Relations and Functions Class 12 Mathematics Important Questions

Students can read the important questions given below for Relations and Functions Class 12 Mathematics. All Relations and Functions Class 12 Notes and questions with solutions have been prepared based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS. You should read all notes provided by us and Class 12 Mathematics Important Questions provided for all chapters to get better marks in examinations. Mathematics Question Bank Class 12 is available on our website for free download in PDF.

Important Questions of Relations and Functions Class 12

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

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

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

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

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!

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

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

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

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,…}

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