Non-Verbal Reasoning for CUET General Aptitude

AnswerA · Figure 1

1. A mirror standing along MN, to the right of the grid, swaps left and right but not top and bottom: a square in column c moves to column $6 - c$ and stays in its row.

2. So the shaded squares (1, 3), (1, 4), (1, 5), (2, 4), (2, 5) (row, column) move to (1, 1), (1, 2), (1, 3), (2, 1), (2, 2).

3. Figure 1 shows exactly these squares.

AnswerB · Figure 2

1. A mirror standing along MN, to the right of the grid, swaps left and right but not top and bottom: a square in column c moves to column $6 - c$ and stays in its row.

2. So the shaded squares (3, 3), (3, 4), (3, 5), (4, 4), (4, 5), (5, 5) (row, column) move to (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1).

3. Figure 2 shows exactly these squares.

AnswerC · Figure 3

1. A mirror standing along MN, to the right of the grid, swaps left and right but not top and bottom: a square in column c moves to column $6 - c$ and stays in its row.

2. So the shaded squares (1, 1), (1, 2), (1, 3), (2, 1), (2, 2) (row, column) move to (1, 3), (1, 4), (1, 5), (2, 4), (2, 5).

3. Figure 3 shows exactly these squares.

AnswerD · Figure 4

1. A mirror standing along MN, to the right of the grid, swaps left and right but not top and bottom: a square in column c moves to column $6 - c$ and stays in its row.

2. So the shaded squares (1, 4), (1, 5), (2, 3), (2, 4), (3, 3), (3, 4) (row, column) move to (1, 1), (1, 2), (2, 2), (2, 3), (3, 2), (3, 3).

3. Figure 4 shows exactly these squares.

AnswerB · Figure 2

1. A mirror standing along MN, to the right of the grid, swaps left and right but not top and bottom: a square in column c moves to column $6 - c$ and stays in its row.

2. So the shaded squares (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 5) (row, column) move to (1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1).

3. Figure 2 shows exactly these squares.

AnswerD · Figure 4

1. Water along MN, below the grid, swaps top and bottom but not left and right: a square in row r moves to row $6 - r$ and stays in its column.

2. So the shaded squares (2, 1), (2, 2), (2, 3), (3, 2), (3, 3) (row, column) move to (3, 2), (3, 3), (4, 1), (4, 2), (4, 3).

3. Figure 4 shows exactly these squares.

AnswerC · Figure 3

1. Water along MN, below the grid, swaps top and bottom but not left and right: a square in row r moves to row $6 - r$ and stays in its column.

2. So the shaded squares (3, 2), (4, 1), (4, 2), (4, 3), (5, 2), (5, 3) (row, column) move to (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 2).

3. Figure 3 shows exactly these squares.

AnswerA · Figure 1

1. Water along MN, below the grid, swaps top and bottom but not left and right: a square in row r moves to row $6 - r$ and stays in its column.

2. So the shaded squares (2, 3), (2, 4), (3, 3), (3, 4), (4, 3) (row, column) move to (2, 3), (3, 3), (3, 4), (4, 3), (4, 4).

3. Figure 1 shows exactly these squares.

AnswerB · Figure 2

1. Water along MN, below the grid, swaps top and bottom but not left and right: a square in row r moves to row $6 - r$ and stays in its column.

2. So the shaded squares (1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 3) (row, column) move to (3, 3), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3).

3. Figure 2 shows exactly these squares.

AnswerC · Figure 3

1. Water along MN, below the grid, swaps top and bottom but not left and right: a square in row r moves to row $6 - r$ and stays in its column.

2. So the shaded squares (3, 5), (4, 3), (4, 4), (4, 5), (5, 4), (5, 5) (row, column) move to (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 5).

3. Figure 3 shows exactly these squares.

AnswerA · Figure 1

1. A mirror standing along MN, to the right of the grid, swaps left and right but not top and bottom: a square in column c moves to column $6 - c$ and stays in its row.

2. So the shaded squares (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 2) (row, column) move to (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4).

3. Figure 1 shows exactly these squares.

AnswerD · Figure 4

1. A mirror standing along MN, to the right of the grid, swaps left and right but not top and bottom: a square in column c moves to column $6 - c$ and stays in its row.

2. So the shaded squares (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 3), (3, 4), (3, 5), (4, 3) (row, column) move to (1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 3).

3. Figure 4 shows exactly these squares.

AnswerC · Figure 3

1. A mirror standing along MN, to the right of the grid, swaps left and right but not top and bottom: a square in column c moves to column $6 - c$ and stays in its row.

2. So the shaded squares (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 2) (row, column) move to (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4).

3. Figure 3 shows exactly these squares.

AnswerD · Figure 4

1. Water along MN, below the grid, swaps top and bottom but not left and right: a square in row r moves to row $6 - r$ and stays in its column.

2. So the shaded squares (3, 2), (4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3), (5, 4) (row, column) move to (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 2).

3. Figure 4 shows exactly these squares.

AnswerA · Figure 1

1. Water along MN, below the grid, swaps top and bottom but not left and right: a square in row r moves to row $6 - r$ and stays in its column.

2. So the shaded squares (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 4), (5, 4) (row, column) move to (1, 4), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4).

3. Figure 1 shows exactly these squares.

AnswerB · Figure 2

1. Water along MN, below the grid, swaps top and bottom but not left and right: a square in row r moves to row $6 - r$ and stays in its column.

2. So the shaded squares (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1), (4, 2) (row, column) move to (2, 1), (2, 2), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3), (5, 2).

3. Figure 2 shows exactly these squares.

AnswerA · Figure 1

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 1 (the vertical fold) gives holes at (2, 1), (2, 4) (row, column).

3. Figure 1 shows these 2 holes.

AnswerB · Figure 2

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 1 (the horizontal fold) gives holes at (1, 2), (4, 2) (row, column).

3. Figure 2 shows these 2 holes.

AnswerC · Figure 3

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 1 (the vertical fold) gives holes at (1, 1), (1, 4) (row, column).

3. Figure 3 shows these 2 holes.

AnswerD · Figure 4

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 1 (the horizontal fold) gives holes at (2, 3), (3, 3) (row, column).

3. Figure 4 shows these 2 holes.

AnswerB · Figure 2

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 2 (the horizontal fold) gives holes at (2, 4), (3, 4) (row, column).

3. Opening step 1 (the vertical fold) gives holes at (2, 1), (2, 4), (3, 1), (3, 4) (row, column).

4. Figure 2 shows these 4 holes.

AnswerA · Figure 1

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 2 (the vertical fold) gives holes at (4, 2), (4, 3) (row, column).

3. Opening step 1 (the horizontal fold) gives holes at (1, 2), (1, 3), (4, 2), (4, 3) (row, column).

4. Figure 1 shows these 4 holes.

AnswerD · Figure 4

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 2 (the horizontal fold) gives holes at (1, 2), (4, 2) (row, column).

3. Opening step 1 (the vertical fold) gives holes at (1, 2), (1, 3), (4, 2), (4, 3) (row, column).

4. Figure 4 shows these 4 holes.

AnswerC · Figure 3

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 2 (the vertical fold) gives holes at (2, 1), (2, 4) (row, column).

3. Opening step 1 (the horizontal fold) gives holes at (2, 1), (2, 4), (3, 1), (3, 4) (row, column).

4. Figure 3 shows these 4 holes.

AnswerD · Figure 4

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 2 (the horizontal fold) gives holes at (1, 3), (4, 3) (row, column).

3. Opening step 1 (the vertical fold) gives holes at (1, 2), (1, 3), (4, 2), (4, 3) (row, column).

4. Figure 4 shows these 4 holes.

AnswerC · Figure 3

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 2 (the vertical fold) gives holes at (4, 1), (4, 4) (row, column).

3. Opening step 1 (the horizontal fold) gives holes at (1, 1), (1, 4), (4, 1), (4, 4) (row, column).

4. Figure 3 shows these 4 holes.

AnswerA · Figure 1

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 2 (the horizontal fold) gives holes at (2, 2), (3, 2) (row, column).

3. Opening step 1 (the vertical fold) gives holes at (2, 2), (2, 3), (3, 2), (3, 3) (row, column).

4. Figure 1 shows these 4 holes.

AnswerB · Figure 2

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 2 (the vertical fold) gives holes at (2, 1), (2, 4) (row, column).

3. Opening step 1 (the horizontal fold) gives holes at (2, 1), (2, 4), (3, 1), (3, 4) (row, column).

4. Figure 2 shows these 4 holes.

AnswerC · Figure 3

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 2 (the horizontal fold) gives holes at (1, 4), (2, 3), (3, 3), (4, 4) (row, column).

3. Opening step 1 (the vertical fold) gives holes at (1, 1), (1, 4), (2, 2), (2, 3), (3, 2), (3, 3), (4, 1), (4, 4) (row, column).

4. Figure 3 shows these 8 holes.

AnswerD · Figure 4

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 2 (the horizontal fold) gives holes at (1, 2), (2, 2), (3, 2), (4, 2) (row, column).

3. Opening step 1 (the vertical fold) gives holes at (1, 2), (1, 3), (2, 2), (2, 3), (3, 2), (3, 3), (4, 2), (4, 3) (row, column).

4. Figure 4 shows these 8 holes.

AnswerA · Figure 1

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 2 (the vertical fold) gives holes at (3, 1), (3, 4), (4, 1), (4, 4) (row, column).

3. Opening step 1 (the horizontal fold) gives holes at (1, 1), (1, 4), (2, 1), (2, 4), (3, 1), (3, 4), (4, 1), (4, 4) (row, column).

4. Figure 1 shows these 8 holes.

AnswerB · Figure 2

1. Open the folds in reverse order. Opening a fold adds the mirror image of every hole across that fold line, because each hole went through both layers.

2. Opening step 2 (the vertical fold) gives holes at (1, 2), (1, 3), (2, 1), (2, 4) (row, column).

3. Opening step 1 (the horizontal fold) gives holes at (1, 2), (1, 3), (2, 1), (2, 4), (3, 1), (3, 4), (4, 2), (4, 3) (row, column).

4. Figure 2 shows these 8 holes.

AnswerA · Figure 1

1. The shape gains one side each time: triangle, square, pentagon, hexagon, so next comes a heptagon.

2. Shaded and unshaded shapes alternate, starting shaded, so the fifth shape is shaded.

3. Figure 1 shows a shaded heptagon.

AnswerB · Figure 2

1. The shape loses one side each time: octagon, heptagon, hexagon, pentagon, so next comes a square.

2. Shaded and unshaded shapes alternate, starting shaded, so the fifth shape is shaded.

3. Figure 2 shows a shaded square.

AnswerC · Figure 3

1. The shape gains one side each time: square, pentagon, hexagon, heptagon, so next comes a octagon.

2. Shaded and unshaded shapes alternate, starting shaded, so the fifth shape is shaded.

3. Figure 3 shows a shaded octagon.

AnswerD · Figure 4

1. The arrow turns 45° clockwise each time: up, up-right, right, down-right, so next it points down.

2. The dot moves 2 places clockwise round the box each time (the 4 corners and 4 edge midpoints are the 8 places): from the bottom-left corner it goes to the top-left corner.

3. Figure 4 shows an arrow pointing down, with a dot at the top-left corner.

AnswerB · Figure 2

1. The arrow turns 90° clockwise each time: right, down, left, up, so next it points right.

2. The dot moves 1 place clockwise round the box each time (the 4 corners and 4 edge midpoints are the 8 places): from the bottom-right corner it goes to the middle of the bottom edge.

3. Figure 2 shows an arrow pointing right, with a dot at the middle of the bottom edge.

AnswerA · Figure 1

1. The arrow turns 45° anticlockwise each time: left, down-left, down, down-right, so next it points right.

2. The dot moves 2 places clockwise round the box each time (the 4 corners and 4 edge midpoints are the 8 places): from the top-left corner it goes to the top-right corner.

3. Figure 1 shows an arrow pointing right, with a dot at the top-right corner.

AnswerD · Figure 4

1. The arrow turns 135° clockwise each time: down, up-left, right, down-left, so next it points up.

2. The dot moves 1 place anticlockwise round the box each time (the 4 corners and 4 edge midpoints are the 8 places): from the bottom-right corner it goes to the middle of the right edge.

3. Figure 4 shows an arrow pointing up, with a dot at the middle of the right edge.

AnswerC · Figure 3

1. The arrow turns 90° clockwise each time: up-right, down-right, down-left, up-left, so next it points up-right.

2. The dot moves 3 places clockwise round the box each time (the 4 corners and 4 edge midpoints are the 8 places): from the middle of the top edge it goes to the bottom-right corner.

3. Figure 3 shows an arrow pointing up-right, with a dot at the bottom-right corner.

AnswerD · Figure 4

1. The arrow turns 90° anticlockwise each time: up, left, down, right, so next it points up.

2. The dot moves 2 places clockwise round the box each time (the 4 corners and 4 edge midpoints are the 8 places): from the middle of the right edge it goes to the middle of the bottom edge.

3. Figure 4 shows an arrow pointing up, with a dot at the middle of the bottom edge.

AnswerC · Figure 3

1. The arrow turns 135° clockwise each time: down-right, left, up-right, down, so next it points up-left.

2. Figure 3 shows an arrow pointing up-left.

AnswerA · Figure 1

1. The arrow turns 135° clockwise each time: up-left, right, down-left, up, so next it points down-right.

2. Figure 1 shows an arrow pointing down-right.

AnswerB · Figure 2

1. The arrow turns 135° anticlockwise each time: down-left, right, up-left, down, so next it points up-right.

2. Figure 2 shows an arrow pointing up-right.

AnswerC · Figure 3

1. The shape gains one side each time: triangle, square, pentagon, hexagon, so next comes a heptagon.

2. Shaded and unshaded shapes alternate, starting shaded, so the fifth shape is shaded.

3. The dot moves 1 place clockwise round the box each time (the 4 corners and 4 edge midpoints are the 8 places): from the bottom-right corner it goes to the middle of the bottom edge.

4. Figure 3 shows a shaded heptagon, with a dot at the middle of the bottom edge.

AnswerD · Figure 4

1. The shape loses one side each time: heptagon, hexagon, pentagon, square, so next comes a triangle.

2. Shaded and unshaded shapes alternate, starting shaded, so the fifth shape is shaded.

3. The dot moves 2 places clockwise round the box each time (the 4 corners and 4 edge midpoints are the 8 places): from the bottom-left corner it goes to the top-left corner.

4. Figure 4 shows a shaded triangle, with a dot at the top-left corner.

AnswerA · Figure 1

1. The shape gains one side each time: square, pentagon, hexagon, heptagon, so next comes a octagon.

2. Shaded and unshaded shapes alternate, starting shaded, so the fifth shape is shaded.

3. The dot moves 1 place anticlockwise round the box each time (the 4 corners and 4 edge midpoints are the 8 places): from the middle of the right edge it goes to the top-right corner.

4. Figure 1 shows a shaded octagon, with a dot at the top-right corner.

AnswerB · Figure 2

1. The shape loses one side each time: octagon, heptagon, hexagon, pentagon, so next comes a square.

2. Shaded and unshaded shapes alternate, starting shaded, so the fifth shape is shaded.

3. The dot moves 3 places clockwise round the box each time (the 4 corners and 4 edge midpoints are the 8 places): from the bottom-right corner it goes to the middle of the left edge.

4. Figure 2 shows a shaded square, with a dot at the middle of the left edge.

AnswerA · 8

1. $1 \times 1$ squares: $3 \times 2 = 6$.

2. $2 \times 2$ squares: $2 \times 1 = 2$.

3. Total $= 6 + 2 = 8$.

AnswerB · 14

1. $1 \times 1$ squares: $3 \times 3 = 9$.

2. $2 \times 2$ squares: $2 \times 2 = 4$.

3. $3 \times 3$ squares: $1 \times 1 = 1$.

4. Total $= 9 + 4 + 1 = 14$.

AnswerC · 6

1. From the top vertex there are 4 lines in all: the two sides and the 2 inner lines. Any 2 of them form a triangle with a horizontal line as the third side.

2. Pairs of lines from the vertex: $\binom{4}{2} = 6$.

3. Horizontal lines that can close them: 1 (the base).

4. Triangles $= 6 \times 1 = 6$.

AnswerD · 10

1. From the top vertex there are 5 lines in all: the two sides and the 3 inner lines. Any 2 of them form a triangle with a horizontal line as the third side.

2. Pairs of lines from the vertex: $\binom{5}{2} = 10$.

3. Horizontal lines that can close them: 1 (the base).

4. Triangles $= 10 \times 1 = 10$.

AnswerC · 8

1. Count by size, starting with the smallest pieces.

2. Smallest triangles: 4. Triangles made of 2 smallest pieces: 4.

3. Total $= 4 + 4 = 8$.

AnswerD · 8

1. Count by size, starting with the smallest pieces.

2. Smallest triangles: 4. Triangles made of 2 smallest pieces: 4.

3. Total $= 4 + 4 = 8$.

AnswerC · 20

1. $1 \times 1$ squares: $4 \times 3 = 12$.

2. $2 \times 2$ squares: $3 \times 2 = 6$.

3. $3 \times 3$ squares: $2 \times 1 = 2$.

4. Total $= 12 + 6 + 2 = 20$.

AnswerD · 14

1. $1 \times 1$ squares: $5 \times 2 = 10$.

2. $2 \times 2$ squares: $4 \times 1 = 4$.

3. Total $= 10 + 4 = 14$.

AnswerB · 18

1. A rectangle is fixed by choosing 2 of the 4 vertical lines and 2 of the 3 horizontal lines.

2. Vertical pairs: $\binom{4}{2} = 6$. Horizontal pairs: $\binom{3}{2} = 3$.

3. Rectangles $= 6 \times 3 = 18$.

AnswerA · 30

1. A rectangle is fixed by choosing 2 of the 5 vertical lines and 2 of the 3 horizontal lines.

2. Vertical pairs: $\binom{5}{2} = 10$. Horizontal pairs: $\binom{3}{2} = 3$.

3. Rectangles $= 10 \times 3 = 30$.

AnswerC · 12

1. From the top vertex there are 4 lines in all: the two sides and the 2 inner lines. Any 2 of them form a triangle with a horizontal line as the third side.

2. Pairs of lines from the vertex: $\binom{4}{2} = 6$.

3. Horizontal lines that can close them: 2 (the base and 1 parallel line).

4. Triangles $= 6 \times 2 = 12$.

AnswerA · 9

1. From the top vertex there are 3 lines in all: the two sides and the 1 inner line. Any 2 of them form a triangle with a horizontal line as the third side.

2. Pairs of lines from the vertex: $\binom{3}{2} = 3$.

3. Horizontal lines that can close them: 3 (the base and 2 parallel lines).

4. Triangles $= 3 \times 3 = 9$.

AnswerD · 36

1. A rectangle is fixed by choosing 2 of the 4 vertical lines and 2 of the 4 horizontal lines.

2. Vertical pairs: $\binom{4}{2} = 6$. Horizontal pairs: $\binom{4}{2} = 6$.

3. Rectangles $= 6 \times 6 = 36$.

AnswerA · 20

1. From the top vertex there are 5 lines in all: the two sides and the 3 inner lines. Any 2 of them form a triangle with a horizontal line as the third side.

2. Pairs of lines from the vertex: $\binom{5}{2} = 10$.

3. Horizontal lines that can close them: 2 (the base and 1 parallel line).

4. Triangles $= 10 \times 2 = 20$.

AnswerB · 45

1. From the top vertex there are 6 lines in all: the two sides and the 4 inner lines. Any 2 of them form a triangle with a horizontal line as the third side.

2. Pairs of lines from the vertex: $\binom{6}{2} = 15$.

3. Horizontal lines that can close them: 3 (the base and 2 parallel lines).

4. Triangles $= 15 \times 3 = 45$.

AnswerA · 16

1. Count by size, starting with the smallest pieces.

2. Smallest triangles: 8. Triangles made of 2 smallest pieces: 4. Triangles made of 4 smallest pieces: 4.

3. Total $= 8 + 4 + 4 = 16$.

AnswerB · 16

1. Count by size, starting with the smallest pieces.

2. Smallest triangles: 6. Triangles made of 2 smallest pieces: 3. Triangles made of 3 smallest pieces: 6. Triangles made of 6 smallest pieces: 1.

3. Total $= 6 + 3 + 6 + 1 = 16$.