Mathematics is one of the core subjects that is the lifeblood of Engineering and Technology. The NCERT Class 12 Maths book is the bible of mathematics for India students. The NCERT class 12 Maths subject contains all the relevant concepts and questions that a student must prepare in order to become expert in this field. Any students who religiously solves all the questions given in NCERT Maths book of class 12 will become a wizard of Mathematics. For that purpose, our experts have toiled hard to give the best solutions of NCERT class 12 Maths for the convenience of students. By going through these solutions, students will be able to understand each and every concept of NCERT Maths class 12. We have included the chapter-wise PDF solution of NCERT Class 12 Mathematics in Hindi and English in this article.
NCERT Solutions Class 12 Maths Updated 2023-24
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. In order to guarantee that students have a deeper conceptual understanding, the solutions cover all the key theorems and equations with thorough explanations. Students can use NCERT Solutions for Class 12 Maths to aid in their preparation for the upcoming 2023–2024 JEE Mains, BITSAT, VITEEE, and other undergraduate engineering entrance exams too.
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
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.
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
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).
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
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.
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).
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.
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).
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= ?(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
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.
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.
CBSE Class 12 Maths NCERT Solutions Unit-V: Linear Programming
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).
CBSE Class 12 Maths NCERT Solutions Unit-VI: Probability
Class 12 Chapter 13 Probability
Conditional probability, multiplication theorem on probability, independent events, total
probability, Bayes’ theorem, Random variable and its probability distribution.
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