CBSE Class 12 Mathematics Relations And Functions Worksheet Set C

Relation and Functions Case Study Questions

CASE STUDY 1:

A general election of Lok Sabha is a gigantic exercise. About 900 million people were eligible to vote and voter turnout was about 75%, the highest ever. Let I be the set of all citizens of India who were eligible to exercise their voting right in general election held in 2019. A relation ‘R’ is defined on I as follows:
R = {(𝑉1,2)∶ 𝑉1,𝑉2 ∈𝐼 and both use their voting right in general election – 2019}. Based on given information, answer the following questions
Q1) Is R a reflexive relation? Justify your answer. 
Q2) Is R a symmetric relation? Justify your answer. 
Q3) Is R a transitive relation? Justify your answer. 
Q4) Is R an equivalence relation? Justify your answer. 

CASE STUDY 2:

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes A i.e. A ={S, D} and B = {1,2,3,4,5,6}, based on given information, answer the following questions.
Q1) Let R : B ⟶ B be defined by R = {(x, y) : y is divisible by x}. Is R an equivalence relation? Justify your answer.
Q2 ) Raji wants to know the number of functions from A to B. How many number of functions are possible?

CASE STUDY 3:

An organization conducted bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let G={g₁,g₂} and B = {b₁,b₂,b₃} where B represents the set of boys selected and G the set of girls who were selected for the final race. based on given information, answer the following questions.
Q1) Ravi wishes to form all the relations possible from B to G. How many such relations are possible? 
Q2) Ravi wants to know among those relations, how many functions can be formed from B to G? 
Q3) Let R: B→B be defined by R = {(𝑥, 𝑦): 𝑥 and y are students of same sex}, then verify whether R is an equivalence relation? 

CASE STUDY 4:

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by 𝑦 = 𝑥². Answer the following questions using the above information.
Q1) Let 𝑓: 𝑅→𝑅 be defined by (𝑥)= 𝑥², then verify whether 𝑓 is a bijective function? 
Q2) Let 𝑓: N→R be defined by (𝑥)= 𝑥², then find the range of R? 
Q3) Let 𝑓: Z→R be defined by (𝑥)= 𝑥², Is f Injective function? Justify your answer?

Question. A relation R on set A = {1, 2, 3, 4, 5} is defined as R = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)} then R is _______________ relation
a) Reflexive
b) Symmetric
c) Transitive
d) Equivalence.
Answer : D

Question. Let R be the relation on set A = { x ∈ Z : x ≤ 20}, defined by R = {(a, b) : Ia - bI is a multiple of 3}, then [4], the equivalence class of 4, is
a) {0, 4, 8, 12, 16, 20}
b) {1, 4, 7, 10, 13, 16, 19}
c) {0, 1, 4, 7, 10, 13, 16, 19}
d) A
Answer : B

Question. If a relation R on the set {a, b, c, d} is defined as R = {(a, b)}, then R is _______________ relation
a) Reflexive
b) Symmetric
c) Transitive
d) simply a relation
Answer : C

Question. The function 𝑓:R → Z, defined as 𝑓(𝑥) = [𝑥] is (Z is set of integers)
a) neither one – one nor onto
b) one – one but not onto
c) onto but not one – one
d) one – one and onto
Answer : C

Question. The function 𝑓(𝑥) = 5 − |sin(4𝑥)| has maximum value ‘a’ and minimum value ‘b’, then (a, b) =
a) (4, 5)
b) (5, 4)
c) (5, 6)
d) (6, 5)
Answer : B

Question. The function 𝑓: R → R, given by 𝑓(𝑥) = |𝑥| is
a) Surjective
b) Injective
c) Bijective
d) neither surjective nor injective.
Answer : D

Question. A relation R on set A = {a, b, c} is defined as R = {(a, b), (b, b)} then R will be _______________ relation when (b, a) will be added
a) Reflexive
b) Symmetric
c) Transitive
d) Equivalence
Answer : B

Question. The function 𝑓: R → R, given by 𝑓(𝑥) = 3𝑥 + 2 is
a) Surjective
b) Injective
c) Bijective
d) neither surjective nor injective.
Answer : C

Question. The maximum number of equivalence relation on the set A = {a, b, c} are
a) 2
b) 3
c) 5
d) 6
Answer : D

Question. A relation R on set A = {a, b, c} is defined as R = {(a, b), (b, b), (c,c), (a, a)} then R will be _______________ relation when (b, a) will be added
a) Reflexive
b) Symmetric
c) Transitive
d) Equivalence.
Answer : D

Question. The function 𝑓:R → R, defined as 𝑓(𝑥) = [𝑥] + x is
a) neither one – one nor onto
b) one – one but not onto
c) onto but not one – one
d) one – one and onto
Answer : D

Please click the link below to download CBSE Class 12 Mathematics Relations And Functions (3).