# Mathematics

The students will learn the following chapters in CBSE class 12 Mathematics. Mathematics numerical problems solutions are provided in detail and can be viewed by clicking on the links provided. This page gives you an overview of various chapters in the class 12 Mathematics syllabus. There are two NCERT recommened books provided for CBSE class 12 Mathematics subject namely
1.
Mathematics Part – I
2.
Mathematics Part – II
Mathematics Part – I
1. Relations And Functions: This chapter focusses on the Types of Relations, Types of Functions, Composition of Functions and Invertible Functions and Binary Operations.

2. Inverse Trigonometric Functions: This chapter focuses on introduction to Iverse Trigonometric Functions, basic concepts and properties.

3. Matrices: In this chapter, the students will be able to learn about the introduction to matrices, definition, order of matrices, types, equality of matrices, operations like addition, multiplication by a scalar, properties of matrix addition, properties of scalar multiplication of a matrix, Transpose of a matrix, properties of transpose of a matrix, symmetric and skew symmetric matrices, elementary operation of transformation of a matrix, invertible matrices, inverse of a matrix by elementary operations.
4. Determinants: In this chapter, students will learn about determinants, properties of determinants, how to find the area of a triangle, Minors and Cofactors, Adjoint and Inverse of a matrix, applications of determinants and matrices, solution of system of linear equations using inverse of a matrix.

5. Continuity and Differentiability: In this chapter students learn about the concept of continuity, alzebra of continuous functions, differentiability, derivatives of composite functions, derivatives of implicit functions, derivatives of inverse trigonometric functions, exponential and logorithmic functions, logorithmic differentiation, derivatives of functions in parametric forms, mean value theorem.
i.
Continuity and Differentiability Exercise 5.1 Solutions
ii.
Continuity and Differentiability Exercise 5.2 Solutions
iii.
Continuity and Differentiability Exercise 5.3 Solutions
iv.
Continuity and Differentiability Exercise 5.4 Solutions
v.
Continuity and Differentiability Exercise 5.5 Solutions
vi.
Determinants Miscellaneous Exercise Solutions
6. Application of Derivatives: In this chapter, students will learn about rate of change of quantities, Increasing and decreasing functions, Tangents and Normals, Approximations, Maxima and Minima, maximum and minimum values of a function in a closed interval.
i.
Application of Derivatives Exercise 6.1 Solutions
ii.
Application of Derivatives Exercise 6.2 Solutions
iii.
Application of Derivatives Exercise 6.3 Solutions
iv.
Application of Derivatives Exercise 6.4 Solutions
v.
Application of Derivatives Exercise 6.5 Solutions
vi.
Determinants Miscellaneous Exercise Solutions
Mathematics Part – II

7. Integrals: In this chapter, students will get an introduction to integrals, learn about integration as an inverse process of differentiation, geometric interpretation of indefinite integral, some properties of indefinite integral, comparision between differentiation and integration, methods of integration, integration by substitution, integration using trigonometric identities, integrals of some particular functions, integration by partial fractions, integration by parts, Integral of the type {\displaystyle\int{e^{x}\displaystyle[f(x) + f'(x)]dx}} and few more types, Definite Integral, Definite integral as the limit of a sum, fundamental theorem of calculus, area function, first fundamental theorem of integral calculus, second fundamental theorem of integral calculus, evaluation of definite integrals by substitution and some properties of definite integrals.
i.
Integrals Exercise 7.1 Solutions
ii.
Integrals Exercise 7.2 Solutions
iii.
Integrals Exercise 7.3 Solutions
iv.
Integrals Exercise 7.4 Solutions
v.
Integrals Exercise 7.5 Solutions
vi.
Integrals Exercise 7.6 Solutions
vii.
Integrals Exercise 7.7 Solutions
viii.
Integrals Exercise 7.8 Solutions
ix.
Integrals Exercise 7.9 Solutions
x.
Integrals Exercise 7.10 Solutions
xi.
Integrals Exercise 7.11 Solutions
xii.
Integrals Miscellaneous Exercise Solutions
8. Application of Integrals: In this chapter, students will learn about area under simple curves, the area of a region bounded by a curve and a line and area between two curves.
i.
Application of Integrals Exercise 8.1 Solutions
ii.
Application of Integrals Exercise 8.2 Solutions
iii.
Application of Integrals Miscellaneous Exercise Solutions

9. Differential Equations: In this chapter, students will learn basic concepts of differential equations, degree of a differential equation, general and particular solutions of a differential equation, formation of a differential equation whose general solution is given, procedure to form a differential equation that will represent a given family of curves, differential equations with variables separable and Homogeneious differential equations.
i.
Differential Equations Exercise 9.1 Solutions
ii.
Differential Equations Exercise 9.2 Solutions
iii.
Differential Equations Exercise 9.3 Solutions
iv.
Differential Equations Exercise 9.4 Solutions
v.
Differential Equations Exercise 9.5 Solutions
vi.
Differential Equations Exercise 9.6 Solutions
vii.
Differential Equations Miscellaneous Exercise Solutions
10. Vector Algebra: In this chapter, students will learn some basic concepts of vector algebra, types of vectors, addition of vectors, multiplication of a vector by a scalar, components of a vector, vector joining two points, section formula, product of two vectors, scalar (or dot) product of two vectors, projection of a vector on a line, vector (or cross) product of two vectors.
i.
Vector Algebra Exercise 10.1 Solutions
ii.
Vector Algebra Exercise 10.2 Solutions
iii.
Vector Algebra Exercise 10.3 Solutions
iv.
Vector Algebra Exercise 10.4 Solutions
v.
Vector Algebra Miscellaneous Exercise Solutions

11. Three dimensional Geometry: In this chapter, students will get an introduction to the three dimensional geometry, direction of cosines and direction ratios of a line, relation between the direction cosines of a line, 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 \overrightarrow{b}, equation of a line passing through two given points, angle between two lines, shortest distance between two lines, distance between two skew lines, distance between parallel lines, 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, plane passing through the intersection of two given planes, coplanary of two lines, angle between two planes, angle between a line and a plane.
i.
Three dimensional geometry Exercise 10.1 Solutions
ii.
Three dimensional geometry Exercise 10.2 Solutions
iii.
Three dimensional geometry Exercise 10.3 Solutions
iv.
Three dimensional geometry Miscellaneous Exercise Solutions
12. Linear Programming: In this chapter, students will learn about linear programming problem and its mathematical formulation, mathematical formulation of the problem, graphical method of solving linear programming problems, different types of linear programming problems.
i.
Linear Programming Exercise 12.1 Solutions
ii.
Linear Programming Exercise 12.2 Solutions
iii.
Linear Programming Miscellaneous Exercise Solutions

13. Probability: In this chapter, students will learn about Conditional probability, properties of conditional probability, multiplication theorem on probability, independent events, Bayes’s theorem, Partition of a sample space, theorem of total probability, random variables and its probability distributions, probability distribution of a random variable, mean of a random variable, variance of a random variable, Bernoulli Trials and Binomial distribution.
i.
Probability Exercise 13.1 Solutions
ii.
Probability Exercise 13.2 Solutions
iii.
Probability Exercise 13.3 Solutions
iv.
Probability Exercise 13.4 Solutions
v.
Probability Exercise 13.5 Solutions
vi.
Probability Miscellaneous Exercise Solutions