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

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

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Most viewed questions in Spatial Aptitude

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GATE CSE 2023 | GA Question: 5
Looking at the surface of a smooth $3$-dimensional object from the outside, which one of the following options is $\text{TRUE}?$ The surface of the object must be concave everywhere. The surface of the object must be convex everywhere. The surface of the object may be concave in some places and convex in other places. The object can have edges, but no corners.
Looking at the surface of a smooth $3$-dimensional object from the outside, which one of the following options is $\text{TRUE}?$The surface of the object must be concave ...
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14 votes
GATE CSE 2022 | GA Question: 10
A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land has equally spaced poles, marked as dots in the below figure. Two ropes, $\text{R1}$ and $\text{R2},$ ... desired plots? A single rope can pass through three poles that are aligned in a straight line. $2$ $4$ $5$ $3$
A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land has equally spaced ...
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2 answers
5 votes
GATE CSE 2023 | GA Question: 10
Which one of the options best describes the transformation of the $2$-dimensional figure $\mathbf{P}$ to $\mathbf{Q}$, and then to $\mathbf{R}$, as shown? $\text{Operation 1:}$ A clockwise rotation by $90^{\circ}$ about an axis ... $180^{\circ}$ about an axis perpendicular to the plane of the figure $\text{Operation 2:}$ A reflection along a vertical line
Which one of the options best describes the transformation of the $2$-dimensional figure $\mathbf{P}$ to $\mathbf{Q}$, and then to $\mathbf{R}$, as shown?$\text{Operation...
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3 answers
8 votes
GATE CSE 2022 | GA Question: 5
A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters. From the additional plates given in the options, which one of the combinations of additional plates would allow ... player should use all the five plates exactly once. The plates can be rotated in their plane. A. B. C. D.
A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters. From the additiona...
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1 answers
11 votes
GATE CSE 2021 Set 1 | GA Question: 2
A polygon is convex if, for every pair of points, $\text{P}$ and $\text{Q}$ belonging to the polygon, the line segment $\text{PQ}$ lies completely inside or on the polygon. Which one of the following is $\underline{\text{NOT}}$ a convex polygon?
A polygon is convex if, for every pair of points, $\text{P}$ and $\text{Q}$ belonging to the polygon, the line segment $\text{PQ}$ lies completely inside or on the polygo...
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5.0k
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2 answers
10 votes
GATE CSE 2021 Set 2 | GA Question: 7
A jigsaw puzzle has $2$ pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.
A jigsaw puzzle has $2$ pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can...
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3 votes
GATE CSE 2024 | Set 2 | GA Question: 9
​​​​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 $3$ $4$ $7$ $8$
​​​​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 cub...
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2 answers
11 votes
GATE CSE 2021 Set 2 | GA Question: 2
A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ___________.
A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ___________.
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3 answers
2 votes
GATE CSE 2024 | Set 1 | GA: 10
​​The least number of squares to be added in the figure to make $\text{A B}$ a line of symmetry is $6$ $4$ $5$ $7$
​​The least number of squares to be added in the figure to make $\text{A B}$ a line of symmetry is$6$$4$$5$$7$
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1 answers
2 votes
GATE CSE 2024 | Set 1 | GA: 9
A rectangular paper of $20 \mathrm{~cm} \times 8 \mathrm{~cm}$ is folded $3$ times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in $\mathrm{cm}$ ) is $18$ $24$ $20$ $21$
A rectangular paper of $20 \mathrm{~cm} \times 8 \mathrm{~cm}$ is folded $3$ times. Each fold is made along the line of symmetry, which is perpendicular to its long edge....
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9 votes
GATE CSE 2021 Set 1 | GA Question: 4
    A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like _______.    
  A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the rev...
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2.5k
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1 answers
1 votes
GATE ECE 2023 | GA Question: 5
How many rectangles are present in the given figure? $8$ $9$ $10$ $12$
How many rectangles are present in the given figure? $8$$9$$10$$12$
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2.3k
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3 answers
0 votes
GATE DS&AI 2024 | GA Question: 10
​​​​​Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what shape does the outer boundary of the resulting cross-section make? A rhombus A triangle An ellipse A hexagon  
​​​​​Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes thro...
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2.2k
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1 answers
11 votes
GATE Civil 2021 Set 1 | GA Question: 7
Consider two rectangular sheets, Sheet $\text{M}$ and Sheet $\text{N}$ of dimensions $6\:\text{cm} \times 4\: \text{cm}$ each. Folding operation $1:$ The sheet is folded into half by joining the short edges of the current shape. Folding operation $2:$ The ... $\text{M}$ is _____________. $13:7$ $3:2$ $7:5$ $5:13$
Consider two rectangular sheets, Sheet $\text{M}$ and Sheet $\text{N}$ of dimensions $6\:\text{cm} \times 4\: \text{cm}$ each.Folding operation $1:$ The sheet is folded i...
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2 answers
9 votes
GATE Mechanical 2021 Set 2 | GA Question: 9
Consider a square sheet of side $1$ unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded shape is again folded along its line of symmetry. The area of each face of the final folded shape, ... units, equal to _________ $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$ $\frac{1}{32}$
Consider a square sheet of side $1$ unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded s...
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1 answers
2 votes
GATE ECE 2023 | GA Question: 10
A $100 \mathrm{~cm} \times 32 \mathrm{~cm}$ rectangular sheet is folded $5$ times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions $100 \mathrm{~cm} \times 1 \mathrm{~cm}$. The total number of creases visible when the sheet is unfolded is ___________. $32$ $5$ $31$ $63$
A $100 \mathrm{~cm} \times 32 \mathrm{~cm}$ rectangular sheet is folded $5$ times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually,...
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2.0k
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1 answers
2 votes
GATE CH 2023 | GA Question: 5
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The given figure consists of $16$ unit squares arranged as shown. In addition to the three black squares ... both $\text{PQ}$ and $\text{MN}$ form lines of symmetry? (The figure is representative) $3$ $4$ $5$ $6$
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.The given fi...
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1.9k
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1 answers
7 votes
GATE ECE 2021 | GA Question: 3
The least number of squares that must be added so that the line $P-Q$ becomes the line of symmetry is ____________ $4$ $3$ $6$ $7$
The least number of squares that must be added so that the line $P-Q$ becomes the line of symmetry is ____________$4$$3$$6$$7$
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1.9k
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1 answers
2 votes
GATE IN 2023 | GA Question: 10
An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The cylinder can be reoriented in any direction within the light beam. Under these ... $\mathbf{S}$ is NOT possible? $\mathrm{P}$ $\mathrm{Q}$ $\mathrm{R}$ $\mathrm{S}$
An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of...
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1.8k
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2 answers
6 votes
GATE Electrical 2021 | GA Question: 3
For a regular polygon having $10$ sides, the interior angle between the sides of the polygon, in degrees, is: $396$ $324$ $216$ $144$
For a regular polygon having $10$ sides, the interior angle between the sides of the polygon, in degrees, is:$396$$324$$216$$144$
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