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GATE 2026 XH2 (English) – Question 7

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

A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

Panel I is a net made of a column of four squares with one more square attached to the right of the top square and one more attached to the left of the bottom square. Top square: a shaded triangle in its lower left corner. Second square: a shaded square in its upper right quarter. Third square: a shaded diamond. Bottom square: a shaded triangle along its lower part. The square on the right has a shaded band across its lower half and the square on the left has a shaded triangle covering half of it. Panel II shows two cubes, (i) and (ii).
  1. Only (i) can correspond to the unfolded cube in Panel I.
  2. Only (ii) can correspond to the unfolded cube in Panel I.
  3. Both (i) and (ii) can correspond to the unfolded cube in Panel I.
  4. Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.

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Correct answer: (A) Only (i) can correspond to the unfolded cube in Panel I.

Explanation

Fold the column of four squares into a ring and treat the two end squares as the lid and the base. Put the diamond square in front. Cube (i) shows the diamond in front, a shaded triangle covering half of the top face with its right angle at the front right corner, and a small shaded patch in the lower back part of the right face. Turning the cube so that the half-shaded end square is on top brings that triangle to exactly this position, and the shaded quarter square then falls on the lower back of the right face, so (i) matches. In cube (ii) the front face shows the corner triangle (the top square of the column) and the top face shows the thin triangle of the bottom square, which are correct. But the right face should then be the end square with the shaded band across its lower half, and (ii) shows a vertical band down the front half of that face instead. So (ii) cannot be folded from this net and only (i) can.