GATE AR 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 12. Imported answers require independent review unless marked reviewed.

Topic practice 12 questionsPage 1 of 2

The four pieces of a puzzle are shown in the figure below.

Diagram for Architecture and Planning question 3

Which one of the figures labelled as P, Q, R, and S can be constructed by using each of the four pieces only once without overlaps?

Your answerChoose one option.

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The given figure is reflected about the horizontal dashed line and then rotated clockwise by 90° about an axis perpendicular to the plane of the figure.

Which one of the following options correctly shows the resultant figure?

Note: The figures shown are representative.

Diagram for Architecture and Planning question 8

Your answerChoose one option.

Diagram for Architecture and Planning question 8 (figure 2)

Diagram for Architecture and Planning question 8 (figure 3)

Diagram for Architecture and Planning question 8 (figure 4)

Diagram for Architecture and Planning question 8 (figure 5)

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Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?

Your answerChoose one option.

Circle; Square; Equilateral triangle; Isosceles triangle

Isosceles triangle; Equilateral triangle; Square; Circle

Equilateral triangle; Isosceles triangle; Square; Circle

Isosceles triangle; Square; Equilateral triangle; Circle

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

Diagram for Architecture and Planning question 2

Your answerChoose one option.

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

Diagram for Architecture and Planning question 9

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

Your answerChoose one option.

Diagram for Architecture and Planning question 9 (figure 2)

Diagram for Architecture and Planning question 9 (figure 3)

Diagram for Architecture and Planning question 9 (figure 4)

Diagram for Architecture and Planning 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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The symbols ◯, ∗, △, and □ are to be filled, one in each box, as shown below. The rules for filling in the four symbols are as follows.

Every row and every column must contain each of the four symbols.

Every 2×2 square defined by bold lines must contain each of the four symbols. Which symbol will occupy the box marked with ‘?’ in the partially filled figure?

Diagram for Architecture and Planning question 5

Your answerChoose one option.

◯

∗

△

□

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An opaque pyramid (shown below), with a square base and isosceles faces, 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 pyramid can be oriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?