📑 Topics on this page (Jump to Topic):
📌 1. Number of Holes
| Number of folds | Layers | 1 punch gives |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 2 | 2 |
| 2 | 4 | 4 |
| 3 | 8 | 8 |
| n | 2ⁿ | 2ⁿ |
- When unfolding, each fold line acts as a mirror line — the hole is reflected across it.
- A hole exactly on the fold line merges into one larger hole (the count reduces).
⚠️ Exam Traps:
- Every fold doubles the layers, even a diagonal fold.
- Unfold in reverse order: the last fold opens first.
📌 2. Cutting
- Cut a triangle from a corner of a folded sheet → on opening, diamonds (◇) or triangles appear at corners/centre.
- A cut at the corner where all folds meet = one shape in the middle on opening.
📌 3. Pattern Completion
- Patterns are usually symmetric both ways — the missing part is the mirror image of the opposite part.
- Check line continuity: lines in the missing part must join the surrounding lines.
📌 4. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. A square sheet is folded once in half and punched once (away from the fold). How many holes on opening? Practice
Correct answer: (B)
1 fold = 2 layers ⇒ 2 holes.
1 fold = 2 layers ⇒ 2 holes.
Q2. A sheet is folded twice and punched once (not on a fold line). How many holes on opening? Practice
Correct answer: (C)
2 folds = 4 layers ⇒ 4 holes.
2 folds = 4 layers ⇒ 4 holes.
Q3. A sheet is folded three times and punched twice (away from folds). Total holes on opening? Practice
Correct answer: (D)
3 folds = 8 layers; 2 × 8 = 16.
3 folds = 8 layers; 2 × 8 = 16.
Q4. A sheet is folded once and punched exactly on the fold line. How many holes on opening? Practice
Correct answer: (A)
A hole on the fold line is one shared hole ⇒ one larger hole.
A hole on the fold line is one shared hole ⇒ one larger hole.
Q5. How many layers does a sheet folded 4 times have? Practice
Correct answer: (B)
2⁴ = 16.
2⁴ = 16.
Q6. A sheet is folded in half left to right and punched in the upper-right area. On opening, where is the second hole? Practice
Correct answer: (C)
Reflection across the vertical fold ⇒ same height, on the left.
Reflection across the vertical fold ⇒ same height, on the left.
Q7. A sheet is folded top to bottom and punched near the upper-left corner of the folded sheet. Where is the second hole on opening? Practice
Correct answer: (D)
Reflection across the horizontal fold ⇒ still on the left, flipped up-down.
Reflection across the horizontal fold ⇒ still on the left, flipped up-down.
Q8. A square sheet is folded along both diagonals (2 folds) and punched once. How many holes on opening? Practice
Correct answer: (A)
Diagonal folds also double layers ⇒ 4 layers ⇒ 4 holes.
Diagonal folds also double layers ⇒ 4 layers ⇒ 4 holes.
Q9. A sheet folded twice is cut at the corner where both folds meet. Where does the cut appear on opening? Practice
Correct answer: (B)
The meeting point of both folds is the centre of the open sheet.
The meeting point of both folds is the centre of the open sheet.
Q10. A sheet folded twice is cut at the outer corner (with open edges). How many corners appear cut on opening? Practice
Correct answer: (C)
The open corner is made of the four real corners ⇒ 4 corners cut.
The open corner is made of the four real corners ⇒ 4 corners cut.
Q11. A sheet folded 3 times is punched once exactly on the last fold line only. How many holes on opening? Practice
Correct answer: (D)
A hole on the last fold merges pairs ⇒ 8/2 = 4 holes.
A hole on the last fold merges pairs ⇒ 8/2 = 4 holes.
Q12. In pattern completion, how is the missing part usually found? Practice
Correct answer: (A)
Patterns are usually symmetric.
Patterns are usually symmetric.
Q13. A sheet folded once is punched 3 times (away from the fold). Total holes on opening? Practice
Correct answer: (B)
3 × 2 = 6.
3 × 2 = 6.
Q14. A sheet is folded in half twice; one punch lies on one fold line (away from the other). Holes on opening? Practice
Correct answer: (C)
4 layers, holes merge in pairs on the fold ⇒ 4/2 = 2.
4 layers, holes merge in pairs on the fold ⇒ 4/2 = 2.
Q15. In what order are folds undone when opening? Practice
Correct answer: (D)
Unfold in reverse order.
Unfold in reverse order.
Q16. A sheet is folded once along a diagonal and punched once. The two holes are symmetric about which line? Practice
Correct answer: (A)
The fold line is the mirror line.
The fold line is the mirror line.
Q17. A rectangular sheet is folded 5 times and punched once (away from folds). Holes on opening? Practice
Correct answer: (B)
2⁵ = 32.
2⁵ = 32.
Q18. A sheet folded twice is punched only at the centre corner (where folds meet). Holes on opening? Practice
Correct answer: (C)
All layers meet at the centre ⇒ one hole at the centre.
All layers meet at the centre ⇒ one hole at the centre.
Q19. A sheet folded twice is punched 3 times (away from folds). Total holes on opening? Practice
Correct answer: (D)
3 × 4 = 12.
3 × 4 = 12.
Q20. A semicircle is cut from the open edge of a sheet folded in half. What appears on opening? Practice
Correct answer: (A)
The open edge is two separate edges ⇒ two semicircles. (Cutting from the fold would give a full circle.)
The open edge is two separate edges ⇒ two semicircles. (Cutting from the fold would give a full circle.)