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Byju's Answer
Standard XIII
Mathematics
Distance Formula
Let A = 3, 4 ...
Question
Let
A
=
(
3
,
4
)
and
B
=
(
6
,
β
)
. If the length of the line segment joining
A
and
B
is less than or equal to
4
, then the number of integral value(s) of
β
is
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Solution
Distance between
A
and
B
is,
√
(
3
−
6
)
2
+
(
4
−
β
)
2
≤
4
Squaring both sides,
0
≤
9
+
(
β
−
4
)
2
≤
16
⇒
−
9
≤
(
β
−
4
)
2
≤
7
⇒
−
√
7
≤
β
−
4
≤
√
7
⇒
4
−
√
7
≤
β
≤
4
+
√
7
Therefore, the integral values of
β
are
2
,
3
,
4
,
5
,
6
Hence, the number of integral values of
β
is
5
.
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Similar questions
Q.
Let
A
=
(
3
,
4
)
and
B
=
(
6
,
β
)
. If the length of the line segment joining
A
and
B
is less than or equal to
4
, then the number of integral value(s) of
β
is
Q.
If the value of the integral
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∫
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e
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R
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α
+
6
β
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and
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denotes the greatest integer less than or equal to
x
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then the value of
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α
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Q.
Let
A
be the set of all points
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α
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β
)
such that the area of triangle formed by the points
(
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,
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Q.
Let the line segment joining
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(
6
,
3
)
and
B
(
−
1
,
−
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)
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P
(
x
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,
y
1
)
and
Q
(
x
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,
y
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x
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2
)
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Let
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