1 vote

An engineer measures THREE quantities, $X, Y$ and $Z$ in an experiment. She finds that they follow a relationship that is represented in the figure below$: ($the product of $X$ and $Y$ linearly varies with $Z)$

Then, which of the following statements is FALSE?

- For fixed $Z$; $X$ is proportional to $Y$
- For fixed $Y$; $X$ is proportional to $Z$
- For fixed $X$; $Z$ is proportional to $Y$
- $XY/Z$ is constant

1 vote

Best answer

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.