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Test Index
JEE Main 30-Jan-2024 Shift 2 Solved Paper
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Section:
Mathematics
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© examsnet.com
Question : 1
Total: 90
Consider the system of linear equations
x
+
y
+
z
=
5
,
x
+
2
y
+
λ
2
z
=
9
x
+
3
y
+
λ
z
=
µ
, where
λ
,
µ
∈
R
. Then, which the following statement is NOT correct?
[30-Jan-2024 Shift 2]
System has infinite number of solution if
λ
=
and
µ
=
13
System is inconsistent if
λ
=
1
and
µ
≠
13
System is consistent if
λ
≠
1
and
µ
=
13
System has unique solution if
λ
≠
1
and
µ
≠
13
Validate
Solution:
👈: Video Solution
|
1
1
1
1
2
λ
2
1
3
λ
|
=
0
⇒
2
λ
2
−
λ
−
1
=
0
λ
=
1
,
−
1
2
|
1
1
5
2
λ
2
9
3
λ
µ
|
=
0
⇒
µ
=
13
Infinite solution
λ
=
1
&
µ
=
13
For unique
sol
n
λ
≠
1
For no
sol
n
λ
=
1
&
µ
≠
13
If
λ
≠
1
and
µ
≠
13
Considering the case when
λ
=
−
1
2
and
µ
≠
13
this will generate no solution case
© examsnet.com
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