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(B) Let the two geometric means be $a$ and $b$ such that $1, a, b, 64$ form a Geometric Progression $(GP)$.In a $GP$,the common ratio $r$ is given by

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$4$ and $16$

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(B) Let the two geometric means be $a$ and $b$ such that $1, a, b, 64$ form a Geometric Progression $(GP)$.In a $GP$,the common ratio $r$ is given by $a_n = a_1 \cdot r^{n-1}$.Here,$a_1 = 1$ and $a_4 = 64$.$64 = 1 \cdot r^{4-1} \Rightarrow r^3 = 64$.Since $64 = 4^3$,we have $r = 4$.The terms are $a = 1 \cdot 4 = 4$ and $b = 4 \cdot 4 = 16$.Thus,the two geometric means are $4$ and $16$.

The two geometric means between the numbers $1$ and $64$ are

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