# GATE Mechanical 2020 Set 2 | GA Question: 9

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?

1. For fixed $Z$; $X$ is proportional to $Y$
2. For fixed $Y$; $X$ is proportional to $Z$
3. For fixed $X$; $Z$ is proportional to $Y$
4. $XY/Z$ is constant

edited

1 vote

Given that, $XY \propto Z \implies XY = k Z;$ where $k$ is constant.

Now, we can verify each and every option.

1. For fixed $Z; X$ is proportional to $Y{\color{Red} {\text{ – False.}}}$
• $XY \propto Z$
• For fixed $Z,$ we can write $XY \propto 1$
• $X \propto \dfrac{1}{Y}\;\text{(or)} \; Y \propto \dfrac{1}{X}$
2. For fixed $Y; X$ is proportional to $Z-$ True.
• $XY \propto Z$
• For fixed $Y,$ we can write $X \propto Z$
3. For fixed $X; Z$ is proportional to $Y-$ True.
• $XY \propto Z$
• For fixed $X$ we can write $Y \propto Z$
4. $XY/Z$ is constant –  True.
• $XY \propto Z$
• $\implies XY = k Z;$ where $k$ is constant.

So, the correct answer is A.

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