GATE ES topic:spatial-aptitude PYQs & Answers

Questions 1–10 of 14. Imported answers require independent review unless marked reviewed.

To continue the sequence of tiles shown, the tile indicated by the question mark should be

Diagram for Environmental Science and Engineering question 2

Your answerChoose one option.

Diagram for Environmental Science and Engineering question 2 (figure 2)

A tile with four dots, one near each corner.

Diagram for Environmental Science and Engineering question 2 (figure 3)

A tile with six dots in two columns of three.

Diagram for Environmental Science and Engineering question 2 (figure 4)

A tile with seven dots: three in each outer column and one in the centre.

Diagram for Environmental Science and Engineering question 2 (figure 5)

A tile with nine dots in a 3 × 3 arrangement.

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Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch over the walkways that join at that junction. The minimum number of guards needed to watch all the walkways is ________.

Diagram for Environmental Science and Engineering question 3

Your answerChoose one option.

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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.

Diagram for Environmental Science and Engineering question 8

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 Environmental Science and Engineering question 9

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

Your answerChoose one option.

Diagram for Environmental Science and Engineering question 9 (figure 2)

Diagram for Environmental Science and Engineering question 9 (figure 3)

Diagram for Environmental Science and Engineering question 9 (figure 4)

Diagram for Environmental Science and 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 cuting 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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How many triangles are present in the given figure?

Diagram for Environmental Science and Engineering question 5

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A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.

The area of the shaded region is ______ cm

Diagram for Environmental Science and Engineering question 10

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The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.

Diagram for Environmental Science and Engineering question 4

What is the maximum number of squares without a “hole in the interior” that can be formed within the 4 × 4 grid using the unit squares as building blocks?

Your answerChoose one option.

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An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.

If the security guard does not move around the posted location and has a 360° view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery?

Your answerChoose one option.

P and Q

Q and S

R and S

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GATE ES topic:spatial-aptitude PYQs

How to practice topic:spatial-aptitude

Question 2

Question 3

Question 8

Question 2

Question 9

Question 10

Question 5

Question 10

Question 4

Question 5