Q.1. Let P = {(x, y) : x2+y2=1, x, y ∈ R}. Then, P is
(a) Reflexive
(b) Symmetric
(c) Transitive
(d) Anti-symmetric
Answer
Answer: (b)Q.2. Let S be the set of all real numbers. Then, the relation R = {(a, b) : 1 +ab > 0} on S is
(a) Reflexive and symmetric but not transitive
(b) Reflexive and transitive but not symmetric
(c) Symmetric, transitive but not reflexive
(d) reflexive, transitive and symmetric
Answer
Answer: (a)Q.3. The relation R = {(1,1), (2, 2), (3, 3)} on set {1, 2, 3} is:
(a) symmetric only
(b) reflexive only
(c) an equivalence relation
(d) transitive only
Answer
Answer: (b)Q.4. If R is a relation in a set A such that (a, a) ∈ R for every a ∈ A, then the relation R is called
(a) symmetric
(b) reflexive
(c) transitive
(d) symmetric or transitive
Answer
Answer: (b)Q.5. Let A = {1, 2, 3} and R={(1, 2), (2, 3)} be a relation in A. Then, the minimum number of ordered pairs may be added, so that R becomes an equivalence relation, is
(a) 7
(b) 5
(c) 1
(d) 4
Answer
Answer: (a)Q.6. Let f : R → R be defined as f(x) = x4, then
(a) f is one-one onto
(b) f is many-one onto
(c) f is one-one but not onto
(d) f is neither one-one nor onto
Answer
Answer: (d)Q.7. Let A={1, 2, 3} and B={a, b, c}, and let f = {(1, a), (2, b), (P, c)} be a function from A to B. For the function f to be one-one and onto, the value of P =
(a) 1
(b) 2
( c) 3
(d) 4
Answer
Answer: (c)Q.8. If
then f (x) is
(a) one to one and onto
(b) many to one and onto
(c) one to one and into
(d) many to one and into
Answer
Answer: (a)Q.9. The function F : R → R defined by f(x) = (x-1) (x-2) (x-3) is
(a) one-one but not onto
(b) onto but not one-one
(c) both one-one and onto
(d) neither one-one and onto
Answer
Answer: (b)Q.10. For real x, let f(x) = x3+5x+1, then
(a) f is one-one but not onto R
(b) f is onto R but not one-one
(c) f is one-one and onto R
(d) f is neither one-one nor onto R