CUET Mathematics MCQs Relations and Functions

Question : Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b , a,b∈ T.Then R is
a) equivalence
b) reflexive but not transitive
c) transitive but not symmetric
d) none of these
Answer : A

Question : If f : R → R be defined by f(x) = 2/x, x ∀ R, then f is
(a) one-one
(b) onto
(c) bijective
(d) f is not defined
Answer : D

Question : If f : R – {3/5} → R be defined by f (x) = 3x + 2/5x - 3 then
(a) f^–1(x) = f (x)
(b) f^–1(x) = –f (x)
(c) fof (x) = –x
(d) f^–1(x) = 1/19 f (x)
Answer : A

Question :  If f: R→ R given by f(x) =(3 − x³)^1/3, find f0f(x)
a) x
b) (3- x³)
c) x³
d) None of these
Answer : A

Question :  If A = {1,2,3}, B = {4,6,9} and R is a relation from A to B defined by ‘ x is smaller than y’. The range of R is
a) {4,6,9}
b) {1}
c) none of these
d) {1, 4,6,9}
Answer : A

Question :  Let us define a relation R in R as a Rb if a≥b .Then R is
a) reflexive, transitive but not symmetric
b) neither transitive nor reflexive but
c) an equivalence relation
d) symmetric ,transitive but not reflexive
Answer : A

Question : The maximum number of equivalence relations on the set A = {2, 3, 4} are
(a) 1
(b) 27
(c) 3
(d) 5
Answer : D

Question : Which of the following functions form Z into Z bijections?
(a) f (x) = x³
(b) f (x) = x + 2
(c) f (x) = 2x + 1
(d) f (x) = x² + 1
Answer : B

Question : If a relation R on the set {1,2,3}be defined by R={(1,2)} then R is
a) transitive
b) none of these
c) reflexive
d) symmetric
Answer : A

Question : Let f:R→R defined by f(x) = 3x. Choose the correct answer
a) ƒ 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 : A

Question : Let A ={1,2,3} 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) symmetric and transitive
c) reflexive but not transitive
d) neither symmetric nor transitive
Answer : A

Question : If f : R → R be the function defined by f (x) = x³ + 5, then f^–1(x) is
(a) (x + 5)^1/3
(b) (x – 5)^1/3
(c) (5 – x)^1/3
(d) (5 – x)
Answer : B

Question : Let A = {1, 2, 3, 4}. Let R be the equivalence relation on A × A defined by (a, b) R (c, d) if a + d = b + c. Then the equivalence class [(1, 3)] is
(a) {(1, 3)}
(b) {(2, 4)}
(c) {(1, 8), (2, 4), (1, 4)}
(d) {(1, 3) (2, 4)}
Answer : D

Question : The relation R = { (1,1),(2,2),(3,3)} on {1,2,3} is
a) an equivalence relation
b) transitive only
c) reflexive only
d) None of these
Answer : A

Question : If f : A → B and g : B → C be the bijective functions, then (gof)–1 is
(a) f^–1og^–1
(b) fog
(c) g^–1of^–1
(d) gof
Answer : A

Question : Let A = {1,2,3}. The number of equivalence relations containing (1,2) is
a) 2
b) 3
c) 4
d) None of these
Answer : A

Question : If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is
(a) reflexive
(b) transitive
(c) symmetric
(d) none of these
Answer : B

Question : Let f : N → R be the function defined by f (x) = 2x - 1/2 and g : Q → R be another function defined by g (x) = x + 2. Then (gof) 3/2 is
(a) 1
(b) – 1
(c) 7/2
(d) 3
Answer : D

Question : If the set A contains 7 elements and the set B contains 8 elements, then number of one-one and onto mappings from A to B is
(a) 24
(b) 120
(c) 0
(d) none of these
Answer : C

Question :  Let f:R→R defined by f(x) = x⁴. Choose the correct answer
a) f is neither one-one nor onto
b) f is oneone but not onto
c) f is many one onto
d) None of these
Answer : A