GATE EC 2022 Set 1 — Question 5

MCQ+1 / -0.33MediumSpatial AptitudeGeneral Aptitude

General Aptitude → Spatial Aptitude

Last updated 5 September 2026

Question

360^\circ

Correct answer (C) Q and S Solution To watch over the entire inner space of the gallery from a single fixed point, that point must have a direct line of sight to every other point in the shaded region. This is equivalent to finding points in the 'kernel' of the polygon. 1. Point P : From P, the bottom-right 'wing' of the gallery is partially obscured by the inner reflex vertex (the 'V' shape in the middle). Thus, P cannot see the entire space. 2. Point R : Similarly, from R, the bottom-left 'wing' is partially obscured by the inner reflex vertex. Thus, R cannot see the entire space. 3. Point Q : Point Q is located centrally such that straight lines can be drawn from it to any point within the shaded region without crossing the boundary walls. It can see the entire space. 4. Point S : Point S is located at the bottom tip. From this position, the entire 'V' shaped gallery is visible as it opens up towards the top. There are no obstructions to the line of sight for any part of the interior. Therefore, the set of all possible locations among P, Q, R, and S is {Q, S}. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (C) Q and S Solution To watch over the entire inner space of the gallery from a single fixed point, that point must have a direct line of sight to every other point in the shaded region. This is equivalent to finding points in the 'kernel' of the polygon. 1. Point P : From P, the bottom-right 'wing' of the gallery is partially obscured by the inner reflex vertex (the 'V' shape in the middle). Thus, P cannot see the entire space. 2. Point R : Similarly, from R, the bottom-left 'wing' is partially obscured by the inner reflex vertex. Thus, R cannot see the entire space. 3. Point Q : Point Q is located centrally such that straight lines can be drawn from it to any point within the shaded region without crossing the boundary walls. It can see the entire space. 4. Point S : Point S is located at the bottom tip. From this position, the entire 'V' shaped gallery is visible as it opens up towards the top. There are no obstructions to the line of sight for any part of the interior. Therefore, the set of all possible locations among P, Q, R, and S is {Q, S}.

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