Relations and Functions Test

Result

Relations and Functions Test - 24

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Weekly Quiz Competition

Question 1
1 / -0

Let R be a relation on the set of integers given by aRb a = 2^k.b for some integer k. Then, R is

A
an equivalence relation

B
reflexive, but not symmetric

C
reflexive and transitive, but not symmetric

D
reflexive and symmetric, but not transitive

E
symmetric and transitive, but not reflexive
Question 2
1 / -0

Let W denote the words in the English dictionary. If in the relation R = {(x, y) ∈ W x W}, the words x and y have at least one letter in common, then R is

A
reflexive, symmetric and not transitive

B
reflexive, symmetric and transitive

C
reflexive, not symmetric and transitive

D
not reflexive, symmetric and transitive
Question 3
1 / -0

R₁ is a relation defined by R₁ = {(a, b)|, a b, a, b R}. R₁ is

A
an equivalence relation on R

B
reflexive, transitive, but not symmetric

C
symmetric, transitive, but not symmetric

D
neither transitive nor reflexive, but symmetric
Question 4
1 / -0

Set N of all natural numbers defines the relation R by aRb if and only if the GCD of a and b is 2. R is

A
reflexive, but not symmetric

B
symmetric only

C
reflexive and transitive

D
reflexive, symmetric and transitive

E
not reflexive, not symmetric and not transitive
Question 5
1 / -0

The inverse of the function y = is

A
log₁₀(2 – x)

B

C

D
Question 6
1 / -0

If,then

A
x = f(y)

B
f(1) = 3

C
y increases with x, for x < 1

D
f is a rational function of x
Question 7
1 / -0

Which of the following functions is an even function?

A
f(x) = x(x² – x⁴)

B
f(x) = sin(5x + x³)

C
f(x) = x² – 3x + 4

D
f(x) = x² +
Question 8
1 / -0

If f(x) = 2x - 6, then f(f(f(-2))) is equal to

A
-58

B
58

C
-64

D
84
Question 9
1 / -0

If , then is equal to

A

B

C

D
x
Question 10
1 / -0

Let R be relation over set N N and is defined by (a, b) R (c, d) a + d = b + c. the R is

A
reflexive only

B
symmetric only

C
transitive

D
equivalence
Question 11
1 / -0

^{_{Let L denote the set of all straight lines in a plane. If a relation R is defined by}},^{_{then R is}}

A
reflexive

B
symmetric

C
transitive

D
None of these
Question 12
1 / -0

If f : [1, ) [2, ) is given by f(x) = x + , then f ^–1(x) is equal to

A

B

C

D
1 +
Question 13
1 / -0

If [x] denotes the greatest integer f(x) = [x]and g(x) = |x|, then the value of is

A
2

B
-2

C
1

D
-1

E
0
Question 14
1 / -0

If the function f: R - {- b} → R - {1} be defined by f(x) = x + a/x + b (a ≠ b), then

A
f is both one-one and onto

B
f o f^-1(x) = x

C
f is one-one, but not onto

D
f is onto, but not one-one
Question 15
1 / -0

The inverse of the function is

A
log₁₀(2 – x)

B

C

D