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UPSC 2016 CDS II Math Paper
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© examsnet.com
Question : 27
Total: 100
Consider the following statements in respect of positive odd integers x and y :
1.
x
2
+
y
2
is even integer.
2.
x
2
+
y
2
is divisible by 4.
Which of the above statements is/are correct ?
[2016 CDS-II]
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Validate
Solution:
Let
x
=
2
n
+
1
and
y
=
2
m
+
1
, where m, n ∊ N be two positive odd integers.
∴
x
2
+
y
2
=
(
2
n
+
1
)
2
+
(
2
m
+
1
)
2
=
4
n
2
+
4
n
+
1
+
4
m
2
+
4
m
+
1
=
4
(
n
2
+
m
2
+
n
+
m
+
2
)
So,
x
2
+
y
2
is an even integer but not divisible by 4
Hence, statement 1 is correct and statement 2 is incorrect.
© examsnet.com
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