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Spatial Aptitude Notes for GATE CS

GATE CS Spatial Aptitude: 1 units and 5 chapters, weightage from 19 previous year questions across 10 papers, a study order by exam weight and 105 practice qu

A question from this chapter

Question 1

Level 1: Warm-up

A rectangular paper of dimensions 16 cm \times 4 cm is folded twice. In each fold, the paper is folded along a line of symmetry perpendicular to one of its edges. What is the minimum possible perimeter (in cm) of the final folded sheet?

Question 2

Level 1: Warm-up

How many lines of symmetry does a standard rectangle (that is not a square) have?

Question 3

Level 1: Warm-up

In a cube net, four squares are arranged in a straight continuous row. If the squares are numbered 1, 2, 3, and 4 from left to right, which pair of squares will become opposite faces when the net is folded into a cube?

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Spatial Aptitude Notes for GATE CS

GATE CS Spatial Aptitude: 1 units and 5 chapters, weightage from 19 previous year questions across 10 papers, a study order by exam weight and 105 practice questions.

About Spatial Aptitude Notes

Full study notes for Spatial Aptitude in GATE CS, organised across 5 chapters. Each chapter page explains concepts from the basics with worked examples and the formulas you need.

GATE CS Spatial Aptitude Unit-wise Weightage from Past Papers

We counted every GATE CS Spatial Aptitude previous year question in our bank (19 questions from 10 papers) and grouped them by unit.

Unit	Chapters	PYQs	Share of section	Avg per paper
Transformation of shapes	5	19	100%	1.9

Suggested Spatial Aptitude Study Order for GATE CS

Transformation of shapes: 100% of past Spatial Aptitude questions, about 1.9 per paper.

Start where the marks are. Units at the top of this list have appeared most often in past GATE CS papers.

Units in GATE CS Spatial Aptitude

Transformation of shapes Notes (5 chapters)

All Spatial Aptitude chapters

One Solved Question from Each Spatial Aptitude Chapter

Question 1 · Paper Folding, Cutting and Unfolding MCQ

A rectangular paper of dimensions $16 cm \times 4 cm$ is folded twice. In each fold, the paper is folded along a line of symmetry perpendicular to one of its edges. What is the minimum possible perimeter (in cm) of the final folded sheet?

A.
16
B.
20
C.
24
D.
34

Correct Answer:

Step-by-Step Solution

Key idea: To minimize the perimeter, halve the largest dimension at each step to make the final shape as close to a square as possible.

Step 1: Initial dimensions $16 cm \times 4 cm$ .

Step 2: Fold 1 perpendicular to $16 cm$ edge $\to 8 cm \times 4 cm$ .

Step 3: Fold 2 perpendicular to $8 cm$ edge $\to 4 cm \times 4 cm$ .

Step 4: Perimeter $= 2 \times (4 + 4) = 16 cm$ .

(Other fold sequences yield perimeters of $20 cm$ or $34 cm$ .)

Answer: 16

Question 2 · Symmetry, Rotation and Reflection MCQ

How many lines of symmetry does a standard rectangle (that is not a square) have?

A.
1
B.
2
C.
4
D.
Infinite

Correct Answer:

Step-by-Step Solution

Key idea: This is a direct recall question about the properties of common geometric shapes, specifically the lines of symmetry of a rectangle.

Step 1: Recall the definition of a line of symmetry (a line that creates identical mirror halves).

Step 2: Test potential lines on a rectangle.

A vertical line through the midpoints of the top and bottom sides creates mirror halves. (1 line)
A horizontal line through the midpoints of the left and right sides creates mirror halves. (1 line)
A diagonal line does NOT create mirror halves (the triangles formed are congruent but not mirror images across the diagonal).

Step 3: Count the valid lines. There are exactly 2 lines of symmetry.

Answer: B

Question 3 · Three-Dimensional Solids, Nets and Orthographic Views MCQ

In a cube net, four squares are arranged in a straight continuous row. If the squares are numbered 1, 2, 3, and 4 from left to right, which pair of squares will become opposite faces when the net is folded into a cube?

A.
1 and 2
B.
1 and 3
C.
2 and 3
D.
1 and 4

Correct Answer:

Step-by-Step Solution

Key idea: This is a <direct_formula> question testing the opposite face rules in straight rows.

Step 1: Recall the separation rule for straight rows. In a continuous straight line of squares, any two squares separated by exactly one square will become opposite faces when folded.

Step 2: Apply the rule to the numbered row (1, 2, 3, 4).

Step 3: Square 1 and Square 3 are separated by Square 2. Therefore, 1 and 3 are opposite.

Step 4: Similarly, Square 2 and Square 4 are separated by Square 3. Therefore, 2 and 4 are opposite.

Step 5: Check the options. Option B correctly identifies the pair 1 and 3.

Answer: B