NCERT Solutions Class 12 Maths

Mathematics is one of the core subjects that is the lifeblood of Engineering and Technology. NCERT Solutions for Class 12 Maths provides a strong conceptual foundation for all of the topics covered in the CBSE Class 12 Maths Syllabus. It covers all of the major theorems and equations in detail to help students grasp them better. Any student who religiously solves all the questions given in the 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. We have included the chapter-wise PDF solution of NCERT Class 12 Mathematics in English in this article.

NCERT Solutions Class 12 Maths

NCERT Solutions for Class 12 Mathematics give a strong conceptual and numerical basis of all the topics included in the CBSE Class 12 Mathematics Syllabus. It covers all the important Concepts, theorems and formulae with brief understanding and explanations to make Learning Comprehensive.  In order to guarantee that students have a deeper conceptual understanding, the solutions cover all the key theorems and equations with thorough explanations.

According to Reuben Hersh, mathematics is a branch of science that deals with numbers, shapes, magnitudes and other numerical parameters to understand the universe. The NCERT solutions provide a composite learning experience and help 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 cover 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 Chapter-Wise

Class 12 Mathematics Syllabus includes a vast tract of concepts like Function and relation, Matrix and Determinant, Differentiation, Integration, and other diverse topics that make 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 functions, binary operations, the 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 illustrations of inverse functions will provide detail logical explanation.

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, the 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 real-life 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/hyperbolas, 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 equations of the type: dy/ dx + py = q, where p and q are functions of x or constants.

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, optimisation, and 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.

Benefits of Class 12 Maths NCERT Solutions

• We provides In-Depth Knowledge of each and every chapter and a brief Conceptual understanding of topics
• We focus on providing level playing fields in terms of Subject knowledge and give logical interpretation to students.
• NCERT solution is presented in a step-by-step solution of each problem, along with detailed videos for better understanding.
• A proper oversight mechanism for reviewing each solution and chapter that is 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 explanations by expert faculty.
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