GATE CS 2023 Set 1 — Question 5

MCQ+1 / -0.33Easy2D & 3D PatternsSpatial AptitudeGeneral Aptitude

General Aptitude → Spatial Aptitude → 2D & 3D Patterns

Last updated 5 September 2026

Question

Looking at the surface of a smooth 3-dimensional object from the outside, which one of the following options is TRUE?

Correct answer (C) The surface of the object may be concave in some places and convex in other places. Solution A smooth 3-dimensional object is one where the surface is continuous and differentiable, meaning it has no sharp edges or corners. A sphere is a smooth object that is convex everywhere. A torus (donut shape) is a smooth object that has regions of positive Gaussian curvature (convex) on the outer part and regions of negative Gaussian curvature (concave) on the inner part when viewed from the outside. Since smooth objects can have both types of regions, option (C) is the only true statement. Option (D) is incorrect because a "smooth" surface by definition does not have edges. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (C) The surface of the object may be concave in some places and convex in other places. Solution A smooth 3-dimensional object is one where the surface is continuous and differentiable, meaning it has no sharp edges or corners. A sphere is a smooth object that is convex everywhere. A torus (donut shape) is a smooth object that has regions of positive Gaussian curvature (convex) on the outer part and regions of negative Gaussian curvature (concave) on the inner part when viewed from the outside. Since smooth objects can have both types of regions, option (C) is the only true statement. Option (D) is incorrect because a "smooth" surface by definition does not have edges.

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