Given that, $XY \propto Z \implies XY = k Z;$ where $k$ is constant.
Now, we can verify each and every option.
- For fixed $Z; X$ is proportional to $Y{\color{Red} {\text{ – False.}}}$
- $XY \propto Z$
- For fixed $Z,$ we can write $XY \propto 1$
- $X \propto \dfrac{1}{Y}\;\text{(or)} \; Y \propto \dfrac{1}{X}$
- For fixed $Y; X$ is proportional to $Z-$ True.
- $XY \propto Z$
- For fixed $Y,$ we can write $X \propto Z$
- For fixed $X; Z$ is proportional to $Y-$ True.
- $XY \propto Z$
- For fixed $X$ we can write $Y \propto Z$
- $XY/Z$ is constant – True.
- $XY \propto Z$
- $\implies XY = k Z;$ where $k$ is constant.
So, the correct answer is A.