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Byju's Answer
Standard XII
Mathematics
Minor
If l12+m12+...
Question
If
l
2
1
+
m
2
1
+
n
2
1
=
1
,
e
t
c
a
n
d
l
1
l
2
+
m
1
m
2
+
n
1
n
2
=
0
and
Δ
=
∣
∣ ∣
∣
l
1
m
1
n
1
l
2
m
2
n
2
l
3
m
3
n
3
∣
∣ ∣
∣
then
A
|
Δ
|
=
3
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B
|
Δ
|
=
2
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C
|
Δ
|
=
1
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D
|
Δ
|
=
0
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Solution
The correct option is
C
|
Δ
|
=
1
We have
Δ
2
=
Δ
⋅
Δ
=
∣
∣ ∣
∣
l
1
m
1
n
1
l
2
m
2
n
2
l
3
m
3
n
3
∣
∣ ∣
∣
⋅
∣
∣ ∣
∣
l
1
m
1
n
1
l
2
m
2
n
2
l
3
m
3
n
3
∣
∣ ∣
∣
Δ
2
=
Δ
⋅
Δ
=
∣
∣ ∣ ∣
∣
l
2
1
+
m
2
1
+
n
2
1
l
1
l
2
+
m
1
m
2
+
n
1
n
2
l
1
l
3
+
m
1
m
3
+
n
1
n
3
l
1
l
2
+
m
1
m
2
+
n
1
n
2
l
2
2
+
m
2
2
+
n
2
2
l
2
l
3
+
m
2
m
3
+
n
2
n
3
l
1
l
3
+
m
1
m
3
+
n
1
n
3
l
2
l
3
+
m
2
m
3
+
n
2
n
3
l
2
3
+
m
2
3
+
n
2
3
∣
∣ ∣ ∣
∣
=
∣
∣ ∣
∣
1
0
0
0
1
0
0
0
1
∣
∣ ∣
∣
=
1
⇒
Δ
=
±
1
⇒
|
Δ
|
=
1
Suggest Corrections
0
Similar questions
Q.
STATEMENT-1:
[
lim
x
→
0
sin
x
x
]
=
0
STATEMENT-2: For
x
∈
(
−
δ
,
δ
)
, where
δ
is positive and
δ
→
0
,
tan
x
>
x
.
Q.
Given
Δ
ABC
∼
Δ
PQR, if
A
B
P
Q
=
1
3
, then find
a
r
Δ
A
B
C
a
r
Δ
P
Q
R
.
Q.
If
l
2
i
+
m
2
i
+
n
2
i
=
1
for
i
=
1
,
2
,
3
&
l
i
l
j
+
m
i
m
j
+
n
i
n
j
=
0
for
i
,
j
∈
{
1
,
2
,
3
}
and
i
≠
j
and
Δ
=
∣
∣ ∣
∣
l
1
m
1
n
1
l
2
m
2
n
2
l
3
m
3
n
3
∣
∣ ∣
∣
,
then
Q.
If both the roots of
a
x
2
+
b
x
+
c
=
0
are real, positive and distinct, then
(where
Δ
=
b
2
−
4
a
x
)
Q.
lf
f
(
x
)
=
2
x
−
3
,
a
=
2
,
l
=
1
and
ϵ
=
0.001
then
δ
>
0
satisfying
0
<
|
x
−
a
|
<
δ
,
|
f
(
x
)
−
l
|
<
ϵ
, is:
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