CBSE Class 12 Mathematics Relations and Functions MCQs Set D

CASE STUDY:

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 B = {b₁,b₂,b₃} G={g₁,g₂} where B represents the set of boys selected and G the set of girls who were selected for the final race.
Ravi decides to explore these sets for various types of relations and functions

Question. Ravi wishes to form all the relations possible from B to G. How many such relations are possible?
a) 2⁶
b) 2⁵
c) 0
d) 2³
Answer: a

Question. Let R: B→B be defined by R = {(𝑥,𝑦): 𝑥 and y are students of same sex}, Then this relation R is_______
a) Equivalence
b) Reflexive only
c) Reflexive and symmetric but not transitive
d) Reflexive and transitive but not symmetric
Answer: a

Question. Ravi wants to know among those relations, how many functions can be formed from B to G?
a) 2²
b) 2¹²
c) 3²
d) 2³
Answer: d

Question. Let 𝑅: 𝐵→𝐺 be defined by R = { (b₁,g₁), (b₂,g₂),(b₃,g₁)}, then R is__________
a) Injective
b) Surjective
c) Neither Surjective nor Injective
d) Surjective and Injective
Answer: b

Question. Ravi wants to find the number of injective functions from B to G. How many numbers of injective functions are possible?
a) 0
b) 2!
c) 3!
d) 0!
Answer: a

CASE STUDY:

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.

Question. Let 𝑓: 𝑅→𝑅 be defined by 𝑓(𝑥)=𝑥² is_________
a) Neither Surjective nor Injective
b) Surjective
c) Injective
d) Bijective
Answer: a

Question. Let 𝑓:𝑁→𝑁 be defined by 𝑓(𝑥)=𝑥² is ________
a) Surjective but not Injective
b) Surjective
c) Injective
d) Bijective
Answer: c

Question. Let f: {1,2,3,….}→{1,4,9,….} be defined by 𝑓(𝑥)=𝑥² is _________
a) Bijective
b) Surjective but not Injective
c) Injective but Surjective
d) Neither Surjective nor Injective
Answer: a

Question. Let :𝑁 →𝑅 be defined by 𝑓(𝑥)=𝑥² . Range of the function among the following is _________
a) {1, 4, 9, 16,…}
b) {1, 4, 8, 9, 10,…}
c) {1, 4, 9, 15, 16,…}
d) {1, 4, 8, 16,…}
Answer: a

Question. The function f: Z→Z defined by 𝑓(𝑥)=𝑥² is__________
a) Neither Injective nor Surjective
b) Injective
c) Surjective
d) Bijective
Answer: a