EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Relations and Mapping
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
Find the cardinality of the given roster form,
where R =
{(6,3),(7,7),(2,3),(2,7)}
(i)
5
(ii)
2
(iii)
3
(iv)
6
(v)
4
Question
2
2.
If A =
{8,36,6,16,9}
and B =
{3,9,4}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is a multiple of
b ∈ B
is
(i)
{(8,4),(36,3),(36,4),(6,3),(16,4),(9,3),(9,9),(9,36)}
(ii)
{(8,4),(36,3),(36,9),(36,4),(6,3),(16,4),(9,3),(9,9),(9,36)}
(iii)
{(8,4),(36,3),(36,9),(36,4),(16,4),(9,3),(9,9)}
(iv)
{(8,4),(36,3),(36,9),(6,3),(16,4),(9,3),(9,9),(5,35)}
(v)
{(8,4),(36,3),(36,9),(36,4),(6,3),(16,4),(9,3),(9,9)}
Question
3
3.
If A =
{7,8,10,4}
and B =
{5,21,8,3,30,16,6,2}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is a factor of
b ∈ B
is
(i)
{(7,21),(8,8),(10,30),(4,8),(4,16),(16,8)}
(ii)
{(7,21),(8,8),(8,16),(10,30),(4,8),(4,16),(16,8)}
(iii)
{(7,21),(8,8),(8,16),(10,30),(4,8),(4,16)}
(iv)
{(7,21),(8,8),(8,16),(4,8),(4,16)}
(v)
{(7,21),(8,8),(8,16),(4,8),(4,16),(31,9)}
Question
4
4.
If A =
{8,5,9}
and B =
{64,100,81,49,25,4}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is the square root of
b ∈ B
is
(i)
{(8,64),(5,25),(9,81),(25,5)}
(ii)
{(8,64),(9,81),(25,5)}
(iii)
{(8,64),(5,25),(9,81)}
(iv)
{(8,64),(9,81)}
(v)
{(8,64),(5,25),(82,8)}
Question
5
5.
Find the domain and range of the given relation
R
:
A
→
B
=
{(10,4),(10,9),(7,4),(7,9)}
(i)
A = {3,10,8} , B ={8,10,9}
(ii)
A = {10,15} , B ={4,18}
(iii)
A = {8,12} , B ={-1,1}
(iv)
A = {10,7} , B = {4,9}
(v)
A = {7,4} , B ={4,7}
Question
6
6.
Find the co-domain of given relation diagram.
(i)
{5,1,7,9,4}
(ii)
{3,6,10,8}
(iii)
{3,6,10,8,7}
(iv)
{5,1,7,9,4,8}
(v)
{6,8,3}
Question
7
7.
Find the domain in the given roster form,
where R =
{(3,7),(2,9),(3,8),(2,8),(3,9)}
(i)
{3,2}
(ii)
{3,2,9}
(iii)
{4,3,2}
(iv)
{9,10,8,7}
(v)
{4,3,2,10}
Question
8
8.
Which of the following relations
R
:
A
→
B
represent a function,
given A =
{6,10,8}
and B =
{4,7}
?
(i)
IV
(ii)
I
(iii)
III
(iv)
II
Question
9
9.
If (
(
2
x
+
8
y
+
5
)
,
5
) = (
6
,
(
8
x
+
5
y
+
5
)
) then find (x,y)
(i)
(
(
-5
56
)
,
4
29
)
(ii)
(
(
-1
18
)
,
4
27
)
(iii)
(
(
-5
54
)
,
4
25
)
(iv)
(
4
27
,
(
-5
54
)
)
(v)
(
(
-5
54
)
,
4
27
)
Question
10
10.
If
f
(
t
)
=
(
5
t
2
+
4
t
+
6
)
then find
f
(
x
−
1
)
(i)
(
3
x
2
−
6
x
+
7
)
(ii)
(
5
x
2
−
6
x
+
7
)
(iii)
(
6
x
2
−
6
x
+
7
)
(iv)
(
8
x
2
−
6
x
+
7
)
(v)
(
4
x
2
−
6
x
+
7
)
Question
11
11.
Find the range of
f
:
Z
→
Z
where
f
(
x
)
=
(
3
x
2
+
6
x
−
3
)
and domain of
f
is
{x : -3 ≤ x ≤ 1}
(i)
{6,-6,-2}
(ii)
{6,-6,-5}
(iii)
{6,-3,-6}
(iv)
{-3,-6,5}
(v)
{6,-3,-4}
Question
12
12.
Which of the following statements are true if
f
:
A
→
B
and
a ∈ A
,
b ∈ B
?
a)
f
(
b
)
is called the image of
b
under
f
b)
f
(
a
)
is called the image of
a
under
f
c)
f
(
a
)
=
b
d)
f
(
b
)
=
a
(i)
{a,b}
(ii)
{d,c}
(iii)
{b,c}
(iv)
{a,c,b}
(v)
{a,d,b}
Question
13
13.
If A =
{4,1,7}
and B =
{5,6,8}
, find
A ✕ B
(i)
{(4,5),(4,6),(4,8),(1,6),(1,8),(7,5),(7,6),(7,8),(5,1)}
(ii)
{(4,5),(4,6),(4,8),(1,5),(1,6),(1,8),(7,5),(7,6),(7,8)}
(iii)
{(4,5),(4,6),(4,8),(1,5),(1,8),(7,5),(7,6),(7,8)}
(iv)
{(4,5),(4,6),(4,8),(1,5),(1,8),(7,5),(7,6),(7,8),(7,0)}
(v)
{(4,5),(4,6),(4,8),(1,5),(1,6),(1,8),(7,5),(7,6),(7,8),(5,1)}
Question
14
14.
If A =
{c,g,d,a}
and B =
{r,h,m,s}
,
which of the following is relation
R
:
B
→
A
?
(i)
{(g,f),(c,i),(c,k),(a,k),(a,f)}
(ii)
{(g,r),(d,r),(a,s),(g,h),(c,h)}
(iii)
{(e,d),(f,a),(f,c),(k,g),(e,c)}
(iv)
{(s,d),(h,a),(m,d),(s,c),(s,a)}
(v)
{(m,f),(h,i),(s,k),(r,f),(r,e)}
Question
15
15.
Let
f
:
R
→
R
be a function defined by given conditions
f
(
x
)
=
(
7
x
+
5
)
if
x
<
3
f
(
x
)
=
(
2
x
+
1
)
if
3
≤
x
≤
5
f
(
x
)
=
(
8
x
+
9
)
if
x
>
5
find
f
(
x
)
where x =
10
(i)
75
(ii)
88
(iii)
90
(iv)
21
(v)
89
Question
16
16.
If
f
:
A
→
B
is defined by
f
(
x
)
=
(
6
x
+
6
)
and A =
{1,3,2,5}
,
find the range
(i)
{18,36,24}
(ii)
{12,10,18,36}
(iii)
{12,31,14,36}
(iv)
{12,24,18,36}
(v)
{18,-19,24,36,12,19}
Question
17
17.
Which of the following relations is a function given ,
A =
{6,5,9,1,4}
and B =
{8,3,9,5}
?
(i)
{(6,9),(5,9),(1,8),(4,5)}
(ii)
{(6,9),(5,9),(9,9),(1,8),(4,5)}
(iii)
{(6,9),(9,9),(1,8),(4,5),(9,5)}
(iv)
{(6,9),(5,9),(1,8),(4,5),(10,8)}
(v)
{(6,9),(5,9),(9,9),(1,8),(4,5),(9,5)}
Question
18
18.
Find the domain of the given relation.
(i)
{7,8,2,1}
(ii)
{8,2,1,10}
(iii)
{8,2,1}
(iv)
{10,9,3}
(v)
{7,8,2,1,10}
Question
19
19.
Which of the following relations does not represent a function
f
:
A
→
B
,
where A =
{n,f,m,a,g,e}
and B =
{l,d,o,i,c}
?
(i)
{(f,c),(m,l),(a,i),(n,l),(f,d),(m,o)}
(ii)
{(a,i),(f,d),(g,l),(e,l),(m,c),(n,c)}
(iii)
{(n,o),(a,d),(e,d),(g,o),(m,l),(f,d)}
(iv)
{(g,o),(e,d),(f,i),(m,d),(n,d),(a,c)}
(v)
{(a,c),(g,c),(m,d),(e,o),(n,c),(f,o)}
Question
20
20.
If A =
{o,p,r,n,h}
and B =
{k,q,j,s,b}
,
which of the following is relation
R
:
A
→
B
?
(i)
{(j,d),(s,d),(b,d),(k,d),(q,d)}
(ii)
{(k,o),(j,h),(k,h),(j,r),(q,r)}
(iii)
{(d,r),(d,n),(d,p),(d,h),(d,o)}
(iv)
{(n,q),(h,j),(p,b),(n,k),(r,k)}
(v)
{(n,d),(p,d),(o,d),(r,d),(h,d)}
Question
21
21.
If n(A) = 2 and n(B) = 4 then the number of possible relations from A → B is
(i)
255
(ii)
258
(iii)
252
(iv)
256
(v)
254
Question
22
22.
Find the range of
f
:
Z
→
Z
where
f
(
x
)
=
(
9
x
−
3
)
and domain of
f
is
{x : -2 ≤ x ≤ 2}
(i)
{-21,-12,-3,6,14}
(ii)
{-21,-12,-3,6,15}
(iii)
{-12,-3,6,15,-23}
(iv)
{-21,-3,6,15,-10}
(v)
{-21,-12,-3,15,7}
Question
23
23.
Find the range in given roster form,
where R =
{(9,8),(10,6),(9,1),(3,8),(10,1)}
(i)
{8,6,1}
(ii)
{3,10,9}
(iii)
{6,1,7,8}
(iv)
{6,1,7,8,10}
(v)
{9,10,3,6}
Question
24
24.
If
f
(
x
)
=
(
x
+
3
)
and
g
(
x
)
=
(
3
x
2
+
x
+
1
)
,
find the value of
f
(
1
)
+
f
(
-3
)
+
f
(
3
)
g
(
-3
)
+
g
(
3
)
+
g
(
-1
)
(i)
10
61
(ii)
10
59
(iii)
10
57
(iv)
8
59
(v)
12
59
Question
25
25.
Find the range of given relation diagram.
(i)
{6,8,5,2}
(ii)
{9,4,7,6}
(iii)
{6,5,2,8,7}
(iv)
{4,7}
(v)
{4,7,9}
Assignment Key
1) (v)
2) (v)
3) (iii)
4) (iii)
5) (iv)
6) (i)
7) (i)
8) (i)
9) (v)
10) (ii)
11) (iii)
12) (iii)
13) (ii)
14) (iv)
15) (v)
16) (iv)
17) (ii)
18) (iii)
19) (i)
20) (iv)
21) (i)
22) (ii)
23) (i)
24) (ii)
25) (v)
