Question 1

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?

Accepted Answer

This tests understanding of how paper layers stack when folded along a diagonal.

Question 2

A rectangular paper is cut horizontally into 3 equal strips. Then each strip is cut vertically into 2 equal pieces. How many total pieces of paper result from these cuts?

Accepted Answer

First cut (horizontal into 3 strips) creates 3 pieces. Second set of cuts (each of the 3 strips cut vertically into 2) multiplies each piece: 3 × 2 = 6 total pieces.

Question 3

A square paper is folded in half to form a rectangle. A small notch is cut from the folded edge (not at a corner). When the paper is unfolded, how many notches will be visible?

Accepted Answer

When the square is folded in half, two layers of paper are aligned. A single cut through the folded edge goes through both layers. Upon unfolding, the cut appears on both halves of the original square, creating 2 notches symmetrically placed.

Question 4

A rectangular piece of paper is folded once diagonally so that the bottom-left corner meets the top-right corner exactly. A single triangular notch is cut from the folded (diagonal) edge at the midpoint. When the paper is unfolded, what shape will the cut-out hole appear as?

Accepted Answer

Step 1: The paper is folded diagonally, placing two layers together along the diagonal fold line. Step 2: A triangular notch is cut at the midpoint of the folded diagonal edge — this cuts through both layers simultaneously. Step 3: Each triangular notch on either side of the fold line is a mirror image of the other. Step 4: When unfolded, the two triangular notches combine along the fold line to form a complete diamond (rhombus) shape. Therefore, the cut-out hole appears as a diamond (rhombus).

Question 5

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 paper from above?

Accepted Answer

When a square is folded along its diagonal, one triangular half folds over the other, creating a double-layered triangle. From above, you see 2 layers of paper stacked together.

Question 6

A rectangular piece of paper is folded once by bringing the top edge down to meet the bottom edge. A hole is then punched through the folded paper. When the paper is unfolded, how many holes will be visible?

Accepted Answer

This tests understanding of how a single punch affects folded paper layers.

Question 7

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 paper from above?

Accepted Answer

When a square is folded along its diagonal, one triangular half folds over the other, creating a double-layered triangle. From above, you see 2 layers of paper stacked together.

Question 8

A rectangular paper is folded in half vertically (left side folds onto right side). Then it is folded in half horizontally (top folds down onto bottom). How many layers of paper exist at the corner where all folds meet?

Accepted Answer

First fold creates 2 layers. Second fold doubles the layers again. At the corner where both folds intersect, there are 4 layers of paper stacked together.

Question 9

A square piece of paper is folded once along its diagonal. After unfolding, how many regions are created by the crease line(s)?

Accepted Answer

When a square is folded along its diagonal and then unfolded, a single diagonal crease divides the square into exactly 2 triangular regions.

Question 10

A square piece of paper is folded once along its diagonal. How many layers of paper will be visible when looking at the folded shape from above?

Accepted Answer

When a square is folded along its diagonal, one triangular half folds onto the other, creating a double-layered triangle. From above, you see the outline of a triangle with 2 layers of paper beneath it.

Question 11

A square paper has a small circle drawn in its center. The paper is folded diagonally (corner to opposite corner), then folded diagonally again in the opposite direction. When you unfold the paper completely, how many circles will be visible?

Accepted Answer

This tests understanding of symmetry and how marks are replicated through diagonal folds.

Question 12

A square piece of paper is folded once along its diagonal. After unfolding, how many triangular regions are created by the fold line?

Accepted Answer

When a square is folded along its diagonal, the fold line divides the square into exactly 2 equal right-angled triangles. Upon unfolding, the diagonal crease remains visible as a single straight line that splits the square into 2 triangular regions.

Question 13

A circular piece of paper is folded in half, then folded in half again (perpendicular to the first fold). When unfolded, the crease pattern will show how many sections?

Accepted Answer

First fold creates 1 crease line dividing the circle into 2 halves. Second perpendicular fold creates another crease line. Two perpendicular diameters divide a circle into 4 equal sections.

Question 14

A rectangular paper is cut along a straight line from the midpoint of one long side to the midpoint of the opposite long side. How many pieces will result?

Accepted Answer

A straight cut from the midpoint of one long side to the midpoint of the opposite long side passes completely through the rectangle, dividing it into exactly 2 pieces.

Question 15

A rectangular paper is folded in half along its length. Then a triangular piece is cut from the folded paper. When unfolded, how many triangular pieces will be present?

Accepted Answer

When paper is folded in half, cutting through both layers creates cuts on both layers. One triangular cut through folded paper results in 2 triangular pieces when unfolded (one from each layer).

Question 16

A square paper has a small circle drawn in its center. The paper is folded diagonally once. After unfolding, how many circles will be visible on the paper?

Accepted Answer

When you fold a square diagonally, the center point (where the circle is) lies exactly on the fold line. The circle remains in the same position after folding and unfolding. Therefore, only 1 circle is visible.

Question 17

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?

Accepted Answer

First vertical fold creates 1 vertical crease dividing the paper into 2 sections. Second horizontal fold creates 1 horizontal crease. When unfolded, these 2 creases (1 vertical + 1 horizontal) divide the paper into 4 rectangular sections.

Question 18

A square paper with a dot marked at its center is folded diagonally. After unfolding, where will the dot appear relative to the fold line?

Accepted Answer

A dot at the center of a square remains at the center regardless of how the square is folded. When folded diagonally, the center point lies exactly on the diagonal fold line. Upon unfolding, the dot will be positioned on the fold line itself.

Question 19

A rectangular paper is folded in half lengthwise, then folded in half again widthwise. If the paper is then unfolded completely, how many rectangular sections will be visible on the paper?

Accepted Answer

First fold (lengthwise) creates 2 sections. Second fold (widthwise) divides each section in half, creating 4 sections total. When unfolded, the crease pattern shows 4 distinct rectangles.

Question 20

A rectangular paper is folded in half lengthwise (along the longer side), then folded in half again widthwise (along the shorter side of the folded rectangle). A small hole is punched through all layers at the center of the resulting folded shape. When the paper is completely unfolded, how many holes will be visible?

Accepted Answer

This question tests understanding of how a single punch through multiple layers creates multiple holes when unfolded, based on the number of layers at the punch location.

RPF Sub-Inspector Paper Folding & Cutting

Paper Folding & Cutting— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Paper Folding & Cutting — Practice Questions

60-Second Revision — Paper Folding & Cutting