GATE 2024 MN – Question 10

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

Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The magnitude of the minimum angle of rotation is

120°
60°
90°
180°

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Show answer and explanation

Correct answer: (A) 120°

Explanation

A body diagonal joins two opposite cube vertices. At either endpoint, three edges and three faces meet symmetrically. A rotation of 120° cycles these three edge directions and carries every vertex and face to an equivalent position.

A smaller positive rotation cannot preserve the three incident edge directions: their permutation requires one-third of a full turn. Thus the minimum is **360°/3=120°, A**.

The hexagonal silhouette seen along the axis can suggest 60°, but matching the outer silhouette alone does not preserve the full cube and its internal visible edges.

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