Paper Folding, Embedded Figures, Figure Matrix and Pattern Completion
Paper Folding, Embedded Figures, Figure Matrix and Pattern Completion
These non-verbal items test how shapes behave when folded, hidden or arranged. In paper folding, every fold doubles the holes when the paper is opened, placed symmetrically about the fold lines. In embedded figures, you trace a simple shape inside a complex one. Figure matrices and pattern completion follow a row, column or symmetry rule.
1. Rules Box
| Type | Rule |
|---|---|
| Paper folded k times, one hole punched through all layers | 2ᵏ holes when opened, mirrored across each fold line |
| Embedded figure | The shape must appear with the same proportions and angles, possibly rotated |
| Figure matrix (3 × 3) | Each row (or column) contains each shape or feature once, or follows a change rule |
| Pattern completion | Use the symmetry of the whole design: mirror across the centre lines or turn by 90° |
Unfold step by step in reverse order: undo the last fold first
A hole punched on a fold line appears once per fold layer on that line (half-holes join into one)
✗ Folded twice, one hole gives 2 holes | ✓ Each fold doubles: 2 × 2 = 4
✗ In a figure matrix, look only at the shapes | ✓ Check every feature: shape, count of dots, shading and orientation
हिंदी नोट: कागज़ मोड़ने के प्रश्नों में हर मोड़ छेदों को दोगुना करता है और खोलने पर छेद मोड़ की रेखा के दोनों ओर सममित आते हैं। आकृति आव्यूह में हर पंक्ति का नियम देखिए: आकृति, बिंदुओं की संख्या, छायांकन।
Exam Pointer: These patterns had no verified NTPC shift in our check (paper folding and embedded figure pages found were from SSC and ALP papers) and are tagged syllabus-based. They are part of the NTPC non-verbal syllabus.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Paper folding and punching
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A square sheet is folded once, left half onto the right half, and one hole is punched through the folded paper near its centre. How many holes are there when it is opened, and where?
One fold doubles the hole: 2 holes, placed as mirror images on either side of the vertical fold line.
Answer: 2 holes, mirrored across the fold
EXAMATLAS LEVEL
Q. A square sheet is folded left onto right and then top onto bottom, and one hole is punched near the free corner of the folded quarter. How many holes appear when it is opened, and how are they arranged?
Two folds give 2 × 2 = 4 holes. Undoing the second fold mirrors the hole across the horizontal line, and undoing the first mirrors both across the vertical line, so there is one hole in each quarter, each near an outer corner.
Answer: 4 holes, one near each corner
Pattern 2: Embedded figures
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. Which of these can be traced inside a square with both diagonals drawn? (a) Triangle (b) Pentagon (c) Circle (d) Hexagon
The diagonals cut the square into triangles; no pentagon, circle or hexagon can be traced along its lines.
Answer: (a) Triangle
EXAMATLAS LEVEL
Q. A large triangle has a line joining the midpoints of two of its sides. Which shape can be traced in it? (a) Trapezium (b) Pentagon (c) Square (d) Circle
The line cuts off a small triangle at the top and leaves a four-sided piece below with one pair of parallel sides: a trapezium.
Answer: (a) Trapezium
Pattern 3: Figure matrix
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. In a 3 × 3 grid, row 1 is circle, square, triangle; row 2 is square, triangle, circle; row 3 is triangle, circle, ?. What is the missing figure?
Each row contains each shape once, so the missing shape is the square.
Answer: Square
EXAMATLAS LEVEL
Q. In a 3 × 3 grid, row 1 is circle with 1 dot, square with 2 dots, triangle with 3 dots; row 2 is square with 2 dots, triangle with 3 dots, circle with 1 dot; row 3 is triangle with 3 dots, circle with 1 dot, ?. What is the missing figure?
Each row has each shape once, and each shape always carries the same number of dots (circle 1, square 2, triangle 3). The missing figure is a square with 2 dots.
Answer: Square with 2 dots
Pattern 4: Pattern completion by symmetry
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A square design has four identical quarters, each turned 90° clockwise from the previous one, going round clockwise. The top-left quarter has an arrow pointing right and the top-right quarter an arrow pointing down. What does the bottom-right quarter show?
Each quarter turns the arrow 90° clockwise: right, down, then left.
Answer: Arrow pointing left
EXAMATLAS LEVEL
Q. A square design is symmetric about both its vertical and horizontal centre lines. The top-left quarter has a dot near the centre of the design and a short line pointing towards the top-left corner. What does the bottom-right quarter contain?
Mirroring across both centre lines sends the top-left quarter to the bottom-right: the dot stays near the centre and the line now points towards the bottom-right corner.
Answer: A dot near the centre and a line towards the bottom-right corner
60-Second Revision
- Each fold doubles the holes; unfold in reverse order.
- Embedded shapes keep their proportions; they may be rotated.
- Figure matrix: check shape, count and shading in every row.
- Pattern completion: use the design's symmetry or turning rule.