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Byju's Answer
Standard XII
Mathematics
Properties of Determinants
The total num...
Question
The total number of distinct
x
∈
R
for which
∣
∣ ∣ ∣
∣
x
x
2
1
+
x
3
2
x
4
x
2
1
+
8
x
3
3
x
9
x
2
1
+
27
x
3
∣
∣ ∣ ∣
∣
=
10
is
Open in App
Solution
x
.
x
2
∣
∣ ∣ ∣
∣
1
1
1
+
x
3
2
4
1
+
8
x
3
3
9
1
+
27
x
3
∣
∣ ∣ ∣
∣
=
10
⇒
x
3
∣
∣ ∣
∣
1
1
1
2
4
1
3
9
1
∣
∣ ∣
∣
+
x
6
∣
∣ ∣
∣
1
1
1
2
4
8
3
9
27
∣
∣ ∣
∣
=
10
⇒
x
3
∣
∣ ∣
∣
0
0
1
1
3
1
2
8
1
∣
∣ ∣
∣
+
x
6
∣
∣ ∣
∣
1
0
0
2
2
6
3
6
24
∣
∣ ∣
∣
=
10
⇒
x
3
(
8
−
6
)
+
x
6
(
48
−
36
)
=
10
⇒
6
x
6
+
x
3
−
5
=
0
⇒
(
6
x
3
−
5
)
(
x
3
+
1
)
=
0
⇒
x
3
=
5
6
,
x
3
=
−
1
⇒
x
=
(
5
6
)
1
3
,
x
=
−
1
⇒
Two distinct value
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Similar questions
Q.
The total number of distinct
x
∈
R
for which
∣
∣ ∣ ∣
∣
x
x
2
1
+
x
3
2
x
4
x
2
1
+
8
x
3
3
x
9
x
2
1
+
27
x
3
∣
∣ ∣ ∣
∣
=
10
is
Q.
∣
∣ ∣ ∣
∣
1
x
x
2
x
2
1
x
x
x
2
1
∣
∣ ∣ ∣
∣
=
(
1
−
x
3
)
2
Q.
∣
∣ ∣ ∣ ∣
∣
4
x
6
X
+
2
8
X
+
1
6
X
9
X
+
3
12
X
8
X
12
X
16
X
+
2
∣
∣ ∣ ∣ ∣
∣
= 0, then x is equal to
Q.
If
f
(
x
)
=
∣
∣ ∣
∣
x
2
−
4
x
+
6
2
x
2
+
4
x
+
10
3
x
2
−
2
x
+
16
x
−
2
2
x
+
2
3
x
−
1
1
2
3
∣
∣ ∣
∣
.
Then the value of
∫
3
−
3
x
2
s
i
n
x
1
+
x
6
.
f
(
x
)
d
x
is
Q.
Value of the determinant
∣
∣ ∣
∣
1
3
5
3
4
5
0
2
3
∣
∣ ∣
∣
i
s
___
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