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Transformation of shapes: translation, rotation, scaling, mirroring, assembling, and grouping, Paper folding, cutting, and patterns in 2 and 3 dimensions

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2024-1} & \textbf{2024-2} &\textbf{2023} &\textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 0&0&1 & 1 &2&1 &0&0.83&2
\\\hline\textbf{2 Marks Count} &2&1&1 & 1&0&1 &1&1&2
\\\hline\textbf{Total Marks} &4&2&3 & 3 &2&3&  \bf{2}&\bf{2.83}&\bf{4}\\\hline
\end{array}}}$$

Recent questions in Spatial Aptitude

#1
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If a Complete Square board has 204 Squares than How many squares are there in 1/4th of the board?
#2
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Examples of mirror and water reflections are shown in the figures below: An object appears as the following image after first reflecting in a mirror and then reflecting on water.The original object is 
#3
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Two identical sheets $\text{A}$ and $\text{B}$, of dimensions $24 \mathrm{~cm} \times 16 \mathrm{~cm}$, can be folded into half using two distinct operations, $\text{FO1}$ ... $ and $\text{B}$ is$14:11$11: 14$18:11$11: 18$
#4
243
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A planar rectangular paper has two $\text{V}$-shaped pieces attached as shown below.This piece of paper is folded to make the following closed three-dimensional object.The number of folds required to form the above object is$9$7$11$8$
#5
235
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​​​Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is$30^{\circ}$60^{\circ}$45^{\circ}$90^{\circ}$
#6
181
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Five cubes of identical size and another smaller cube are assembled as shown in Figure $\text{A}$. If viewed from direction $\text{X}$, the planar image of the ... $\text{A}$) will appear as 
#7
272
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Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The ... $60^{\circ}$90^{\circ}$180^{\circ}$
#8
145
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0 answers
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In the $4 \times 4$ array shown below, each cell of the first three columns has either a cross $(X)$ or a number, as per the given rule.\begin{ ... $1$2$3$
#9
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1 answers
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Three different views of a dice are shown in the figure below.The piece of paper that can be folded to make this dice is   
#10
2.4k
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3 answers
0 votes
Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting ... outer boundary of the resulting cross-section make?A rhombusA triangleAn ellipseA hexagon 
#11
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2 answers
3 votes
​​​​A cube is to be cut into $8$ pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube.The minimum number of such cuts required is$3$4$7$8$
#12
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1 answers
2 votes
A rectangular paper of $20 \mathrm{~cm} \times 8 \mathrm{~cm}$ is folded $3$ times. Each fold is made along the line of symmetry, which is perpendicular to its ... $ ) is$18$24$20$21$
#13
3.5k
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3 answers
2 votes
​​The least number of squares to be added in the figure to make $\text{A B}$ a line of symmetry is$6$4$5$7$
#14
635
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0 answers
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The assembly shown below has three teethed circular objects (Pinions) and two teethed flat objects (Racks), which are perfectly mating with each ... the anticlockwise direction.Object $\mathrm{Q}$ rotates in the clockwise direction.
#15
690
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1 answers
6 votes
The numbered net shown is folded to form a cube. What is the product of the numbers on the four faces sharing an edge with the face numbered 1?120144180240
#16
336
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1 answers
4 votes
The diagram shows a square divided into eight pieces. Which shape is not one of those pieces?
#17
375
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1 answers
3 votes
In the diagram, a figure is formed dividing a square into eight identical pieces using its two diagonals and the two lines joining the midpoints of opposite sides, ... in line L.Which of the following shows the final position of the figure?
#18
252
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1 answers
0 votes
Consider two cones joined at a common circular base. If we cut a plane passing through the vertices of both cones, what type of shape will be formed by the intersection of the plane with the combined cones?RhombusTriangleHexagonEllipse