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UPSC NDA I 2011 Mathematics Paper
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© examsnet.com
Question : 15
Total: 120
If
1
b
−
a
+
1
b
−
c
=
1
a
+
1
c
then
a
,
b
,
c
are in
A
P
GP
HP
None of the above
Validate
Solution:
Given
1
b
−
a
+
1
b
−
c
=
1
a
+
1
c
⇒
1
b
−
a
−
1
c
=
1
a
−
1
b
−
c
⇒
c
−
b
+
a
(
b
−
a
)
c
=
b
−
c
−
a
a
(
b
−
c
)
⇒
c
−
b
+
a
(
b
−
a
)
c
=
−
(
c
−
b
+
a
)
a
(
b
−
c
)
⇒
a
(
b
−
c
)
=
−
(
b
−
a
)
c
⇒
a
b
−
a
c
=
−
b
c
+
a
c
⇒
b
(
a
+
c
)
=
2
a
c
⇒
b
=
2
a
c
a
+
c
.
Clearly
a
,
b
,
c
are in H.P.
© examsnet.com
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