GATE PI Spatial Aptitude PYQs & Answers

Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–10 of 13. Imported answers require independent review unless marked reviewed.

Topic practice 13 questionsPage 1 of 2

The figure below is supposed to show three non-overlapping shapes – one oval and two triangles. Which one of the following figures P, Q, R, or S fits the missing portion indicated by ‘?’ and completes the oval and the two triangles?

Diagram for Production and Industrial Engineering question 2

Your answerChoose one option.

Diagram for Production and Industrial Engineering question 2 (figure 2)

Diagram for Production and Industrial Engineering question 2 (figure 3)

Diagram for Production and Industrial Engineering question 2 (figure 4)

Diagram for Production and Industrial Engineering question 2 (figure 5)

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Which one of the following figures P, Q, R, or S, correctly shows the 45° clockwise-rotated version of figure (I)?

Diagram for Production and Industrial Engineering question 5

Your answerChoose one option.

Diagram for Production and Industrial Engineering question 5 (figure 2)

Diagram for Production and Industrial Engineering question 5 (figure 3)

Diagram for Production and Industrial Engineering question 5 (figure 4)

Diagram for Production and Industrial Engineering question 5 (figure 5)

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Based on the relationship between each polygon and the number inside it, the value of ‘X’ is _____.

Diagram for Production and Industrial Engineering question 8

Your answerChoose one option.

720

596

240

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A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius r cm as shown in the figure. The side of the dodecagon is d cm. All the triangles (numbered 1 to 12) in the figure are used to form squares of side r cm and each numbered triangle is used only once to form a square.

The number of squares that can be formed and the number of triangles required to form each square, respectively, are:

Note: The figure shown is representative.

Your answerChoose one option.

3; 4

4; 3

3; 3

3; 2

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The 15 parts of the given figure are to be painted such that no two adjacent parts with shared boundaries (exclude corners) have the same color. The minimum number of colors required is

Your answerChoose one option.

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Three different views of a dice are shown in the figure below.

Diagram for Production and Industrial Engineering question 9

The piece of paper that can be folded to make this dice is

Your answerChoose one option.

Diagram for Production and Industrial Engineering question 9 (figure 2)

Diagram for Production and Industrial Engineering question 9 (figure 3)

Diagram for Production and Industrial Engineering question 9 (figure 4)

Diagram for Production and Industrial Engineering question 9 (figure 5)

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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?

Your answerChoose one option.

A rhombus

A triangle

An ellipse

A hexagon

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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, what is the minimum number of squares that must be colored black, such that both PQ and MN form lines of symmetry? (The figure is representative)

Your answerChoose one option.

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Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

Your answerChoose one option.

circle

regular octagon

regular pentagon

rhombus

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A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.

What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?

Your answerChoose one option.

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GATE PI Spatial Aptitude PYQs

How to practice Spatial Aptitude

Question 2

Question 5

Question 8

Question 8

Question 2

Question 9

Question 10

Question 5

Question 10

Question 5