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JEE Main 5 Apr 2024 Shift 1 Solved Paper
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© examsnet.com
Question : 6
Total: 90
If the system of equations
11
x
+
y
+
λ
z
=
−
5
2
x
+
3
y
+
5
z
=
3
8
x
−
19
y
−
39
z
=
µ
has infinitely many solutions, then
λ
4
−
µ
is equal to :
[5 Apr 2024 Shift 1]
49
45
47
51
Validate
Solution:
👈: Video Solution
11
x
+
y
+
λ
z
=
−
5
2
x
+
3
y
+
5
z
=
3
8
x
−
19
y
−
39
z
=
µ
for infinite sol.
D
=
|
11
1
λ
2
3
5
8
−
19
−
39
|
=
0
⇒
11
(
−
117
+
95
)
−
1
(
−
78
−
40
)
+
λ
(
−
38
−
24
)
⇒
11
(
−
22
)
+
118
−
λ
(
62
)
=
0
⇒
62
λ
=
118
−
242
⇒
λ
=
−
124
62
=
−
2
D
1
=
|
−
5
1
−
2
3
3
5
µ
−
19
−
39
|
=
0
⇒
−
5
(
−
117
+
95
)
−
1
(
−
117
−
5
µ
)
−
2
(
−
57
−
3
µ
)
=
0
⇒
−
5
(
−
22
)
+
117
+
5
µ
+
114
+
6
µ
=
0
⇒
11
µ
=
−
110
−
231
=
−
341
⇒
µ
=
−
31
λ
4
−
µ
=
(
−
2
)
4
−
(
−
31
)
=
16
+
31
=
47
© examsnet.com
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