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UPSC NDA I 2012 Mathematics Paper
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© examsnet.com
Question : 16
Total: 120
If
p
,
q
,
r
are in
AP
as well as
GP
, then which one of the following is correct?
p
=
q
≠
r
p
≠
q
≠
r
p
≠
q
=
r
p
=
q
=
r
Validate
Solution:
A.P.
→
2
q
=
p
+
r
. . . (1)
G.P.
→
q
2
=
p
r
⇒
0
=
√
p
r
2
√
p
r
=
p
+
r
p
+
r
−
2
√
p
r
=
0
(
√
p
)
2
+
(
√
r
)
2
−
2
√
p
⋅
√
r
=
0
(
√
p
−
√
r
)
2
=
0
√
p
=
√
r
p
=
r
. . . (2)
2
q
=
2
p
q
=
p
. . . (3)
from (2) and (3)
p
=
q
=
r
.
© examsnet.com
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