# 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)**