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ISI Entrance Examination
2018 ISI Entrance Examination
1
ISI 2018 #1
ISI 2018 #1
Source: ISI 2018 B.Stat / B.Math Entrance Exam
May 13, 2018
isi
2018
Indian Statistical Institute
Problem Statement
Find all pairs
(
x
,
y
)
(x,y)
(
x
,
y
)
with
x
,
y
x,y
x
,
y
real, satisfying the equations
sin
(
x
+
y
2
)
=
0
,
∣
x
∣
+
∣
y
∣
=
1
\sin\bigg(\frac{x+y}{2}\bigg)=0~,~\vert x\vert+\vert y\vert=1
sin
(
2
x
+
y
)
=
0
,
∣
x
∣
+
∣
y
∣
=
1
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