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Byju's Answer
Standard XII
Mathematics
Middle Terms
If ∑i=1nai=...
Question
If
∑
n
i
=
1
→
a
i
=
0
where
∣
∣
→
a
i
∣
∣
=
1
for all
i
then the value of
∑
1
≤
i
<
j
≤
n
∑
→
a
i
→
a
j
is
A
−
n
2
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B
−
n
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C
n
2
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D
n
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Solution
The correct option is
B
−
n
2
n
∑
i
=
1
→
a
i
=
0
(
n
∑
i
=
1
→
a
i
)
.
(
n
∑
i
=
1
→
a
i
)
=
n
∑
i
=
1
∣
∣
→
a
i
∣
∣
2
+
2
n
∑
1
≤
i
<
j
≤
n
∑
→
a
i
.
→
a
j
∑
1
≤
i
<
j
≤
n
∑
→
a
i
.
→
a
j
=
−
n
2
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0
Similar questions
Q.
If
n
∑
i
=
1
→
a
i
=
0
where
∣
∣
→
a
i
∣
∣
=
1
,
∀
i
,
then the value of
∑
1
≤
i
<
j
≤
n
∑
→
a
i
.
→
a
j
is equal to
Q.
If
|
a
i
|
<
2
,
i
∈
{
1
,
2
,
3...
n
}
. Prove that for no
z
,
|
z
|
<
1
3
and
n
∑
i
=
1
a
i
z
i
=
1
can occur simultaneously.
Q.
The value of
A
i
A
j
where
j
=
1
,
2
,
3
,
.
.
.
n
is
Q.
If
n
∏
i
=
1
a
i
=
1
and
n
∏
i
=
1
(
1
+
a
i
)
≥
x
n
, where
a
i
,
i
=
1
,
2
,
…
,
n
is positive real numbers, then the value of
x
is
Q.
A
i
=
x
−
a
i
|
x
−
a
i
|
,
i
=
1
,
2
,
.
.
.
.
.
,
n
,
and
a
1
<
a
2
<
a
3
<
.
.
.
.
.
<
a
n
.
If
1
≤
m
≤
n
,
m
∈
N
,
then the value of
R
=
lim
x
→
a
+
m
(
A
1
A
2
.
.
.
.
A
n
)
is
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