WorksheetsRelations and Functions Quiz
Total questions: 26
Worksheet time: 13mins
If {1, 2, 3} and let R = {(1,1), (2,2), (3,3), (1,2), (2,1), (2,3), (3,2)}, Then R is:
Reflexive, symmetric but not transitive
symmetric, transitive but not reflexive
Reflexive and transitive but not symmetric
an equivalence relation
Let R be a relation defined on Z by aR b if a >= b, Then R is:
symmetric, transitive but not reflexive
Reflexive, symmetric but not transitive
Reflexive and transitive but not symmetric
an equivalence relation
Let R be a relation defined on Z as follows: (2,2) and (2,5) if a + b = 7, Then domain of R is:
{3, 4, 5}
{0, 3, 4, 5}
{0, 3, 4, 5, ±}
none of these
The relation R defined on the set {1, 2, 3, 4, 5} by {(a,b) : 16 - a^2 < b} is given by:
{(1,1), (2,1), (3,1), (4,1), (2,3)}
{(2,2), (3,2), (4,2), (2,4)}
{(3,3), (4,3), (5,4), (3,4)}
none of these
Let R be a relation defined on Z as follows: (x,y) if |x - y| <= 1. Then R is:
Reflexive and transitive
Reflexive and symmetric
Symmetric and transitive
an equivalence relation
Let {1, 2, 3} and {1, 4, 6, 9} and R is a relation from A to B defined by 'x is greater than y'. Then range of R is given by:
{1, 4, 6, 9}
{4, 6, 9}
{1}
none of these
A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by 'x is relatively prime to y'. Then the domain of R is given by:
{2, 3, 5}
{3, 5}
{2, 3, 4}
{2, 3, 4, 5}
In the set Z of integers, which of the following relation R is not an equivalence relation?
if xRy then x <= y
if xRy then x = y
if xRy then x - y is an even integer
if xRy then x mod 3 ≡ y
Let f and g be defined by f(x) = 2x^2 + 3 and g(x) = 4x - 5, then (f o g)(0) is:
20
25
40
10
Let f(x) = x and g(x) = x, then (f o g)(1) is given by:
0
1
1
2
Let the function f: R - {1} -> R - {1} be defined by f(x) = (ax + b)/(x + c), then:
f is one-one but not onto
f is onto but not one-one
f is both one-one and onto
none of these
The function f: [0, ∞) -> R given by f(x) = 1/(x + 1) is:
f is both one-one and onto
f is one-one but not onto
f is onto but not one-one
neither
The function given by f(x) = x/(x + 1) is:
f is both one-one and onto
f is one-one but not onto
f is onto but not one-one
neither one-one nor onto
Which of the following functions from Z to itself are bijections?
f(x) = 3x
f(x) = x + 2
f(x) = x + 21
f(x) = x^2 + x
If the function defined by f(x) = 2x^2 - 4x + 5 is a bijection, then B is:
R
[1, ∞)
[4, ∞)
[5, ∞)
The function defined by f(x) = (x - 1)(x - 2)(x - 3) is:
f is one-one but not onto
f is onto but not one-one
f is both one-one and onto
neither one-one nor onto
Let f(x) = 2x and g(x) = 2x. Then the solution set of the equation fog(x) = gof(x) is:
R
{0}
{0, 2}
none of these
If f(x) = 3x - 5, then f^(-1)(x):
is given by (x + 5)/3
is given by 5/3 + x
does not exist because f is not one-one
does not exist because f is not onto
The inverse of the function given by f(x) = e^x/(e^x - 1) is:
log(2x + 1)/x
log(2x + 2)/x
log(2x - 1)/x
none of these
Let f(x) = 1/(1 - x), then fofof(x) is:
x ∈ R
{1}
{0, 1}
none of these
Let f(x) = sin(x) and g(x) = 2, then:
fog(2) = π
fog(2) = π
hofog = hogof
hofog = hogof
If g(x) = 2x^2 + 2 and g(f(x)) = 2x - 5, then f(x) is equal to:
2x - 3
2x + 3
2x + 1
2x - 1
If f(x) = sin(x) and g(x) = sin(f(x)), then g(x) is given by:
1 - x
x
1 + x
x - 1
If the binary operation * on Z is defined by a*b = 2a^2 - 4ab + b, then value of (2 * 3) * 4 is:
233
33
55
-55
If * be a binary operation on R defined by a*b = a + b, then * is:
Commutative but not associative
Associative but not Commutative
Neither commutative nor associative
Commutative and associative
For the binary operation * defined on {-1, 1} by the rule a*b = a + b, the inverse of a is:
-a
1/a + 1
1/a
2/a
