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AIEEE 2005 Math Solved Paper
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© examsnet.com
Question : 34
Total: 71
The system of equations
α
x
+
y
+
z
=
α
−
1
x
+
α
y
+
z
=
α
−
1
x
+
y
+
α
z
=
α
−
1
has infinite solutions, if
α
is
−
2
either
−
2
or
1
not
−
2
1
Validate
Solution:
a
x
+
y
+
z
=
α
−
1
x
+
α
y
+
z
=
α
−
1
x
+
y
+
z
α
=
α
−
1
∆
=
|
α
1
1
1
α
1
1
1
α
|
=
α
(
α
2
−
1
)
−
1
(
α
−
1
)
+
1
(
1
−
α
)
=
α
(
α
−
1
)
(
α
+
1
)
−
1
(
α
−
1
)
−
1
(
α
−
1
)
For infinite solutions,
∆
=
0
⇒
(
α
−
1
)
[
α
2
+
α
−
1
−
1
]
=
0
⇒
(
α
−
1
)
[
α
2
+
α
−
2
]
=
0
⇒
α
=
−
2
,
1
But
α
≠
1
.
∴
α
=
−
2
© examsnet.com
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