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UPSC NDA I and II 2020 Math Solved Paper
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© examsnet.com
Question : 27
Total: 120
If
p
2
,
q
2
and
r
2
(where
p
,
q
,
r
>
0
) are in GP, then which of the following is/are correct?
1.
p
,
q
and
r
are in GP.
2.
ln
p
,
ln
q
and
ln
r
are in
A
P
.
Select the correct answer using the code given below :
[NDA-I 2020]
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Validate
Solution:
👈: Video Solution
(1)
p
2
,
q
2
and
r
2
in G.P.
Then,
(
q
2
)
2
=
p
2
.
r
2
⇒
q
2
=
(
p
2
.
r
2
)
1
2
⇒
q
2
=
p
.
r
Hence,
p
,
q
and
r
in G.P.
(2) As,
q
2
=
p
.
r
Taking log on both sides, we have
ln
(
q
2
)
=
ln
(
p
.
r
)
2
ln
(
q
)
=
ln
p
+
ln
r
Hence,
ln
p
,
ln
q
and
ln
r
are in A.P.
© examsnet.com
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