Question 8 - Case Based Questions (MCQ) - Chapter 1 Class 12 Relation and Functions

Last updated at April 16, 2024 by Teachoo

Question

Riya and Maya are two friends studying in the same class. While doing their mathematics project on Relation and Functions they have to collect the name of five metro cities and four cities other than metro cities of India; and present the name of cities in the form of sets. They have collected the names of cities and write the in the form of sets given as follows:
A = {Five Metro cities of India} = {Delhi, Mumbai, Bangalore, Calcutta, Pune}
B = {Bihar, Agra, Jaipur, Ahmedabad}

Question 1

How many functions exist from Set A to Set B?
(a) 512 (b) 1024
(c) 2048 (d) 254

Question 2

Riya wants to know how many relations are possible from set A to set B?
(a) 220 (b) 210
(c) 225 (d) 512

Question 3

Let R: A → A defined by R = {(
x, y
): Total number of vehicles in Delhi is less than total number of vehicles in Mumbai}. Then relation R is

(a) Reflexive
(b) Symmetric
(c) Both Reflexive and Symmetric
(d) Neither Reflexive nor Symmetric

Question 4

How many reflexive relations can be defined on set B?
(a) 25 (b) 210
(c) 412 (d) 212

Question 5

How many symmetric relations defined on set A?
(a) 25 (b) 210
(c) 215 (d) 26

Transcript

Question Riya and Maya are two friends studying in the same class. While doing their mathematics project on Relation and Functions they have to collect the name of five metro cities and four cities other than metro cities of India; and present the name of cities in the form of sets. They have collected the names of cities and write the in the form of sets given as follows: A = {Five Metro cities of India} = {Delhi, Mumbai, Bangalore, Calcutta, Pune} B = {Bihar, Agra, Jaipur, Ahmedabad}
Question 1 How many functions exist from Set A to Set B? (a) 512 (b) 1024 (c) 2048 (d) 254
Given
A = {Delhi, Mumbai, Bangalore, Calcutta, Pune}
B = {Bihar, Agra, Jaipur, Ahmedabad}
So, A has 5 elements, B has 4 elements
Numbers of functions from A to B = 4 × 4 × 4 × 4 × 4
= 45
= 1024
So, the correct answer is (b)
Question 2 Riya wants to know how many relations are possible from set A to set B? (a) 220 (b) 210 (c) 225 (d) 512
Given
A = {Delhi, Mumbai, Bangalore, Calcutta, Pune}
B = {Bihar, Agra, Jaipur, Ahmedabad}
Numbers of Relation from A to B
= 2Numbers of elements of A × Number of elements of B
= 25 × 4
= 220
So, the correct answer is (a)
Question 3 Let R: A → A defined by R = {(x, y): Total number of vehicles in Delhi is less than total number of vehicles in Mumbai}. Then relation R is (a) Reflexive (b) Symmetric (c) Both Reflexive and Symmetric (d) Neither Reflexive nor Symmetric
Given
R = {(x, y): Total number of vehicles in Delhi is less than total number of vehicles in Mumbai }
Check Reflexive
Since x is cannot be less than x (i.e. x < x is not possible)
∴ (x, x) ∉ R
∴ R is not reflexive
Check symmetric
To check whether symmetric or not,
If (x, y) ∈ R, then (y, x) ∈ R
If (x, y) ∈ R, then x < y
but (y, x) ∉ R as y < x is not true
∴ R is not symmetric
Thus, R is Neither Reflexive nor Symmetric
So, correct answer is (d)
Question 4 How many reflexive relations can be defined on set B? (a) 25 (b) 210 (c) 412 (d) 212
Given
B = {Bihar, Agra, Jaipur, Ahmedabad}
Number of reflexive relations if there are n elements
= 𝟐^(𝒏^𝟐 −𝒏)
Since B has 4 elements, putting n = 4
Number of reflexive relations = 2^(4^2 − 4)
= 2^(16 − 4)
= 𝟐^𝟏𝟐
So, the correct answer is (d)
Question 5 How many symmetric relations defined on set A? (a) 25 (b) 210 (c) 215 (d) 26
Given
A = {Delhi, Mumbai, Bangalore, Calcutta, Pune}
Number of symmetric relations if there are n elements
= 𝟐^((𝒏(𝒏 + 𝟏) )/𝟐 )
Since A has 5 elements, putting n = 5
Number of symmetric relations = 2^((5(5 + 1) )/2)
= 2^((5 × 6)/2)
= 𝟐^𝟏𝟓
So, the correct answer is (c)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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