A) \[1\] and \[64\]
B) \[4\] and \[16\]
C) \[2\] and\[16\]
D) \[8\] and \[16\]
Correct Answer: B
Solution :
Let \[{{G}_{1}}\] and \[{{G}_{2}}\] be the two geometric means between \[1\] and\[64\]. \[i.e.,\] \[1,\,\,{{G}_{1}},\,\,{{G}_{2}},\,\,64\] Here, \[a=1,\] \[\therefore \] \[64={{a}^{3}}\Rightarrow {{4}^{3}}={{r}^{3}}\] \[\Rightarrow \] \[r=4\] \[\therefore \] \[{{G}_{1}}=ar=1\times 4=4\] and \[{{G}_{2}}=a{{r}^{2}}=1\times {{4}^{2}}=16\]
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