GATE Mechanical 2020 Set 2 | GA Question: 9

Question

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?

• A. For fixed $Z$; $X$ is proportional to $Y$
• B. For fixed $Y$; $X$ is proportional to $Z$
• C. For fixed $X$; $Z$ is proportional to $Y$
• D. $XY/Z$ is constant

Answer 1

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

Now, we can verify each and every option.

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

So, the correct answer is A.

Answer 2

A.