NCERT solution has published a solution book for 12 class maths so students can get prepare for their board exam as well as competitive exams like JEE and NEET. In the class 12 maths NCERT textbook, there are 13 chapters, in this book problems and solution of all 13 chapters provided. NCERT Book has got ready by the best teachers.
Chapters in NCERT solution book:
.Probability
. Relation and functions
. Linear programming
. Inverse trigonometric functions
. 3-dimensional geometry
. Matrices
. Vector algebra
. Determinants
.Differential equations
.Continuity and differentiability
. Application of integrals
. Application of derivatives
. Integrals
Chapter descriptions:
Probability: There are 5 exercises in the chapter probability
. Introduction
. Conditional probability and properties of conditional probability
.Multiplication theorem on probability
. Independents events
.Baye’s theorem, the partition of a sample space and theorem of total probability
. Random variables and its probability distributions, the probability distribution of random variables, Mean of random variable and variance of a random variable
. Bernoulli’s trials and binomial distribution, Bernoulli trials, and the binomial distribution.
Linear programming: There are 2 exercises in chapter linear programming
. Introduction
. Linear programming problem and its mathematical formulation
. Different types of linear programming problem
3-dimensional geometry: There are 3 exercises in chapter three-dimensional geometry.
. Introduction
. Direction cosines and direction ratios of a line, Relation between the direction cosines of a line and direction cosines of a line passing through two points
. Equation of a line in space, equation of a line through a given point and parallel to a given vector and Equation of a line passing through two given points
. The angle between two lines
.The Shortest distance between two lines, the distance between two skew lines and distance between parallel lines
. The plane, equation of a plane in normal form, equation of a plane perpendicular to a given vector and passing through a given point, equation of a plane passing through three non-collinear points, intercept form of the equation of a plane and plane passing through the intersection of two given planes
.Coplanarity of two lines
. Angles between two pints
. The distance of a point from a plane
. The angle between a line and a plane
Vector equations: There are 4 exercises in vector equations
. Introduction
. Some basic concepts
. Types of vectors
.Addition of vectors
. Multiplication of a vector by a scalar, components of a vector, vector joining two points and section formula
. Scalar product of two vectors, Projection of a vector on a line and vector product of two vectors
Differential Equations: There are 6 exercises in differential equations
. Introduction
. Basic concepts, Order of a differential equation and degree of a differential equation
. General and particular solutions of a differential equation
. Formation of a differential equation whose general solution is given and procedure to form a differential equation that will represent a given family of curves
. Methods of solving first order, first-degree differential equations, differential equations with variables separable, homogeneous differential equations and linear differential equations
Application of integrals: There are 2 exercises in the application of integrals
. Introduction
. The area under simple curves
. The area between two curves
Integrals: There are 11 exercises in integrals this is the 7th chapter of the NCERT textbook.
. Integrals
. Introduction
. Integration as an inverse process of differentiation
. Methods of integration
. Integrals of some particular functions
. Integrals by partial fractions
. Integration by parts
. Definite integral
. The fundamental theorem of calculus
. Evaluation of definite integrals by substitution
. Some properties of definite integrals
Applications of derivatives: There are 5 exercises in the application of derivatives
. Introduction
. Rate of change of quantities
. Increasing and decreasing functions
.Tangents and normals
.Approximations
. Maxima and minima
Continuity and differentiability: There are 8 exercises in-continuity and differentiability
. Introduction
. Continuity
.Differentiability
. Exponential and logarithmic functions
. Logarithmic differentiation
.Derivatives of functions in parametric forms
. Second-order derivative
. Mean value theorem
Determinants: There are 6 exercises in determinants
. Introduction
. Determinants, determinant of the matrix of order one, determinant of the matrix of order two, determinant of the matrix of order 3×3
. Properties of determinants
. Area of a triangle
. Minors and cofactors
. Adjoint and inverse of matrix and Adjoint of a matrix
. Applications of determinants and matrices and solution of a system of linear equations using the inverse of a matrix
Matrix: There are 4 exercises in Matrix
. Introduction
.Matrix and order of a matrix
. Types of matrices and equality of matrices
. Operations on matrices, Addition of matrices, Multiplication of a matrix by a scalar, Properties of matrix addition, properties of scalar multiplication of a matrix, Multiplication of matrices and properties of multiplication of matrices
. Transpose of a matrix and properties of the transpose of the matrices
. Symmetric and skew-symmetric matrices
.Elementary operation of a matrix
.Invertible matrices and the inverse of a matrix by elementary operations
Inverse trigonometric functions: There are 2 exercises in inverse trigonometric functions
. Introduction
. Basic concepts
. Properties of inverse trigonometric functions
Relations and functions: This is the 1st chapter in the NCERT textbook in this chapter there are 4 exercises
. Introduction
. Types of relations
. Types of functions
. Composition of functions and invertible function
. Binary operations
Chapter-wise important questions for class 12 maths:
. Probability
. Baye’s theorem and probability distribution
. Conditional probability and independent events
. Relation and functions
. Concept of relations and functions
. Binary operations
.Inverse trigonometric functions
. Inverse trigonometric functions
. 3-dimensional geometry
. Direction cosines and lines
. Plane
.Linear programming
. Linear programming
. Matrices
. Matrix and operations of matrices
. The inverse of a matrix by elementary operations
. Transpose of a matrix and symmetric matrix
. Vector algebra
. Algebra of vectors
. Dot and cross products of two vectors
. Determinants
. Expansion of determinants
. Properties of determinants
. The inverse of a matrix and application of determinants and
Matrix
. Differential equations
. Formation of differential equations
. The solution of different types of differential equations
. Continuity and differentiability
. Continuity
. Differentiability
. Application of derivatives
. Maxima and minima
. Tangents and normals
. Rate measure approximations and increasing-decreasing
Functions
. Integrals
.Types of integrals
