This page covers SSC CHSL Paper Folding & Cutting with complete concept notes, 27 graded practice MCQs, key points and exam-specific tips. Free to study.
Core ConceptRead this first — the foundation of the topic
Core Concept
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.
Exam PatternsWhat 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.
ShortcutsUse 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.
Worked ExampleSolve 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.
Exam TrapsCommon mistakes students make — avoid these
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.
Key Points to Remember
Each fold doubles the number of holes created by cuts
Holes appear symmetrically around all fold lines
Formula: Number of holes = 2^(folds) × number of cuts
Position of holes mirrors across each fold axis
Shape of cut remains same, only position multiplies
Count fold steps carefully before applying formula
Draw imaginary lines at fold positions to check symmetry
Work backwards from cut to unfold position step by step
Exam-Specific Tips
SSC CGL typically includes 1-2 paper folding questions per exam
Maximum folds shown in SSC questions is usually 3-4 folds
Most common cuts are circles, triangles, and small rectangles
Questions always provide exactly 4 answer options showing unfolded patterns
Each fold creates one axis of symmetry in the final pattern
Corner cuts are the most frequently tested cutting positions
Questions are worth 2 marks each in SSC CGL Tier-I
Time allocation should be maximum 1 minute per question
Practice MCQs
Paper Folding & Cutting — Practice Questions
27graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 27
A rectangular paper is folded in half vertically, then folded in half horizontally. If you unfold it completely, how many rectangular sections will the creases divide the paper into?
Practice 2easy
A square paper with a dot marked at its center is folded diagonally once. After unfolding, how many dots will be visible on the paper?
Practice 3easy
A rectangular paper is cut horizontally into 2 pieces, then one piece is cut vertically into 2 pieces. How many total pieces result from these two cuts?
Practice 4easy
A rectangular paper is folded in half lengthwise, then folded in half again widthwise. If you unfold it completely, how many rectangular sections will the creases divide the paper into?
Practice 5easy
A square paper is folded in half to form a rectangle, then folded in half again to form a smaller square. If you make one straight cut through the folded paper, how many separate pieces will result when you unfold completely?
Practice 6easy
A rectangular paper is cut with a single straight cut from one edge to the opposite edge, passing through the center. The paper is then unfolded. How many pieces result from this single cut?
Practice 7easy
A square paper with a dot marked at its centre is folded diagonally. After unfolding, how many dots will be visible on the paper?
Practice 8easy
A circular piece of paper is folded in half to form a semicircle, then folded in half again. When unfolded, how many curved sections will be created by the fold lines?
Practice 9easy
A square piece of paper is folded once along its diagonal. How many layers of paper will be visible if you look at the folded shape from above?
Practice 10medium
A square paper is folded along one diagonal to form a triangle. This triangle is then folded along its median (from the right angle to the midpoint of the hypotenuse). After complete unfolding, which statement is true about the crease pattern?
Practice 11medium
A square paper with a dot marked at its center is folded diagonally twice (both diagonals). After both folds, a small cut is made at the center of the resulting folded shape. How many cuts will appear on the original unfolded square?
Practice 12medium
A square piece of paper is folded along its diagonal, then the resulting triangle is folded in half along its height. After unfolding completely, how many distinct regions will be visible on the paper?
Practice 13medium
A rectangular paper is folded once vertically (left edge meets right edge), then folded once horizontally (top edge meets bottom edge). A hole is punched through all layers at the center of the resulting square. When the paper is completely unfolded, how many holes will be visible?
Practice 14medium
A rectangular paper (length 2× width) is folded in half lengthwise (along the longer dimension), then folded in half again widthwise (along the shorter dimension of the now-folded rectangle). Two corners of the resulting small rectangle are cut off at 45° angles. After complete unfolding, how many corners of the original rectangle will have cuts?
Practice 15medium
A square piece of paper is folded along its diagonal, then the resulting triangle is folded in half along its height. After unfolding completely, how many distinct regions will be visible on the original square?
Practice 16medium
A rectangular paper is folded in half lengthwise. Then it is folded in half again widthwise. A triangular piece is cut from one corner of the folded paper. When unfolded, how many triangular pieces will be missing from the original paper?
Practice 17medium
A square paper is folded along one diagonal, creating a triangle. This triangle is then folded in half along a line parallel to its base. A small square is punched at the apex of the resulting folded shape. How many squares will appear on the original unfolded paper?
Practice 18hard
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 19hard
A rectangular paper (length 16 cm, width 8 cm) is folded in half along its length, then folded in half along its width. A hole is punched at a point that is 2 cm from the top-left corner of the folded paper. When the paper is completely unfolded, how many holes will be visible, and where will they be located relative to the original corners?
Practice 20hard
A square paper is folded such that one corner touches the opposite corner (diagonal fold), then folded again so that the new top-left corner touches the new bottom-right corner. After these two folds, a triangular piece is cut from the folded paper. When completely unfolded, the resulting shape has how many sides, and what is its symmetry type?
7 more practice questions in the Study Panel
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