Patterns and Functions in Grade XII

Hello friends as I believe you have understood the previous topics. Today we are going to discuss about Patterns, relations, and functions which you have to face in grade XII. As you have heard these terms in your previous classes but today we will discuss them in detail. Firstly we will learn about pattern.

You all are familiar with the term algebra pattern, here we are to discuss about the number pattern especially in series. It will be well understood by an example.

Find the value of X in given series

20, 42 ,66, 92, X, 150, 182

For this type of series you just need to check the pattern and if you found the pattern then it is very easy to solve. Now for above problem

42 is greater than 20 by 22

66 is greater than 42 by 24

92 is greater than 66 by 26

Now you can check that the difference between the number is also in a pattern 22,24,26 and so on so next number in difference series will be 28 and X will be 92+28=120, and you solved the problem so you just need to find pattern then it is very easy. Now move to another example and find the advance pattern.

A group of lecturer were at a conference meeting. Every lecturer exchanges his class record with each additional lecturer who were there. If there were 11 lecturers how many class record were exchanged?

To solve this type of problem we just need to focus on number of class note exchanged so class notes will be exchanged=10+9+8+7+6+5+4+3+2+1=55

Number of class notes exchanged=55*2=110

This problem is little hard to understand but I don’t think it’s tough you just need to practice. Now let's move to function and relation.

If we denote relation by R. If R is the relation from set (C,D) and (C,D) belongs to R then we can say C is related to D under the relation of R. There are many types of relations which are as follows

identity Relations

The relation IB’on a set B is called identity relation on B, if IB = (x, y) | x = y

So it will be in identity only when x=y

Universal Relation

If a relation R is A*A than R in universal relation with A

Void Relation

As we know that null set is the sub set of every set so we can say that null set has a void relation with every set.

Reflexive relation

A relation R on a set B is called reflexive if (n, n) belongs to n in R for all n belongs to B

Symmetric relation

if any set (x,y) belong to R than (y,x ) will also belong to R

Transitive relation

If in a group two parameters are common and they are in a relation R then the other 2 parameters are in transtive relation

Now we will talk about functions

There are mainly 3 types of function

1. Injective Function

If we find the value of function at two parameters and value comes the same then it is called injective function

2. Surjective function

A function is said to be surjective only if its range lies within the domain

3. Bijective Function

A function is said to bijective only if it has the properties of injective and surjective. Also see Average Value of a Function.

This is all about patterns, relations, and functions and I hope that this article will help you in understanding this topic.

In upcoming posts we will discuss about Limits at Infinity in Grade XII and Line of best fit - least squares regression. Visit our website for information on 12th biology Maharashtra board syllabus