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NIMCET 2011 Question Paper with solutions
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© examsnet.com
Question : 29
Total: 120
If three positive real numbers
a
,
b
,
c
(
c
>
a
)
are in HP, then
log
(
a
+
c
)
+
log
(
a
−
2
b
+
c
)
is
2
log
(
c
−
b
)
2
log
(
a
+
c
)
2
log
(
c
−
a
)
log
a
+
log
b
+
log
c
Validate
Solution:
Since,
b
=
2
a
c
a
+
c
(given)
∴
log
(
a
+
c
)
+
log
(
a
+
c
−
2
b
)
=
log
[
{
a
+
c
)
2
−
(
a
+
c
)
2
b
]
=
log
[
(
a
+
c
)
2
−
(
a
+
c
)
2
b
]
=
log
[
(
a
+
c
)
2
−
4
a
c
]
=
log
(
c
−
a
)
2
=
2
log
(
c
−
a
)
© examsnet.com
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