NCERT Solutions for Class 12 Maths has been written to help students like you who are appearing for different board exams as well as the JEE. It provides sound knowledge and understanding of all important concepts covered in each chapter in the Class 12 Maths NCERT textbook. There are 13 important chapters from the NCERT textbook. Both problems and their detailed solutions are provided. The solutions have been devised by India’s best teachers to help students grasp basic concepts better and faster.

NCERT Maths Class 12 Chapters are mentioned below:

Chapter 1 Relations and Functions

Chapter 2 Inverse Trigonometric Functions

Chapter 3 Matrices

Chapter 4 Determinants

Chapter 5 Continuity and Differentiability

Chapter 6 Application of Derivatives

Chapter 7 Integrals

Chapter 8 Application of Integrals

Chapter 9 Differential Equations

Chapter 10 Vector Algebra

Chapter 11 Three Dimensional Geometry

Chapter 12 Linear Programming

Chapter 13 Probability

TERM I  MCQ TYPES ( 2021 -2022)

Unit-I: Relations and Functions 1. Relations and Functions Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions. 2. Inverse Trigonometric Functions Definition, range, domain, principal value branch. Unit-II: Algebra 1. 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). 2. 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. 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. Unit-III: Calculus 1. 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. 2. 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). Unit-V: Linear Programming 1. 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).

TERM II MCQ TYPES (2021 -2022)

Unit-III: Calculus 1. 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  Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals. 2. Applications of the Integrals Applications in finding the area under simple curves, especially lines, parabolas; area of circles /ellipses (in standard form only) (the region should be clearly identifiable). 3. 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. Unit-IV: Vectors and Three-Dimensional Geometry 1. 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. 2. 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. Unit-VI: Probability 1. Probability Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution.