Class 12

Adden On 2019-Jan-27
1 Books
(24 Reviews)
Class 12 Mathematics - CBSE
Relations and Functions
Relations and Functions edited


Integral is motivated by the problem of defining and calculating the area of the region bounded by the graph of the functions. In this Chapter, we shall confine ourselves to the study of indefinite and definite integrals and their elementary properties including some techniques of integration. In this chapter we will cover-
  • Introduction of Integrals
  • Integration as an Inverse Process of Differentiation
    • Geometrical interpretation of indefinite integral
    • Some properties of indefinite integral
    • comparison between differentiation and integration
  • Methods of Integration
    • Integration by substitution
    • Integration using trigonometric identities
  • Integrals of some Particular Functions
  • Integration by Partial Fraction
  • Integration by Parts
    • Integral of the type
    • Integral of some more types
  • Definite  Integral
    • Definite integral as the limit of a sum
  • Fundamental Theorem of Calculus
    • Area function
    • First fundametal theorum of integral calculus
    • Second fundamental theorum of integral calculus 
  • Evaluation of definite Integrals by Substitution
  • Some Properties of Definite Integrals
Differential Equations
In general, an equation involving derivative (derivatives) of the dependent variable with respect to independent variable (variables) is called a differential equation. In this chapter, we will study some basic concepts related to differential equation, general and particular solutions of a differential equation, formation of differential equations, some methods to solve a first order - first degree differential equation and some applications of differential equations in different areas.
  • Introduction
  • Basic Concepts
    • Order of a differential equation
    • Degree of a differential equation
  • General and Particular Solution of a Differential Equation
  • Formation of a Differential Equation whose General Solution is given
    • Procedure to form a differential equation that will repersent a given family of curves
  • Methods of Solving First Order,First Degree Differential Equations
    • Differential equations with variable separable
    • Homogeneous differential equations
    • Linear differential equations
Continuity & Differentiability
Continuity and Differentiability None
Differential Equations
Differential Equations None
Vector Algebra
In mathematics, physics and engineering, we come across two type of quantities:- Scalar quantities such as length, mass, time, distance, speed, area, volume, etc. Vector quantities like displacement, velocity, acceleration, force, weight, etc. In this chapter, we will study some of the basic concepts about vectors, various operations on vectors, and their algebraic and geometric properties. These two type of properties, when considered together give a full realisation to the concept of vectors, and lead to their vital applicability in various areas as mentioned above.
  • 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
    • 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 
Three Dimensional Geometry
In this chapter we will use vector algebra to three-dimensional geometry. The purpose of this approach to 3-dimensional geometry is that it makes the study simple. And also we shall study the direction cosines and direction ratios of a line joining two points and also discuss the equations of lines and planes in space under different conditions, an angle between two lines, two planes, a line and a plane, a shortest distance between two skew lines of a point from a plane. We shall also translate these results in the Cartesian form which, at times, presents a more clear geometric and analytic picture of the situation.
  • Introduction
  • Direction Cosince and Direction Ratios of a Line
    • Relations 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
    • Equation of a line passing through two given points
  • Angle between two Lines
  • Shortest Distance between Two Lines
    • Distance between skew lines
    • Distance between parallel lines
  • Plane
    • Equation of a plane in normal form
    • Equation of a plane perpendicular to a given vector and pssing 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
  • Coplanarity of Two Lines
  • Angle between Two Planes
  • Distance of a Point from a Plane
  • Angle between a Line and a Plane
In this chapter, we shall discuss the important concept of conditional probability of an event given that another event has occurred, which will be helpful in understanding the Bayes' theorem, multiplication rule of probability and independence of events. We shall also learn an important concept of random variable and its probability distribution and also the mean and variance of a probability distribution. In the last section of the chapter, we shall study an important discrete probability distribution called Binomial distribution.
  • Introduction
  • Conditional Probability
    • Properties of conditional probabilty
  • Multiplication Theorum on Probabilty
  • Independent Events
  • Baye's Theorum
    • Partition of a sample space
    • Theorum of total probabilty
  • 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
    • Bernoulli trials
    • Binomial distribution