GATE Electrical 2022 | GA | Question: 9

Question

The letters $\text{P, Q, R, S, T}$ and $\text{U}$ are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order.

Consider the following statements:

• The line segment joining $\text{R}$ and $\text{S}$ is longer than the line segment joining $\text{P}$ and $\text{Q}$.
• The line segment joining $\text{R}$ and $\text{S}$ is perpendicular to the line segment joining $\text{P}$ and $\text{Q}$.
• The line segment joining $\text{R}$ and $\text{U}$ is parallel to the line segment joining $\text{T}$ and $\text{Q}$.

Based on the above statements, which one of the following options is $\text{CORRECT}?$

• A. The line segment joining $\text{R}$ and $\text{T}$ is parallel to the line segment joining $\text{Q}$ and $\text{S}$
• B. The line segment joining $\text{T}$ and $\text{Q}$ is parallel to the line joining $\text{P}$ and $\text{U}$
• C. The line segment joining $\text{R}$ and $\text{P}$ is perpendicular to the line segment joining $\text{U}$ and $\text{Q}$
• D. The line segment joining $\text{Q}$ and $\text{S}$ is perpendicular to the line segment joining $\text{R}$ and $\text{P}$

Answer 1

Given that,  the following statements:

• The line segment joining $\text{R}$ and $\text{S}$ is longer than the line segment joining $\text{P}$ and $\text{Q}$.
• The line segment joining $\text{R}$ and $\text{S}$ is perpendicular to the line segment joining $\text{P}$ and $\text{Q}$.
• The line segment joining $\text{R}$ and $\text{U}$ is parallel to the line segment joining $\text{T}$ and $\text{Q}$.

Based on the above statements, we can draw the ${\color{Blue}{\text{regular convex hexagon.}}}$

Now, we can see all the options. 

• A. The line segment joining $\text{R}$ and $\text{T}$ is parallel to the line segment joining $\text{Q}$ and $\text{S}{\color{Green}{-\text{True}.}}$
• B. The line segment joining $\text{T}$ and $\text{Q}$ is parallel to the line joining $\text{P}$ and $\text{U}{\color{Red}{-\text{False}.}}$
• C. The line segment joining $\text{R}$ and $\text{P}$ is perpendicular to the line segment joining $\text{U}$ and $\text{Q}{\color{Red}{-\text{False}.}}$
• D. The line segment joining $\text{Q}$ and $\text{S}$ is perpendicular to the line segment joining $\text{R}$ and $\text{P}{\color{Red}{-\text{False}.}}$

Correct Answer $:\text{A}$

Comments

There is another possibility where $T$ and $U$ are swapped, which also satisfies only option $A$ and also fulfills all three conditions.