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NCERT Class 12- Mathematics: Chapter β 1 Relations and Functions Part 12
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
R = { (1,1) , (2,2) , (3,3) , (1,2) , (2,3) , (1,3) }
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 βΉ 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)