GATE 2025 IN GA Q.4: solution and answer

GATE 2025 · INGA Q.4 · 1 mark · MCQ

The paper as shown in the figure is folded to make a cube where each square corresponds to a particular face of the cube. Which one of the following options correctly represents the cube?

Note: The figures shown are representative.

GATE 2025 IN GA question 4: A cube net of six equal squares in a cross shape. — Figure from the GATE 2025 IN paper. It is part of the question.

(A)
Figure — cube: front face an open triangle pointing up, top face a filled black circle, right face blank
(B)
Figure — cube: front face an open triangle, top face blank, right face a filled black triangle
(C)
Figure — cube: front face an open triangle, top face blank, right face blank
(D)
Figure — cube: front face an open triangle, top face a filled black triangle, right face a filled black circle

Answer and solution

ANSWER

(A): the cube with the open triangle on the front, the filled circle on top and a blank face on the right.

Official answer: ASource: Official answer key, GATE 2025 IN (IIT Roorkee)

Rule for a cross-shaped net: along any straight line of squares, two squares with exactly one square between them fold onto opposite faces, and a square's four edge-sharing neighbours fold onto the four faces adjacent to it.
Fold with the open triangle $△$ as the front face. The square above it (filled circle $∙$ ) becomes the top, the square below it (open circle $\circ$ ) becomes the bottom, and the blank squares on its left and right become the left and right faces.
The fourth square in the middle row (filled triangle $▲$ ) is two squares from $△$ , with the blank square between them, so it folds round to the back.
The opposite pairs are therefore $△ \leftrightarrow ▲$ , $∙ \leftrightarrow \circ$ and blank $\leftrightarrow$ blank (the first and third squares of the middle row). Opposite faces can never be seen together on one cube drawing.
(B) shows $△$ and $▲$ next to each other. They are opposite faces, so (B) is impossible.
(D) shows $△$ on the front and $▲$ on top. These are opposite faces too, so (D) is impossible.
(C) shows two blank faces next to each other (top and right). The only two blank faces are opposite each other, so (C) is impossible.
(A) shows $△$ on the front, $∙$ on top and a blank face on the right. This matches the fold in step 2 exactly: $∙$ is on the edge the triangle's apex points to, and the blank square to the right of $△$ in the net becomes the right face. So (A) is correct.

KEY IDEA

In a cross-shaped net, two squares with exactly one square between them fold onto opposite faces. That gives the pairs open triangle / filled triangle, filled circle / open circle and blank / blank. Any cube drawing that shows two faces from the same pair side by side is impossible, and that rules out (B), (C) and (D).

WATCH OUT FOR

Picking (C) because blank faces look like they cannot contradict anything. The net has only two blank squares, and they are opposite each other (first and third in the middle row), so two blank faces can never share an edge. A second trap is assuming the two triangles are adjacent because they sit in the same row of the net. In fact they are two squares apart, so they are opposite faces.

From the GATE 2025 IN paper. Every question of this paper · Download the full paper · All 23 Spatial questions, with notes

GATE 2025 IN GA Q.4: solution and answer

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