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UPSC CDS-2 2020 Math Solved Paper
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© examsnet.com
Question : 1
Total: 100
The harmonic mean and the geometric mean of two numbers are 10 and 12 respectively. What is their arithmetic means?
25
3
√
120
11
14.4
Validate
Solution:
We have, H.M. = 10 and G.M. = 12
Let a and b two numbers.
We know that G.M.
=
√
a
b
and
H
.
M
.
=
2
a
b
a
+
b
⇒
12
=
√
a
b
⇒
a
b
=
144
and,
10
=
2
a
b
a
+
b
⇒
10
=
2
×
144
a
+
b
⇒
a
+
b
2
=
144
10
=
14.4
We know that A.M. =
a
+
b
2
⇒ A.M. = 14.4
© examsnet.com
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