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Agniveer Army CEE Paper Folding & Cutting

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This page covers Agniveer Army CEE Paper Folding & Cutting with complete concept notes, 6 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Paper Folding & Cutting— Rules & Concept

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

6graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

A rectangular sheet of paper is folded in half along its length, then folded in half again along its width. If the sheet is then unfolded completely, how many rectangular sections will be visible on the paper?

Practice 2easy

A square sheet of paper is folded diagonally to form a triangle, then folded diagonally again in the same direction. If a small corner is cut from the folded paper, how many separate pieces will result when the paper is completely unfolded?

Practice 3medium

A rectangular piece of paper is folded along its diagonal, and then one corner is cut off with a straight cut perpendicular to the fold. When the paper is unfolded, how many separate pieces result?

Practice 4medium

A square sheet is folded in half twice (first horizontally, then vertically), creating 4 layers. A triangular piece is cut from the folded corner. How many triangular pieces appear when the paper is completely unfolded?

Practice 5medium

A rectangular paper is folded into thirds along its length, creating 3 layers. A small circle is punched through the middle layer only (not the top or bottom). When unfolded, how many circular holes are visible?

Practice 6hard

A rectangular sheet of paper is folded along its diagonal, then folded in half along the perpendicular bisector, and finally folded along a line parallel to one of the original sides. If the original sheet measures 16 cm × 12 cm, and after all three folds a single straight cut is made perpendicular to the longest visible edge, how many separate pieces will result when the paper is completely unfolded?

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
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