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JEE Main Math Class 12 Determinants Part 2 Questions
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© examsnet.com
Question : 34
Total: 117
If the system of equations
x
+
2
y
+
3
z
=
3
4
x
+
3
y
−
4
z
=
4
8
x
+
4
y
−
λ
z
=
9
+
µ
has infinitely many solutions, then the ordered pair
∣
(
λ
,
µ
)
is equal to
[24-Jan-2023 Shift 2]
(
72
5
,
21
5
)
(
−
72
5
,
−
21
5
)
(
72
5
,
−
21
5
)
(
−
72
5
,
21
5
)
Validate
Solution:
x
+
2
y
+
3
z
=
3
. . . . (i)
4
x
+
3
y
−
4
z
=
4
. . . . (ii)
8
x
+
4
y
−
λ
z
=
9
+
µ
. . . . (iii)
(i)
×
4
−
(
ii)
⇒
5
y
+
16
z
=
8
.
.
.
.
.
.
(iv)
(ii)
×
2
−
(
iii)
⇒
2
y
+
(
λ
−
8
)
z
=
−
1
−
µ
.
.
.
.
.
.
(v)
(iv)
×
2
−
(
iii)
×
5
⇒
(
32
−
5
(
λ
−
8
)
)
z
=
16
−
5
(
−
1
−
µ
)
For infinite solutions
⇒
72
−
5
λ
=
0
⇒
λ
=
72
5
21
+
5
µ
=
0
⇒
µ
=
−
21
5
⇒
(
λ
,
µ
)
≡
(
72
5
,
−
21
5
)
© examsnet.com
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