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GATE 2026 IN GA Q.7: solution and answer

GATE 2026 · INGA Q.7 · 2 marks · MCQ

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?

GATE 2026 IN GA question 7: A vertical line separates Panel I (left) from Panel II (right).Tap to open full size
Figure from the GATE 2026 IN paper. It is part of the question.
Figure description

A vertical line separates Panel I (left) from Panel II (right). Panel I is a cross-shaped net of six equal squares: a centre square with one square above it, one to its left, one to its right, and a column of two squares below it. All four edges of the centre square are dashed, and so is the edge between the two lower squares. Every other outline is solid. Shading (grey on white): - Top square: a grey right isosceles triangle in its bottom-right corner. Its legs are half the side, lying along the bottom edge (shared with the centre square) and along the right edge. - Left square: grey everywhere except a white quarter-square in its top-right corner, the corner that touches the centre square's top-left corner. The grey region is L-shaped (three quarters of the square). - Centre square: a thin grey vertical stripe down the middle, running the full height. - Right square: a grey quarter-square in its top-right corner (the outer top corner). - Square directly below the centre: a thin grey horizontal stripe across the middle, running the full width. - Bottom square: its lower half is grey. Panel II shows two cubes in oblique view. Each shows its front, top and right faces. (i) Front face: grey with a white quarter-square in its bottom-left corner. Right face: lower half grey, and the boundary is horizontal at mid-height (parallel to the face's top edge). Top face: white with a thin grey stripe at mid-depth, parallel to the front edge. (ii) Front face: white with a grey right isosceles triangle in its bottom-right corner (legs half the side, along the bottom and right edges). Top face: the front half, next to the front edge, is grey. Right face: a grey quarter-square in its top-front corner.

  1. (A)

    Only (i) can correspond to the unfolded cube in Panel I.

  2. (B)

    Only (ii) can correspond to the unfolded cube in Panel I.

  3. (C)

    Both (i) and (ii) can correspond to the unfolded cube in Panel I.

  4. (D)

    Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.

Answer and solution

ANSWER

(B) Only (ii) can correspond to the unfolded cube in Panel I.

Official answer: BSource: Official answer key, GATE 2026 IN (IIT Guwahati)

  1. Name the faces. T = top square (triangle), L = left square ( grey), C = centre square (vertical stripe), R = right square (grey quarter), S = square below C (horizontal stripe), H = bottom square (half grey).

  2. Opposite faces in a cross net: two squares that are one square apart in a straight row are opposite. So T–S, C–H and L–R are the opposite pairs. Any two faces that are not in the same pair share an edge.

  3. Fold with C facing you. T becomes the top, L the left, R the right, S the bottom and H the back. H is hinged to S, so H's grey lower half becomes the upper half of the back face, which is the half along its edge with T.

  4. Where each marking ends up: the triangle on T sits at the corner where T meets C and R, with its legs along the T–C and T–R edges. L is white only in the quarter at the corner where it meets T and C. R's grey quarter is at the corner where R, T and H meet. The stripe on S runs parallel to the S–H edge and at right angles to the S–L edge.

  5. Cube (i): the front must be L, because it is the only -grey face. The right face must be H, because it is the only half-grey face. The top face carries a thin stripe, so it is C or S. C is opposite H and cannot touch the right face, so the top face is S.

  6. In (i), L's white quarter is diagonally opposite the corner it shares with H and S (the top-right corner of the front face), which is correct. H's grey half is the half away from S (the lower half of the right face), which is also correct. But the stripe on S must meet the S–L edge (the top face's front edge) at a right angle and run from front to back. The drawing shows it parallel to the front edge, so (i) is impossible.

  7. Cube (ii): the front is T (the only face with a triangle), the top is H (half grey) and the right face is R (grey quarter). No two of these are an opposite pair, so all three can meet at one corner, the corner shared by T, R and H.

  8. Check (ii) against the fold. The triangle on T lies on the R edge, at the end away from H, so it should be at the bottom-right of the front face ✓. H's grey half lies along its edge with T, so the front half of the top face should be grey ✓. R's grey quarter touches the corner shared with T and H, so it should be at the top-front of the right face ✓. On the folded cube the three faces also go round that corner in the same order as in the drawing (top, then right, then front, clockwise), so (ii) is not a mirror image.

  9. Only (ii) can come from the net, so the answer is (B).

KEY IDEA

In a cross-shaped net, squares one apart in a straight line become opposite faces, and every other pair shares an edge. Fix one face as the front, fold the net, and note which edge or corner each marking touches. A drawn cube is possible only if all three visible faces can meet at one corner, each marking touches the right edge or corner, and the faces go round the corner in the right order (no mirror image).

WATCH OUT FOR

Accepting (i) because its three faces (L, S, H) can meet at a corner and the two big markings, L's white quarter and H's grey half, are in the right places, without checking which way the thin stripe on S runs. That stripe has to cross the S–L edge at a right angle, so it cannot be parallel to the front edge. A second common slip is forgetting that H turns over when it folds onto S: its lower half in the net becomes the half of the back face next to T.

From the GATE 2026 IN paper. Every question of this paper · Download the full paper · All 23 Spatial questions, with notes

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