GATE ECE 2022 | GA Question: 5

Question

An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.

If the security guard does not move around the posted location and has a $360^{\circ}$ view, which one of the following correctly represents the set of $\text{ALL}$ possible locations among the locations $\text{P, Q, R}$ and $\text{S},$ where the security guard can be posted to watch over the entire inner space of the gallery.

• A. $\text{P}$ and $\text{Q}$
• B. $\text{Q}$
• C. $\text{Q}$ and $\text{S}$
• D. $\text{R}$ and $\text{S}$

Answer 1

Given that,  the plan of the gallery where the boundary walls are ${\color{Purple}{\text{opaque}}}$ (not able to be seen through; not transparent).

If the security guard will be posted on ${\color{Red}{\text{‘P’}}}$ then he/she can’t watch the visibility side of ${\color{Magenta}{\text{‘R’}}}$ and vice versa. But if the security guard will be posted at ${\color{Blue}{\text{‘Q’}}}$ and ${\color{Green}{\text{‘S’}}}$ then the security guard can watch over the entire inner space of the gallery.

Correct Answer $:\text{C}$

Answer 2

• P: Placing the guard at P wouldn't allow them to see the corner area behind the inward protrusion of the wall. So, P is not a feasible location.
• Q: From Q, the guard can see the entire shaded area except for the small corner section behind the inward protrusion on the opposite side. Therefore, Q is a feasible location, but not optimal as it leaves a blind spot.
• R: Similar to P, placing the guard at R wouldn't allow them to see the corner area behind the inward protrusion on the opposite side. So, R is not a feasible location.
• S: Standing at S, the security guard has a clear line of sight to all corners and edges of the shaded area. This position eliminates any blind spots and ensures complete coverage of the inner space. Therefore, S is the only optimal location among the given options.

Therefore, the only correct answer is:

(C) Q and S

While Q provides partial coverage, only S offers complete visibility of the entire inner space without any blind spots.