Allied & ICAR Exam Bank • ALLIED_1808MCQ • 2 Marks
Section 8: General Aptitude
Analytical & Spatial Aptitude
Subtopic: Spatial Reasoning & 3D Representations
Question Statement:
Two closed wire loops in three-dimensional space are linked together like adjacent links in a chain (a Hopf link). Can they be separated without cutting either loop or moving into a fourth dimension?
Options:
(A) No, they have a non-zero linking number (+1 or -1) and are topologically inseparable
(B) Yes, by continuous deformation in 3D space
(C) Yes, if one loop is rotated by 90 degrees
(D) Yes, by shrinking one loop to zero
Answer Key:
A
Step-by-Step Solution & Explanation
The Hopf link has a topological linking number of 1. It is fundamentally impossible to separate linked loops in 3D without cutting.