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AP EAMCET Engineering 20 Apr 2019 Shift 1 Paper
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© examsnet.com
Question : 5
Total: 160
If [x] is the greatest integer less than or equal to x and |x| is the modulus of a. then the system of three equations
2y + 3|y| + 5[z] = 0. x + [y| - 2[z] = 4. x + |y| + [z] = 1 has
a unique solution
finitely many solutions
infinitely many solutions
no solution
Validate
Solution:
Consider the system of equations,
2
x
+
3
|
y
|
+
5
[
z
]
=
0
x
+
|
y
|
−
2
[
z
]
=
4
x
+
|
y
|
+
[
z
]
=
1
Then by Cramer's rule,
x
=
∆
1
∆
|
y
|
=
∆
2
∆
[
z
]
=
∆
3
∆
Where
∆
=
|
2
3
5
1
1
−
2
1
1
1
|
=
2
(
1
+
2
)
−
3
(
1
+
2
)
+
5
(
1
−
1
)
=
−
3
and
∆
1
=
|
0
3
5
4
1
−
2
1
1
1
|
=
0
(
1
+
2
)
−
3
(
4
+
2
)
+
5
(
4
−
1
)
=
−
3
and
∆
2
=
|
2
0
5
1
4
−
2
1
1
1
|
=
2
(
4
+
2
)
−
0
(
1
+
2
)
+
5
(
1
−
4
)
=
−
3
and,
∆
3
=
|
2
3
0
1
1
4
1
1
1
|
=
2
(
1
−
4
)
−
3
(
1
−
4
)
+
0
(
1
−
1
)
=
3
This implies
x
=
−
3
−
3
=
1
And
|
y
|
=
−
3
−
3
=
1
And
[
z
]
=
−
3
3
=
−
1
This implies,
z
∈
[
−
1
,
0
)
So, the system has infinitely many solutions.
© examsnet.com
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