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UPSC CDS Math Basic operation and Factorisation Questions
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© examsnet.com
Question : 53
Total: 77
If
(
s
−
a
)
+
(
s
−
b
)
+
(
s
−
c
)
=
s
, then the value of
(
s
−
a
)
2
+
(
s
−
b
)
2
+
(
s
−
c
)
2
a
2
+
b
2
+
c
2
will be
[2016 CDS-I]
3
1
0
-1
Validate
Solution:
(
s
−
a
)
+
(
s
−
b
)
+
(
s
−
c
)
=
s
⇒
2
s
=
a
+
b
+
c
.....(1)
(
s
−
a
)
2
+
(
s
−
b
)
2
+
(
s
−
c
)
2
+
s
2
a
2
+
b
2
+
c
2
=
4
s
2
−
2
s
(
a
+
b
+
c
)
+
a
2
+
b
2
+
c
2
a
2
+
b
2
+
c
2
=
4
s
2
−
4
s
2
+
a
2
+
b
2
+
c
2
a
2
+
b
2
+
c
2
[Using(1)]
=
1
Trick :
Lest
s
=
5
,
a
=
5
,
b
=
2
,
c
=
3
Then,
(
5
−
5
)
+
(
5
−
2
)
+
(
5
−
3
)
=
0
+
3
+
2
=
5
∴
(
5
−
5
)
2
+
(
5
−
2
)
2
+
(
5
−
3
)
2
+
5
2
5
2
+
2
2
+
3
2
=
9
+
4
+
25
25
+
4
+
9
=
1
Note:
For solving such type questions, students are advised to select the value of s, a, b and c such that these values must satisfy the given condition.
© examsnet.com
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