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Question
Mathematics
Let S = (a, b) a, b ∈ Z , 0 le a, b le 18 . The number of lines in R2 passing through (0, 0) and exactly one other point in S is
Q. Let
S
=
{(
a
,
b
)
a
,
b
∈
Z
,
0
≤
a
,
b
≤
18
}
. The number of lines in
R
2
passing through
(
0
,
0
)
and exactly one other point in
S
is
2027
154
KVPY
KVPY 2014
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A
16
B
22
C
28
D
32
Solution:
We have,
S
=
{(
a
,
b
)
:
a
,
b
∈
Z
,
0
≤
a
,
b
≤
18
}
Number of line in
R
2
passing through
(
0
,
0
)
and one other point in
S
is
34
.
(
1
,
17
)
,
(
2
,
17
)
,
(
3
,
17
)
,
...
,
(
18
,
17
)
=
17
points
(
17
,
1
)
,
(
17
,
2
)
,
(
17
,
3
)
,
...
,
(
17
,
18
)
=
17
points
∴
Total number of lines
=
34