A standard six-sided die net is laid out in a cross shape: the central column has four squares numbered from top to bottom as 1, 2, 4, 6. Square 3 is attached to the left of square 2, and square 5 is attached to the right of square 2. When this net is folded to form a 3D cube, which face will be directly opposite to face 2?

(A) Face 6

(B) Face 4

(C) Face 5

(D) Face 1

Answer Key:

Verified in official key

### 1. Strategy & Theoretical Principles In any straight strip of squares in a cube net, alternating faces (separated by one intervening square) fold to become mutually opposite faces. ### 2. Analytical Formulation In the central vertical column containing squares in sequence: $[1, 2, 4, 6]$: - Face 1 and Face 4 are separated by Face 2 $\implies$ Face 1 is opposite Face 4. - Face 2 and Face 6 are separated by Face 4 $\implies$ Face 2 is opposite Face 6. - The two lateral side flaps (Face 3 on the left and Face 5 on the right) fold upward to form the remaining pair of opposite faces $\implies$ Face 3 is opposite Face 5. ### 3. Step-by-Step Verification Therefore, the face directly opposite to Face 2 is **Face 6**. ### 4. Distractor Forensics - **Face 6:** Correct opposite face. - **Face 4:** Adjacent face along the vertical column. - **Face 5:** Lateral adjacent face. - **Face 1:** Opposite to face 4, not face 2. ### 5. Exam Trap & Standard Reference - **Trap Alert:** In a linear 4-square strip, positions 1 & 3 are opposite, and positions 2 & 4 are opposite. - **Standard Reference:** GATE General Aptitude Official Syllabus - Spatial Reasoning (Cube Nets).

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