CBSE CLASS 12
We provide world-class e-learning content for CBSE Class 12 students that helps them learn their subjects in the easiest and lively way. We focus on student problems and provide solutions in the best possible way. We cover all CBSE Class 12 related courses
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We also provide sample papers, solutions, articles on important topics and other study materials based on the latest syllabus of the Board “CBSE” for classes 11 and 12.
We have 3D animation videos, presentations, samples and documents based on the latest CBSE Board guidelines with features like simulation.
Our team has developed the content in such a way that it becomes interesting and easy to learn for both online and offline students.
Our focus is to provide exact and productive solutions, so that students can get effective points/marks in cost-effective time.
We are offering more courses for CBSE Class 11, CBSE Class 10, CBSE Class 9 and CBSE Classes 1-8.
Online and offline solutions for mathematics cbse class 12
maths cbse class 12 – we provide solutions for maths and other subjects.
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Few Concepts in details
(Note: To clearly understand the concept, please watch our respective 3D animated videos while reading this article, as the illustrations are based on that.)
function
Aim:
In this session we will understand the concept of function. We have plotted points on a graph paper. Points are given by their coordinates. (4, 5), (-5, 4), (-3.5, -4), etc.
We know that the first number gives us the x-coordinate, that is, the distance from the origin along the x-axis, and the second number gives us the y-coordinate, that is, the distance from the origin along the y-axis. That’s why if we change the order of the numbers, we get a different point. (4, 5) and (5, 4) are two different points. Such an arrangement of pairs of numbers where order must be maintained is called an ordered pair.
The vector product of two sets, AxB = {(a, b) I ae A and be B} To explore all the possibilities, let’s have two sets. Set A with five robots and set B with seven bicycles.
Now we match a robot with the bike matching its color.
Box I:Green robot with green bicycle. Blue robot with blue bike etc. In this box we find that each robot has only one bike to itself.
box 2: Let the orange bike be replaced with a light green bike.
Now we find that the orange robot does not have a bicycle of its own.
box 3:Take the light green and purple bikes and replace them with orange bikes. Matching sets again.
Now we find that the orange robot has two bicycles to himself. Thus we observe that in the first case each robot in set A has a bicycle to itself, and there are 2 spare bicycles. In the second case there is a robot without a matching bike and finally in the third case we have a robot that has more than one matching bike. These conditions lead us to the definition of a function.
A function is a subset of the vector product of two non-empty sets A and B, such that each element of set A has a unique image in set B.
The function is represented by lowercase letters, for example, Function f:A->B. The set A is called Domain and the set B Co domain. This further implies that no element of A can have more than one image in B. And there must also be no element of A that does not have an image in B. Mathematically it implies that no two ordered pairs will have the same first element.
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CBSE class 12
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