Byju's Answer
Standard XII
Mathematics
Properties of Determinants
If x≠ 0, ...
Question
If
x
≠
0
,
∣
∣ ∣
∣
x
+
1
2
x
+
1
3
x
+
1
2
x
4
x
+
3
6
x
+
3
4
x
+
4
6
x
+
4
8
x
+
4
∣
∣ ∣
∣
=
0
, then
x
+
1
is equal to
A
x
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B
0
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C
2
x
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D
3
x
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Solution
The correct option is
B
0
Given
∣
∣ ∣
∣
x
+
1
2
x
+
1
3
x
+
1
2
x
4
x
+
3
6
x
+
3
4
x
+
4
6
x
+
4
8
x
+
4
∣
∣ ∣
∣
=
0
⇒
2
∣
∣ ∣
∣
x
+
1
2
x
+
1
3
x
+
1
2
x
4
x
+
3
6
x
+
3
2
x
+
2
3
x
+
2
4
x
+
2
∣
∣ ∣
∣
=
0
[
using
R
1
→
2
R
1
−
R
3
]
⇒
2
∣
∣ ∣
∣
0
x
2
x
2
x
4
x
+
3
6
x
+
3
2
x
+
2
3
x
+
2
4
x
+
2
∣
∣ ∣
∣
=
0
⇒
2
∣
∣ ∣
∣
0
x
0
2
x
4
x
+
3
−
2
x
−
3
2
x
+
2
3
x
+
2
−
2
x
−
2
∣
∣ ∣
∣
=
0
[using
C
3
→
C
3
−
2
C
2
]
⇒
−
4
x
[
2
x
2
+
2
x
−
(
2
x
+
3
)
(
x
+
1
)
]
=
0
⇒
−
4
x
[
2
x
2
+
2
x
−
(
2
x
2
+
2
x
+
3
x
+
3
)
]
=
0
⇒
4
x
(
3
x
+
3
)
=
0
⇒
x
+
1
=
0
[
∵
x
≠
0
,
g
i
v
e
n
]
Suggest Corrections
0
Similar questions
Q.
If
x
≠
0
, then
1
+
sec
x
+
sec
2
x
+
sec
3
x
+
sec
4
x
+
sec
5
x
is equal to
Q.
If a function
f
(
x
)
is given by
f
(
x
)
=
x
1
+
x
+
x
(
x
+
1
)
(
2
x
+
1
)
+
x
(
2
x
+
1
)
(
3
x
+
1
)
+
.
.
.
.
.
.
+
∞
, then at
x
=
0
,
f
(
x
)
Q.
If
∣
∣ ∣
∣
x
+
2
2
x
+
3
3
x
+
4
2
x
+
3
3
x
+
4
4
x
+
5
3
x
+
5
5
x
+
8
10
x
+
17
∣
∣ ∣
∣
=
0
then
x
is equal to
Q.
If
2
(
x
−
2
)
+
3
(
4
x
−
1
)
=
0
, then the value of
x
is-
Q.
Solution of inequality
(
x
−
1
)
2
(
x
+
1
)
3
(
x
−
4
)
<
0
is
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