This page covers RRB NTPC Paper Folding & Cutting with complete concept notes, 11 graded practice MCQs, key points and exam-specific tips. Free to study.
When paper is folded and cut, the cuts create symmetric patterns when unfolded. Each fold creates a mirror effect. The number of holes depends on how many times the paper was folded
💡Key Rules
First, count the number of folds carefully. Each fold doubles the number of holes. One cut on a paper folded once = 2 holes. One cut on a paper folded twice = 4 holes.
Second, holes appear symmetrically around fold lines. Third, the position of holes mirrors across each fold line. Fourth, the shape of holes remains the same, only position changes.
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Exam Patterns
What examiners ask — read before attempting PYQs
SSC CGL typically asks 1-2 questions on this topic. Questions show 2-4 folding steps followed by cutting. You get 4 answer choices showing different unfolded patterns. The cuts are usually simple shapes - circles, triangles, or small squares.
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Shortcuts
Use these to save 30–60 seconds per question
Use the 'Fold Count Formula' - Number of holes = 2^(number of folds) × number of cuts. For symmetry, imagine drawing lines where folds occurred. Holes must appear symmetrically on both sides of these imaginary lines.
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Worked Example
Solve this step-by-step before moving on
1
Step 1
Count folds = 2 folds (vertical + horizontal)
2
Step 2
Count cuts = 1 cut (one circle)
3
Step 3
Apply formula = 2^2 × 1 = 4 holes
4
Step 4
Determine positions - Original cut was at top-right of folded paper. When unfolded, holes appear at all four corners (top-right, top-left, bottom-right, bottom-left) due to symmetry around both fold lines.
5
Step 5
Verify symmetry - Draw imaginary vertical and horizontal lines through center. Holes are symmetric around both lines.
Advanced Trick: For complex folding, trace the cut position backwards through each fold. Start from the final cut position and mirror it across each fold line in reverse order.
Common Mistake: Students often forget to account for all folds or miscalculate symmetry. Remember that each fold creates a new axis of symmetry. Also, don't confuse the number of paper layers with the number of holes. Focus on fold lines, not thickness.
Test Paper Folding & Cutting under exam conditions
A square piece of paper is folded once along its diagonal. Then it is folded again along the midline of the resulting triangle. After unfolding completely, how many creases will be visible on the paper?
Practice 2easy
A rectangular paper is folded once vertically down the middle. Without unfolding, it is then folded once horizontally across the middle. If you cut out a small square from the top-right corner of the twice-folded paper, how many square pieces will be removed from the original unfolded paper?
Practice 3easy
A square paper is folded diagonally, then the resulting triangle is folded in half along its height. If you make one small hole near the folded corner (the corner where all layers meet), how many holes will appear when the paper is completely unfolded?
Practice 4medium
A square piece of paper is folded diagonally to form a triangle, then folded diagonally again (perpendicular to the first diagonal). A small triangular piece is cut from the folded paper's right angle vertex. How many triangular pieces are removed from the original square when unfolded?
Practice 5medium
A rectangular paper is folded in half lengthwise, then folded in half widthwise. Three corners of the folded paper are cut off at 45° angles. When the paper is completely unfolded, how many corners of the original rectangle remain uncut?
Practice 6medium
A rectangular paper measuring 8 cm × 4 cm is folded in half along its length (8 cm side), then folded in half again along the width of the resulting rectangle. Two opposite corners of the final folded paper are cut off. When unfolded, how many corners of the original rectangle are cut?
Practice 7hard
A square piece of paper is folded diagonally once, then the resulting triangle is folded in half along its altitude from the right angle. After unfolding completely, how many distinct regions are created on the original square?
Practice 8hard
A square paper is folded in half along a diagonal, then folded in half again along the perpendicular bisector of one of the equal sides of the resulting triangle. After making a straight cut perpendicular to the second fold line, passing through the midpoint of the folded paper's longest edge, how many pieces are created when the paper is completely unfolded?
Practice 9hard
A rectangular paper (length 12cm, width 8cm) is folded in half along its length, then folded in half again along the new width. A hole is punched at coordinates (2cm, 1cm) on the folded paper (measuring from the top-left corner of the folded configuration). When unfolded, how many holes appear and at which positions relative to the original rectangle's corners?
Practice 10hard
A square paper is folded along a diagonal, then the resulting isosceles right triangle is folded along the line parallel to the hypotenuse passing through the midpoint of one of the equal sides. If the original square has side length 4cm, what is the total length of all crease lines visible on the unfolded paper?
Practice 11hard
A rectangular paper (10cm × 6cm) is folded so that the top-right corner touches the bottom-left corner. The paper is then cut along the fold line. How many pieces result, and what are their shapes?
60-Second Revision — Paper Folding & Cutting
Remember: Each fold doubles the hole count from cuts
Formula: Holes = 2^(number of folds) × cuts made
Trick: Holes must be symmetric around all fold lines
Method: Count folds first, then apply symmetry rules
Trap: Don't confuse paper thickness with number of holes
Speed tip: Eliminate options that violate symmetry immediately