GATE CE topic:spatial-aptitude PYQs & Answers — Page 2

Questions 11–20 of 28. Imported answers require independent review unless marked reviewed.

Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction X, the planar image of the assembly appears as Figure B.

If viewed from direction Y, the planar image of the assembly (Figure A) will appear as

Diagram for Civil Engineering question 9

Your answerChoose one option.

Diagram for Civil Engineering question 9 (figure 2)

Diagram for Civil Engineering question 9 (figure 3)

Diagram for Civil Engineering question 9 (figure 4)

Diagram for Civil Engineering question 9 (figure 5)

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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 magnitude of the minimum angle of rotation is

Your answerChoose one option.

120°

60°

90°

180°

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In how many ways can cells in a 3 × 3 grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown.

Diagram for Civil Engineering question 3

Your answerChoose one option.

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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 figure below consists of 20 unit squares arranged as shown. In addition to the given black squares, up to 5 more may be coloured black. Which one among the following options depicts the minimum number of boxes that must be coloured black to achieve two lines of symmetry? (The figure is representative)

Diagram for Civil Engineering question 5

Your answerChoose one option.

c, d, i

c, i

c, d, i, f, g

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Consider a circle with its centre at the origin (O), as shown. Two operations are allowed on the circle.

Operation 1: Scale independently along the x and y axes. Operation 2: Rotation in any direction about the origin.

Which figure among the options can be achieved through a combination of these two operations on the given circle?

Your answerChoose one option.

Diagram for Civil Engineering question 5 (figure 2)

Diagram for Civil Engineering question 5 (figure 3)

Diagram for Civil Engineering question 5 (figure 4)

Diagram for Civil Engineering question 5 (figure 5)

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A square of side length 4 cm is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius 2 cm, as shown.

The area of the shaded region is ______ cm

Diagram for Civil Engineering question 10

Your answerChoose one option.

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In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXR, RUZ and SPQ is

Your answerChoose one option.

Area of SPQ = Area of RUZ = Area of PXR

Area of SPQ = Area of PXR − Area of RUZ

Area of PXR = Area of SPQ − Area of RUZ

Area of PXR = Area of RUZ − Area of SPQ

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For the picture shown above, which one of the following is the correct picture representing reflection with respect to the mirror shown as the dotted line?

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In the square grid shown on the left, a person standing at P2 position is required to move to P5 position.

The only movement allowed for a step involves, “two moves along one direction followed by one move in a perpendicular direction”. The permissible directions for movement are shown as dotted arrows in the right.

For example, a person at a given position Y can move only to the positions marked X on the right.

Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is

Your answerChoose one option.

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Consider a cube made by folding a single sheet of paper of appropriate shape. The interior faces of the cube are all blank. However, the exterior faces that are not visible in the above view may not be blank.

Which one of the following represents a possible unfolding of the cube?