Ans: B
I is a geometric sequence.
I is a geometric sequence.
$\begin{array}{lllllll}
\dfrac{2^{2m}}{2^m} & = & \dfrac{2^{3m}}{2^{2m}} & = & \dfrac{2^{4m}}{2^{3m}} & = & 2^m
\end{array}$
Therefore, there is a common ratio $2^m$.
II is not a geometric sequence.
$\begin{array}{rcl}
\dfrac{2m^2}{m} & = & 2m
\end{array}$
However,
$\begin{array}{rcl}
\dfrac{3m^4}{2m^2} & = & \dfrac{3}{2}m^2
\end{array}$
There is no common ratio.
III is a geometric sequence.
$\begin{array}{lllll}
\dfrac{\log m^2}{\log m} & = & \dfrac{2\log m}{\log m} & = & 2
\end{array}$
$\begin{array}{lllll}
\dfrac{\log m^4}{\log m^2} & = & \dfrac{4\log m }{2\log m} & = & 2
\end{array}$
$\begin{array}{lllll}
\dfrac{\log m^8}{\log m^4} & = & \dfrac{8\log m}{4\log m} & = & 2
\end{array}$
Therefore, there is a common ratio $2$.
