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GATE 2023 ME – Question 10

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 2 marks · Multiple choice

An opaque pyramid (shown below), with a square base and isosceles faces, is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The pyramid can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?

a pyramid with a square base. Four shadows are shown: P is a convex pentagon (a rectangle with a pointed end), Q is a non-convex shape with a notch (a V-shaped indent) on its upper edge, R is a convex four-sided kite and S is a square.
  1. P
  2. Q
  3. R
  4. S

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Show answer and explanation

Correct answer: (B) Q

Explanation

The shadow of a convex solid in parallel light is always a convex shape, because it is the projection of a convex set. The pyramid is convex, so every possible shadow is convex. P, R and S are convex and can be obtained (S from a view along the axis, P and R from tilted views). Shadow Q has a notch, so it is not convex and cannot be a shadow of the pyramid.