GATE CS 2025 Set 1 | Question 9

MCQ · 2 marks · −0.66

A square paper, shown in figure (I), is folded along the dotted lines as shown in the figures (II) and (III). Then a few cuts are made as shown in figure (IV). Which one of the following patterns will be obtained when the paper is unfolded?

Note: The figures shown are representative.

Figures (I) to (IV): (I) a square sheet; (II) the sheet with a dotted fold line along the diagonal from the top-left to the bottom-right corner; (III) the folded triangle with a dotted fold line from its right-angle corner to the middle of its long side; (IV) the final small triangle, long side on top, with a triangle cut at the middle of the top side, a half-square cut on the left side and a small bar cut touching the right side.
  1. Option A:
    Unfolded square with small squares near the top-left and bottom-right corners, step-shaped cuts near the top-right and bottom-left corners, and a triangle at the middle of each edge pointing towards that edge
     (correct)
  2. Option B:
    Unfolded square with diamonds near the top-left and bottom-right corners, step-shaped cuts near the top-right and bottom-left corners, and a triangle at the middle of each edge pointing towards that edge
  3. Option C:
    Unfolded square with small squares near the top-left and bottom-right corners and step-shaped cuts near the top-right and bottom-left corners; the triangles at the left and right edges point outward, but those at the top and bottom edges point inward
  4. Option D:
    Unfolded square with one small square at the centre, step-shaped cuts near the top-right and bottom-left corners, and a triangle at the middle of each edge pointing towards that edge

Answer

(A)

Explanation

The two folds run along the two diagonals, so (IV) has four layers: its top side is the four outer edges of the sheet, its left side lies on the first fold (top-left to bottom-right diagonal) and its right side on the second fold. Unfolding mirrors every cut across both diagonals.

  • The top triangle appears at the middle of all four edges, each pointing towards its edge, which rules out (C).
  • The half-square on the first fold opens into a full square with sides parallel to the edges, near the top-left and near the bottom-right corner, which rules out (B) (diamonds) and (D) (one square at the centre).
  • The bar touching the second fold joins its mirror image to form the step shapes near the other two corners.

Answer: A