# NCERT Class 12-Mathematics: Chapter – 1 Relations and Functions Part 12 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 29:

Consider the non-empty set consisting of children in a family and a relation R defined as if is brother of . Then R is

(A) Symmetric but not transitive

(B) Transitive but not symmetric

(C) Neither symmetric nor transitive

(D) Both symmetric and transitive

Answer: (B)

Question 30:

The maximum number of equivalence relations on the set are

(A)

(B)

(C)

(D)

Answer: (D)

Question 31:

If a relation R on the set be defined by , then R is

(A) Reflexive

(B) Transitive

(C) Symmetric

(D) None of these

Answer: (B)

Question 32:

Let us define a relation R in R as if . Then R is

(A) An equivalence relation

(B) Reflexive, transitive but not symmetric

(C) Symmetric, transitive but not reflexive

(D) Neither transitive nor reflexive but symmetric.

Answer: (B)

Question 33:

Let and consider the relation

.

Then R is

(A) Reflexive but not symmetric

(B) Reflexive but not transitive

(C) Symmetric and transitive

(D) Neither symmetric, nor transitive

Answer: (A)

Question 34:

The identity element for the binary operation defined on as is

(A)

(B)

(C)

(D) None of these

Answer: (C)

Question 35:

If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is

(A)

(B)

(C)

(D) None of these

Answer: (C)

Question 36:

Let and . Then the number of surjections from A into B is

(A)

(B)

(C)

(D) None of these

Answer: (B)

Question 37:

Let be defined by . Then is

(A) One-One

(B) Onto

(C) Bijective

(D) is not defined

Answer: (D)

Question 38:

Let be defined by and by . Then is

(A)

(B)

(C)

(D)

Answer: (A)