EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Relations and Mapping
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
If A =
{10,4,9}
and B =
{9,64,16,25,81,100}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is the square root of
b ∈ B
is
(i)
{(10,100),(9,81)}
(ii)
{(10,100),(4,16),(82,8)}
(iii)
{(10,100),(9,81),(16,4)}
(iv)
{(10,100),(4,16),(9,81)}
(v)
{(10,100),(4,16),(9,81),(16,4)}
Question
2
2.
If A =
{7,1,2,5,9,8}
and B =
{3,8,1,4,9}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is equal of
b ∈ B
is
(i)
{(1,1),(9,9),(9,7)}
(ii)
{(1,1),(9,9),(8,8),(2,2)}
(iii)
{(1,1),(9,9),(8,8),(4,4)}
(iv)
{(1,1),(9,9),(8,8)}
(v)
{(1,1),(8,8)}
Question
3
3.
If
f
(
x
)
=
(
6
x
+
4
)
and
g
(
y
)
=
(
2
y
+
8
)
, then find
f
(
1
)
,
g
(
1
)
(i)
11,11
(ii)
10,10
(iii)
7,8
(iv)
13,13
(v)
9,9
Question
4
4.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{4,3,7,9}
and B =
{1,2,8,5}
?
(i)
IV
(ii)
III
(iii)
I
(iv)
II
Question
5
5.
Which of the following relations is a function given ,
A =
{3,5,10,9,6}
and B =
{2,10,8,5}
?
(i)
{(3,2),(5,8),(10,10),(9,10),(6,10)}
(ii)
{(3,2),(5,8),(9,10),(6,10),(11,9)}
(iii)
{(3,2),(5,8),(10,10),(9,10),(6,10),(8,5)}
(iv)
{(3,2),(5,8),(9,10),(6,10)}
(v)
{(3,2),(10,10),(9,10),(6,10),(8,5)}
Question
6
6.
Let
f
:
R
→
R
be a function defined by given conditions
f
(
x
)
=
(
8
x
+
7
)
if
x
<
-7
f
(
x
)
=
(
9
x
+
3
)
if
-7
≤
x
≤
2
f
(
x
)
=
(
7
x
+
2
)
if
x
>
2
find
f
(
x
)
where x =
-12
(i)
-82
(ii)
-89
(iii)
-105
(iv)
-88
(v)
-90
Question
7
7.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{10,1,3,5}
and B =
{4,9,7,8,6,2}
?
(i)
{(10,7),(1,2),(5,2),(3,9)}
(ii)
{(10,4),(1,9),(5,4),(3,8)}
(iii)
{(3,6),(5,7),(5,9),(1,6)}
(iv)
{(10,2),(5,9),(1,2),(3,8)}
(v)
{(5,8),(3,4),(1,7),(10,6)}
Question
8
8.
Write the relation
R
:
A
→
B
in the given diagram,
where A =
{3,7,8}
and B =
{10,2,4,6,9}
(i)
{}
(ii)
{(7,10),(8,2),(7,9),(3,2),(3,6),(7,2),(8,4),(7,6),(9,7)}
(iii)
{(7,10),(8,2),(3,2),(3,6),(7,2),(8,4),(7,6),(9,7)}
(iv)
{(7,10),(8,2),(7,9),(3,2),(7,2),(8,4),(7,6)}
(v)
{(7,10),(8,2),(7,9),(3,2),(3,6),(7,2),(8,4),(7,6)}
Question
9
9.
Which of the following relations
R
:
A
→
B
represent a function,
given A =
{5,8,6}
and B =
{10,9,2}
?
(i)
II
(ii)
III
(iii)
IV
(iv)
I
Question
10
10.
If
f
(
x
)
=
(
6
x
+
3
)
and
g
(
x
)
=
(
9
x
2
+
5
x
+
2
)
,
find the value of
f
(
-6
)
+
f
(
-3
)
+
f
(
1
)
g
(
-3
)
+
g
(
1
)
+
g
(
4
)
(i)
(
-13
84
)
(ii)
(
-37
250
)
(iii)
(
-39
250
)
(iv)
(
-39
248
)
(v)
(
-41
250
)
Question
11
11.
If A =
{9,2,10,5}
and B =
{4,3,8}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is less than
b ∈ B
is
(i)
{(2,4),(2,8),(5,8),(3,2)}
(ii)
{(2,4),(2,3),(5,8)}
(iii)
{(2,4),(2,3),(2,8),(5,8),(3,2)}
(iv)
{(2,4),(2,3),(2,8),(5,8)}
(v)
{(2,4),(2,3),(5,8),(9,1)}
Question
12
12.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{8,5,1}
and B =
{10,3,6}
?
(i)
III
(ii)
IV
(iii)
II
(iv)
I
Question
13
13.
If A =
{k,h,s,d,r}
and B =
{f,b,p,o,n}
,
which of the following is relation
R
:
B
→
A
?
(i)
{(r,g),(k,g),(d,g),(s,g),(h,g)}
(ii)
{(g,d),(g,r),(g,k),(g,s),(g,h)}
(iii)
{(f,r),(b,s),(f,k),(f,h),(p,k)}
(iv)
{(b,g),(f,g),(o,g),(n,g),(p,g)}
(v)
{(d,n),(h,o),(s,o),(k,f),(d,b)}
Question
14
14.
Find the range of
f
:
Z
→
Z
where
f
(
x
)
=
(
x
+
2
)
and domain of
f
is
{x : -4 ≤ x ≤ 0}
(i)
{-2,-1,0,1}
(ii)
{-2,-1,1,2}
(iii)
{-2,-1,0,1,2}
(iv)
{-2,-1,0,2}
(v)
{-1,0,1,2,-3}
Question
15
15.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{5,1,8,7}
and B =
{4,2,6,9,10,3}
?
(i)
{(1,10),(8,4),(5,3),(7,10)}
(ii)
{(5,4),(8,10),(1,2),(7,9)}
(iii)
{(8,3),(1,9),(5,9),(7,6)}
(iv)
{(5,9),(7,4),(1,2)}
(v)
{(8,4),(5,9),(7,10),(1,3)}
Question
16
16.
Find the domain of the given relation.
(i)
{1,4,3,6,5}
(ii)
{6,1,4,3,5}
(iii)
{6,1,4,3}
(iv)
{9,5,10}
(v)
{1,3,6}
Question
17
17.
If A =
{7,3}
and B =
{1,10,8}
, find
A ✕ B
(i)
{(7,1),(7,10),(7,8),(3,1),(3,10),(3,8)}
(ii)
{(7,1),(7,10),(7,8),(3,1),(3,10),(3,8),(8,7)}
(iii)
{(7,1),(7,10),(3,1),(3,10),(3,8),(8,7)}
(iv)
{(7,1),(7,10),(7,8),(3,10),(3,8)}
(v)
{(7,1),(7,10),(7,8),(3,10),(3,8),(2,2)}
Question
18
18.
Find the co-domain of given relation diagram.
(i)
{1,3,8}
(ii)
{10,7,2,5,8}
(iii)
{10,7,2,5}
(iv)
{2,10,5,7}
(v)
{1,3,8,2}
Question
19
19.
If n(A) = 2 and n(B) = 2 then the number of possible relations from A → B is
(i)
13
(ii)
16
(iii)
18
(iv)
15
(v)
14
Question
20
20.
Find the cardinality of the given roster form,
where R =
{(3,9),(10,5),(3,2),(2,5),(9,9),(9,5)}
(i)
8
(ii)
7
(iii)
4
(iv)
5
(v)
6
Question
21
21.
If A =
{2,10}
and B =
{7,5}
, then
A ✕ B
is
(i)
I
(ii)
II
(iii)
IV
(iv)
III
Question
22
22.
Find the range of
f
:
Z
→
Z
where
f
(
x
)
=
(
4
x
2
+
3
x
−
2
)
and domain of
f
is
{x : 4 ≤ x ≤ 8}
(i)
{74,113,160,215,278}
(ii)
{74,160,215,278,112}
(iii)
{113,160,215,278,76}
(iv)
{74,113,215,278,158}
(v)
{74,113,160,278,216}
Question
23
23.
Find the range in given roster form,
where R =
{(9,8),(3,8),(3,6),(9,7),(3,7)}
(i)
{8,7,6,1}
(ii)
{8,6,7}
(iii)
{1,3,9}
(iv)
{9,3,6}
(v)
{7,6}
Question
24
24.
Which of the following relations does not represent a function
f
:
A
→
B
,
where A =
{c,g,a,k,b,l}
and B =
{m,f,d,h,j,e}
?
(i)
{(g,e),(l,j),(k,m),(c,f),(a,j),(b,m)}
(ii)
{(a,f),(b,e),(g,j),(k,h),(l,m),(c,h)}
(iii)
{(l,f),(c,e),(a,f),(g,d),(b,e),(k,e)}
(iv)
{(a,j),(c,d),(l,j),(b,f),(a,d),(g,f)}
(v)
{(a,j),(b,m),(c,d),(l,m),(g,j),(k,j)}
Question
25
25.
Which of the following are true?
a)
(a,b)
≠
{a,b}
b)
a
∈
(a,b)
c)
(a,b)
∈
{(a,b)}
d)
(a,b)
⊂
{a,b}
e)
(a,b) = (b,a)
(i)
{d,c,a}
(ii)
{d,c}
(iii)
{b,a}
(iv)
{a,c}
(v)
{e,b,a}
Assignment Key
1) (iv)
2) (iv)
3) (ii)
4) (iii)
5) (i)
6) (ii)
7) (iii)
8) (v)
9) (i)
10) (iii)
11) (iv)
12) (ii)
13) (iii)
14) (iii)
15) (iv)
16) (iii)
17) (i)
18) (i)
19) (iv)
20) (v)
21) (iii)
22) (i)
23) (ii)
24) (iv)
25) (iv)
