EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Relations and Mapping
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
Find the range of
f
:
Z
→
Z
where
f
(
x
)
=
(
6
x
2
+
x
−
9
)
and domain of
f
is
{x : -1 ≤ x ≤ 3}
(i)
{-4,-9,-2,48,18}
(ii)
{-4,-9,-2,17,48}
(iii)
{-4,-2,17,48,-7}
(iv)
{-9,-2,17,48,-5}
(v)
{-4,-9,-2,17,46}
Question
2
2.
If
f
(
x
)
=
(
8
x
+
5
)
and
g
(
x
)
=
(
x
2
+
3
x
+
2
)
,
find the value of
f
(
-6
)
+
f
(
-2
)
+
f
(
-3
)
g
(
-2
)
+
g
(
-3
)
+
g
(
4
)
(i)
(
-75
32
)
(ii)
(
-71
32
)
(iii)
(
-73
32
)
(iv)
(
-77
34
)
(v)
(
-23
10
)
Question
3
3.
Find the co-domain of given relation diagram.
(i)
{3,10,5,9,6}
(ii)
{2,4,6,1,5}
(iii)
{2,4,6,1}
(iv)
{6,4,1}
(v)
{3,10,5,9}
Question
4
4.
Which of the following relations is a function
f
:
A
→
B
,
where A =
{j,c,a,i,g,h}
and B =
{f,b,c,m,i}
?
(i)
{(j,f),(i,f),(a,b),(h,i),(g,f),(c,b),(b,a)}
(ii)
{(j,f),(i,f),(a,b),(h,i),(g,f),(c,b)}
(iii)
{(j,f),(i,f),(a,b),(g,f),(c,b)}
(iv)
{(j,f),(i,f),(h,i),(g,f),(c,b),(b,a)}
(v)
{}
Question
5
5.
If n(A) = 2 and n(B) = 2 then the number of possible relations from A → B is
(i)
14
(ii)
16
(iii)
12
(iv)
17
(v)
15
Question
6
6.
If A =
{5,10}
and B =
{1,8}
, then
A ✕ B
is
(i)
I
(ii)
III
(iii)
II
(iv)
IV
Question
7
7.
Write the relation
R
:
A
→
B
in the given diagram,
where A =
{9,2,10}
and B =
{5,4,8,3,7}
(i)
{(9,3),(10,8),(9,8),(10,3),(9,4),(10,4),(2,8)}
(ii)
{(9,3),(10,8),(10,3),(10,5),(9,4),(10,4),(2,8),(8,9)}
(iii)
{(9,3),(10,8),(9,8),(10,3),(10,5),(9,4),(10,4),(2,8),(8,9)}
(iv)
{(9,3),(10,8),(9,8),(10,3),(10,5),(9,4),(10,4),(2,8)}
(v)
{(9,3),(10,8),(9,8),(10,5),(9,4),(10,4),(2,8),(4,9)}
Question
8
8.
If A =
{g,m,a,p}
and B =
{i,b,j,r}
,
which of the following is relation
R
:
A
→
B
?
(i)
{(j,e),(i,d),(j,l),(i,k),(r,d)}
(ii)
{(g,d),(p,e),(a,d),(a,e),(a,l)}
(iii)
{(m,i),(a,j),(g,j),(a,b),(p,j)}
(iv)
{(b,a),(r,g),(i,a),(b,g),(b,p)}
(v)
{(l,m),(e,g),(k,a),(k,g),(k,p)}
Question
9
9.
If
f
(
x
)
=
(
9
x
+
1
)
, then find
f
(
3
)
(i)
28
(ii)
27
(iii)
25
(iv)
29
(v)
31
Question
10
10.
If
f
(
t
)
=
(
8
t
2
+
9
t
+
8
)
then find
f
(
8
x
+
5
)
(i)
(
515
x
2
+
712
x
+
253
)
(ii)
(
510
x
2
+
712
x
+
253
)
(iii)
(
511
x
2
+
712
x
+
253
)
(iv)
(
512
x
2
+
712
x
+
253
)
(v)
(
513
x
2
+
712
x
+
253
)
Question
11
11.
If A =
{7,2,6,4,1}
and B =
{3,7,2,10,9,4}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is equal of
b ∈ B
is
(i)
{(7,7),(2,2),(4,4),(10,10)}
(ii)
{(7,7),(2,2),(5,3)}
(iii)
{(7,7),(2,2),(4,4)}
(iv)
{(7,7),(2,2),(4,4),(1,1)}
(v)
{(7,7),(4,4)}
Question
12
12.
If A =
{7,8,20,40,9}
and B =
{10,5,3}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is a multiple of
b ∈ B
is
(i)
{(20,10),(20,5),(40,5),(9,3)}
(ii)
{(20,10),(20,5),(40,10),(40,5),(9,3)}
(iii)
{(20,10),(20,5),(40,5),(9,3),(11,39)}
(iv)
{(20,10),(40,10),(40,5),(9,3),(5,20)}
(v)
{(20,10),(20,5),(40,10),(40,5),(9,3),(5,20)}
Question
13
13.
Find the cardinality of the given roster form,
where R =
{(3,2),(7,2),(5,2),(3,3),(2,3)}
(i)
5
(ii)
4
(iii)
6
(iv)
7
(v)
2
Question
14
14.
Find the domain and range of the given relation
R
:
A
→
B
=
{(3,10),(3,1),(3,6),(2,10),(2,1),(2,6),(9,10),(9,1),(9,6),(5,10),(5,1),(5,6)}
(i)
A = {2,5,-1,12} , B ={17,14,1}
(ii)
A = {9,5,2,6} , B ={10,1,2}
(iii)
A = {5,2,9,7,6} , B ={7,10,5,6}
(iv)
A = {3,2,9,5} , B = {10,1,6}
(v)
A = {2,5,3,16} , B ={1,6,20}
Question
15
15.
Find the range in given roster form,
where R =
{(1,7),(6,5),(9,8),(4,5),(6,8)}
(i)
{1,6,9,4,7}
(ii)
{4,2,6,1,9}
(iii)
{7,5,8}
(iv)
{7,10,8,5}
(v)
{7,10,8,5,2}
Question
16
16.
Find the domain in the given roster form,
where R =
{(5,10),(5,3),(4,3),(8,6),(5,6)}
(i)
{6,10,7,3,1}
(ii)
{8,5,4,2,9,7}
(iii)
{8,5,4,2,9}
(iv)
{5,4,8}
(v)
{5,4,8,10}
Question
17
17.
If
f
:
A
→
B
is defined by
f
(
x
)
=
(
3
x
+
3
)
and A =
{8,10,6,7}
,
find the range
(i)
{24,33,46,21}
(ii)
{33,21,34,27}
(iii)
{19,27,21,33,-10,24}
(iv)
{27,33,21,24}
(v)
{24,33,21}
Question
18
18.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{1,7,10,2}
and B =
{5,9,8,4,6}
?
(i)
{(10,4),(7,5),(2,8)}
(ii)
{(10,8),(2,6),(1,6),(7,6)}
(iii)
{(1,5),(2,8),(10,6),(7,5)}
(iv)
{(2,8),(1,5),(7,5),(10,9)}
(v)
{(7,5),(10,4),(1,8),(2,5)}
Question
19
19.
If
f
(
x
)
=
(
3
x
+
2
)
and
g
(
y
)
=
(
6
y
+
4
)
, then find
f
(
1
)
,
g
(
2
)
(i)
7,19
(ii)
4,15
(iii)
2,13
(iv)
5,16
(v)
6,17
Question
20
20.
If A =
{3,8,10}
and B =
{9,6}
, find
A ✕ B
(i)
{(3,9),(3,6),(8,9),(10,9),(10,6),(7,7)}
(ii)
{(3,9),(3,6),(8,9),(10,9),(10,6)}
(iii)
{(3,9),(3,6),(8,9),(8,6),(10,9),(10,6),(9,8)}
(iv)
{(3,9),(3,6),(8,9),(8,6),(10,9),(10,6)}
(v)
{(3,9),(3,6),(8,6),(10,9),(10,6),(9,8)}
Question
21
21.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{5,9,10}
and B =
{8,3,7,6}
?
(i)
I
(ii)
III
(iii)
IV
(iv)
II
Question
22
22.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{9,2,7}
and B =
{3,10,6,1}
?
(i)
II
(ii)
I
(iii)
IV
(iv)
III
Question
23
23.
If A =
{10,4,8,9}
and B =
{36,30,16,6,7,3,5,12}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is a factor of
b ∈ B
is
(i)
{(10,30),(4,36),(4,16),(8,16),(9,36)}
(ii)
{(10,30),(4,36),(4,12),(8,16),(9,36),(16,4)}
(iii)
{(10,30),(4,36),(4,16),(4,12),(8,16),(9,36),(16,4)}
(iv)
{(10,30),(4,36),(4,16),(8,16),(9,36),(13,3)}
(v)
{(10,30),(4,36),(4,16),(4,12),(8,16),(9,36)}
Question
24
24.
Find the range of given relation diagram.
(i)
{6,1,2,4,8}
(ii)
{8,9,6}
(iii)
{9,8,7}
(iv)
{4,2,1,6}
(v)
{6,2,4}
Question
25
25.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{10,4,5,9,3}
and B =
{8,1,7,6}
?
(i)
{(3,1),(4,7),(10,6),(9,6),(5,8)}
(ii)
{(3,6),(5,8),(10,1),(9,6),(4,7)}
(iii)
{(5,6),(9,8),(3,8),(4,8),(10,1)}
(iv)
{(4,6),(3,1),(10,1),(9,1),(3,8)}
(v)
{(10,8),(5,8),(4,6),(3,6),(9,8)}
Assignment Key
1) (ii)
2) (iii)
3) (v)
4) (ii)
5) (v)
6) (iii)
7) (iv)
8) (iii)
9) (i)
10) (iv)
11) (iii)
12) (ii)
13) (i)
14) (iv)
15) (iii)
16) (iv)
17) (iv)
18) (i)
19) (iv)
20) (iv)
21) (iii)
22) (ii)
23) (v)
24) (iv)
25) (iv)
