relations and functions is fundamental for higher-level mathematics and lays the groundwork for topics like calculus, algebra, and discrete mathematics.

### Chapter 2: Inverse Trigonometric Functions

- Description: In this chapter, students study inverse trigonometric functions such as arcsin, arccos, and arctan. They learn about the principal value branches, properties, and graphs of these functions.

- Importance: Inverse trigonometric functions are essential in solving trigonometric equations and have applications in fields like physics, engineering, and computer graphics.

### Chapter 3: Matrices

- Description: Matrices are arrays of numbers enclosed in brackets. Students learn about different types of matrices, operations on matrices (addition, subtraction, multiplication), properties of matrices, and determinants.

- Importance: Matrices have applications in various fields including computer graphics, quantum mechanics, and cryptography. Understanding matrices is crucial for solving systems of linear equations and linear transformations.

### Chapter 4: Determinants

- Description: Determinants are mathematical objects that are used to characterize square matrices. In this chapter, students study the properties of determinants, cofactors, and applications of determinants in solving systems of linear equations.

- Importance: Determinants play a key role in solving linear equations, finding inverses of matrices, and understanding geometric transformations. They are also used in calculus and differential equations.

### Chapter 5: Continuity and Differentiability

- Description: This chapter deals with the concepts of continuity and differentiability of functions. Students learn about limits, continuity, differentiability, and rules of differentiation.

- Importance: Understanding continuity and differentiability is essential for studying calculus. These concepts are used to analyze the behavior of functions and solve various mathematical problems.

### Chapter 6: Application of Derivatives

- Description: In this chapter, students learn about the applications of derivatives in optimization, finding tangents and normals, and solving related rates problems.

- Importance: The application of derivatives is widespread in various fields such as physics, economics, engineering, and biology. It helps in solving real-world problems involving rates of change and optimization.

### Chapter 7: Integrals

- Description: Integrals are mathematical objects that represent the area under a curve. Students learn about indefinite and definite integrals, integration techniques, and applications of integrals in finding areas and volumes.

- Importance: Integrals are fundamental in calculus and have applications in physics, engineering, economics, and statistics. They are used to solve problems involving accumulation and continuous change.

### Chapter 8: Application of Integrals

- Description: This chapter focuses on the applications of integrals in finding areas bounded by curves, areas between curves, and volumes of solids of revolution.

- Importance: The application of integrals is crucial for solving problems in geometry, physics, engineering, and economics. It helps in finding quantities such as areas, volumes, and centroids.

### Chapter 9: Differential Equations

- Description: Differential equations are equations that involve derivatives of unknown functions. Students learn about different types of differential equations, methods of solving first-order and linear differential equations, and applications of differential equations.

- Importance: Differential equations model various phenomena in science and engineering. They are used to describe rates of change and predict future behavior in areas such as physics, chemistry, biology, and economics.

### Chapter 10: Vector Algebra

- Description: Vectors are quantities that have both magnitude and direction. In this chapter, students study vectors and operations on vectors such as addition, subtraction, scalar multiplication, dot product, and cross product.

- Importance: Vector algebra is essential in physics, engineering, and computer science. It is used to represent physical quantities such as force, velocity, and displacement and to solve problems involving direction and magnitude.

### Chapter 11: Three Dimensional Geometry

- Description: This chapter deals with the study of points, lines, and planes in three-dimensional space. Students learn about direction cosines, direction ratios, equations of lines and planes, distance between two points, and angle between two lines or planes.

- Importance: Three-dimensional geometry is crucial for understanding spatial relationships and is applied in fields such as architecture, engineering, computer graphics, and navigation.

### Chapter 12: Linear Programming

- Description: Linear programming is a method used to find the best outcome in a mathematical model with linear relationships. Students learn about the formulation of linear programming problems, graphical and simplex methods for solving them, and applications of linear programming in real-life situations.

- Importance: Linear programming is used in operations research, economics, business management, and engineering to optimize resource allocation, production planning, transportation, and scheduling.

### Chapter 13: Probability

- Description: Probability is the measure of the likelihood that an event will occur. In this chapter, students learn about basic concepts of probability, conditional probability, independence of events, random variables, and probability distributions.

- Importance: Probability theory is widely used in various fields including statistics, finance, insurance, and gaming. It helps in making informed decisions under uncertainty and analyzing the outcomes of random experiments.

## Benefits of Solving NCERT Solutions for Class 12 Maths

Class 12 Mathematics NCERT solutions are designed to replicate the actual exam, providing students with a chance to practice in a similar environment. Some key benefits of class 12 mathematics NCERT solutions include:

**Exam Simulation Technique:** Studying Class 12maths NCERT solutions helps students become accustomed to the exam format, manage their time effectively, and handle exam pressure.

**Identify Strengths and Weaknesses:** By Solving NCERT solved maths class 12 Solutions, students can evaluate their performance, pinpoint areas needing improvement, and focus on their weaknesses. This process enhances their overall performance and leads to better results in the actual exam.

**Time Management Skills:** 12 class math solution are great for developing time management skills. Since most exams have strict time limits, practicing with class 12 mathematics solution teaches students to allocate their time wisely and complete the test within the given timeframe.

**Confidence Boost:** Performing well in 12 class NCERT solutions boosts students’ confidence. This increased confidence reduces stress and anxiety, making them feel more prepared for the actual board exam.

**Familiarity with the Exam Pattern**: 12th class math NCERT tests mirror the exam pattern, helping students get used to the format. This familiarity makes students feel more comfortable and less anxious during the actual CBSE Board exam.

## FAQs on NCERT Solutions for Class 12 Maths

**Q1: Where can students download ML Aggarwal Solutions for Class 9 Maths?Answer: **Students can access NCERT Solutions for Class 12 Maths both online and offline through links available on the our website. These solutions are prepared by highly experienced faculty members with extensive knowledge in their subjects, and they follow the current CBSE guidelines.

**Q2: How many chapters are in Class 12 Maths?Answer: **There are a total of 13 chapters in the Class 12 Maths book.

**Q3: What is the best source for Class 12 CBSE exam preparation?Answer: **NCERT books are the best study materials for Class 12 annual exam preparation. Memorizing concepts and important formulas just a few days before exams is not effective. Instead, students should consistently study and practice throughout the year. Besides NCERT Books, students can refer to other textbooks to practice additional problems. Completing sample papers and previous years’ question papers can help students become familiar with key concepts and the exam pattern.

**Q4: Is the CBSE Class 12 Maths difficult to score marks?Answer:** No, scoring marks in CBSE Class 12 Maths is not difficult. Students should focus on understanding the concepts and the steps to solve problems. Remembering these effectively will lead to better performance. We provide solutions from different authors to help students prepare accurately for their exams.

**Q5: Why is CBSE Class 12 Maths important in the board exams?Answer: **CBSE Class 12 Maths is important in board exams because it focuses on numerical formulas and theorems. If students understand the problems well, solving them in the exam becomes easy. Mastery of these concepts also helps students achieve good ranks in competitive exams.