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# NCERT Solutions Class 12 Maths

## NCERT Solutions Class 12 Maths (MATHEMATICS)

NCERT Solutions for Class 12 Mathematics gives a strong conceptual and numerical basis of all the topics included in CBSE Class 12 Mathematics Syllabus. It covers all the important Concepts, theorems and formulae with brief understanding and explanations to make Learning Comprehensive.

NCERT Solutions for Class 12 Mathematics Syllabus has been given in the links below. Students can access these solutions directly by clicking on the links given below. The pdf files given can also be downloaded and viewed at your convenience.

According to Reuben Hersh, mathematics is a branch of science that deals with numbers, shapes, magnitudes and other numerical parameters to understand universe. The NCERT solutions provide a composite learning and provides students to develop skills with logical reasoning. The difficult topics and concepts are simplified and explained in these solutions to make them easier. The NCERT Solutions not only covers the full CBSE syllabus but they are also enough to cover the basics and fundamentals of all the topics required in competitive exams such as JEE and other competitive examinations. The designed solutions can be easily understood by the students as they are provided in a simple language.

## NCERT Solutions for Class 12 Maths in English Free PDF Download

Class 12: Chapter 1 Relations and Functions

Class 12: Chapter 2 Inverse Trigonometric Functions

Class 12: Chapter 3 Matrices

Class 12: Chapter 4 Determinants

Class 12: Chapter 5 Continuity and Differentiability

Class 12: Chapter 6 Applications of Derivatives

Class 12: Chapter 7 Integrals

Class 12: Chapter 8 Applications of Integrals

Class 12: Chapter 9 Differential Equations

Class 12: Chapter 10 Vector Algebra

Class 12: Chapter 11 Three dimensional Geometry

Class 12: Chapter 12 Linear Programming

Class 12: Chapter 13 Probability

## NCERT Solutions for Class 12 Maths in Hindi Free PDF Download

कक्षा 12 गणित अध्याय 1. सम्बन्ध तथा फलन

कक्षा 12 गणित अध्याय 2. प्रतिलोम त्रिकोणमितीय फलन

कक्षा 12 गणित अध्याय 3. आव्यूह

कक्षा 12 गणित अध्याय 4. सारणिक

कक्षा 12 गणित अध्याय 5.  सततता तथा अवकलनीयता

कक्षा 12 गणित अध्याय 6. अवकलनों के अनुप्रयोग

कक्षा 12 गणित अध्याय 7. समाकलन

कक्षा 12 गणित अध्याय 8. समाकलनों के अनुप्रयोग

कक्षा 12 गणित अध्याय 9. अवकल समीकरण

कक्षा 12 गणित अध्याय 10. सदिश

कक्षा 12 गणित अध्याय 11. त्रिविमीय ज्यामिति का परिचय

कक्षा 12 गणित अध्याय 12. रैखिक प्रोग्रामन

कक्षा 12 गणित अध्याय 13. प्रायिकता

## NCERT Solutions for Class 12 Maths (Mathematics) Chapter-Wise

Class 12 Mathematics Syllabus includes vast tract of concepts like Function and relation, Metrix and Determinant, Differentiation, Integration, and other diverse topics that makes mathematics interesting and scoring in prominent examinations. The Detailed concepts are discussed below:

## Ncert Solutions Class 12 Maths Unit-I: Relations and Functions

1. ### Class 12 Chapter 1 Relations and Functions

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions. The composition of functions and invertible function, binary operations, Domain and Range of function and other miscellaneous examples.

1. ### Class 12 Chapter 2 Trigonometric Functions

Definition, range, domain, principal value branch. Glimpse of inverse trigonometric functions, properties of functions and the conceptual understanding of inverse functions. The graphs and illustration of inverse functions will provide detail logical explaination.

## Ncert Solutions Class 12 Maths Unit-II: Algebra

1. ### Class 12 Chapter 3 Matrices

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a   matrix, symmetric and skew symmetric matrices.

Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices, Invertible matrices; (Here all matrices will have real entries).

1. ### Class 12 Chapter 4 Determinants

Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Properties of Determinant. Adjoint and inverse of a square matrix. Solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

## Ncert Solutions Class 12 Maths Unit-III: Calculus

1. ### Class 12 Chapter 5 Continuity and Differentiability

Continuity and differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.

1. ### Class 12 Chapter 6 Applications of Derivatives

Applications of derivatives: increasing/decreasing functions, tangents and normals, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations).

1. ### Class 12 Chapter 7 Integrals

Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.

1. ### Class 12 Chapter 8 Applications of the Integrals

Applications in finding the area under simple curves, especially lines, parabolas; area of circles /ellipses/ hyperbola, parabola (in standard form only) (the region should be clearly identifiable).

1. ### Class 12 Chapter 9 Differential Equations

Definition, order and degree, general and particular solutions of    a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree of the type: dy/dx= 𝑓(y/x). Solutions of linear differential equation of the type:

dy/ dx + py = q

where p and q are functions of x or constant.

## Ncert Solutions Class 12 Maths Unit-IV: Vectors and Three-Dimensional Geometry

1. ### Class 12 Chapter 10 Vectors

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, multiplication of a vector by a scalar, 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.

1. ### Class 12 Chapter 11 Three-dimensional Geometry

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Distance of a point from a plane.

## Ncert Solutions Class 12 Maths Unit-V: Linear Programming

1. ### Class 12 Chapter 12 Linear Programming

Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems. graphical method of solution for problems in two variables, feasible and infeasible regions (bounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

## Ncert Solutions Class 12 Maths Unit-VI: Probability

1. ### Class 12 Chapter 13 Probability

Conditional probability, multiplication theorem on probability, independent events, total

probability, Bayes’ theorem, Random variable and its probability distribution.

## Benefits of ADDA247 NCERT Solutions

• Adda247 provides In-Depth Knowledge of each and every chapter and brief Conceptual understanding of topics.
• We focus on providing level playing fields in terms of Subject knowledge and gives logical interpretation to students.
• NCERT solution presented in Step-by-step solution of each problem along with their detailed videos for better understanding.
• Proper Oversight mechanism for reviewing the Each solution and chapter that approved by our Subject Matter Experts and only then updated, brings to you.
• Free PDF and videos on our YouTube channel for Classes 1 – 12 with detailed explanation by expertise faculty.
• We believe in quality content with simple and composite learning that brings you at the edge of success.

## Why you should trust Adda247 for Ncert Solutions Class 12 Maths

Adda247 provides most prominent, accurate and reliable information with in-depth knowledge that is verified by Subject Matter Experts provided expertise in particular subjects. Every solution in Adda247 that has been prepared and gone through a mechanism of creating to simplify then modify it to give a simple touch for conceptual and logical learning after that it is then verified by Subject Matter Experts later it presented to you that ensures the demand and need of students. In Adda247 there is a whole team that is dedicated towards content creating along with revising and reviewing then updating under the surveillance of experts.

### Best Subject Matter Experts For Ncert Solutions for Maths

Adda247 have one of the best Subject Matter Experts in our panel who review, decide, modify and approves each and every chapter-wise solutions before presented to you. These experts come along with great expertise and experience in their fields and gone through a proper process of validating quality content. The content we provided to our students interpreted through an integrated framework of multiple steps and simplification of content as we understands the demands of students, so that we provide then effective and efficient solution that makes learning easy and better understandable

### Chapter-wise Pdf Notes and Ncert Solutions with videos

At Adda247 we provide chapter-wise notes, conceptual videos and Question practice videos which are explained with detailed analysis and thorough understanding. We provide comprehensive notes by diverging chapters into topics and topics into sub-topics for clear understanding of students, which make our notes easy to catch and gives brief knowledge of concepts and logic behind the each and every topic.

## FAQ’S Related to Ncert Solutions Class 12 Maths

Yes, Adda247 strictly follow NCERT guidelines and solutions as provided by the CBSE Pedagogy curriculum. We update the syllabus as per NCERT and CBSE notification.

1. Is NCERT Mathematics enough for boards?

Yes, NCERT Mathematics enough for board and Adda247 provides clear conceptual understanding in their content.

1. Will I get complete syllabus notes for Mathematics Class 12 in Adda247?

Yes, at Adda247 we provide you with the complete syllabus of mathematics for Class 12, along with detailed notes, their solutions, and chapter pdf and important topics. We also provides videos for better understanding of concepts. For more videos, You can refer to our YouTube channel Adda247.

1. How many chapters are there in class 12th Mathematics?

There are total 13 chapters in class 12th Mathematics as given in the pdf of Syllabus of Adda247.

1. How can I score 100 Mathematics in CBSE Class 12?

You can score full marks in Math by doing practice daily and follow the strategy of Adda247 on their Youtube channel name as Adda247.

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