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Question
The two geometric means between the numbers 1 and 64 are
Options
(a) 1 and 64
(b) 4 and 16
(c) 2 and 16
(d) 8 and 16
(e) 3 and 16
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Solution
(b) 4 and 16
\[\text{ Let the two G . M . s between 1 and 64 be G_1 and G_2 } . \]
\[\text{ Thus, 1, G_1 , G_2 and 64 are in G . P } . \]
\[ 64 = 1 \times r^3 \]
\[ \Rightarrow r = \sqrt[3]{64}\]
\[ \Rightarrow r = 4\]
\[ \Rightarrow G_1 = ar = 1 \times 4 = 4\]
\[\text{ And }, G_2 = a r^2 = 1 \times 4^2 = 16\]
\[\text{ Thus, 4 and 16 are the required G . M . s } .\]
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