Match the 3D object to its correct 2D perspective view.

Problem Analysis:

The task involves analyzing different images and determining the correct views or projections of objects. Let's solve each part step by step.

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#### Part (a): Dice Representation
The image shows a 3D representation of a die with visible dots on its faces. We need to determine which of the given options (I, II, III) correctly represents the side view of the die.

1. Understanding the Die:
- The die is a cube with dots on each face.
- From the given 3D view, we can see three faces:
- Front face: 4 dots (arranged in a square pattern).
- Top face: 2 dots (diagonally opposite each other).
- Right face: 3 dots (in an L-shape).

2. Determining the Side View:
- The side view will show the right face of the die, which has 3 dots arranged in an L-shape.
- Among the options:
- (I) Shows 2 dots.
- (II) Shows 2 dots.
- (III) Shows 1 dot.

3. Correct Answer:
- None of the options (I, II, III) match the 3-dot L-shape on the right face.
- Therefore, there seems to be a mismatch in the provided options. However, based on the standard interpretation, the correct side view should show 3 dots in an L-shape.

Conclusion for Part (a):
The problem might have an error in the options provided. If we assume the options are correct, none of them represent the side view accurately.

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#### Part (b): House Representation
The image shows a 3D representation of a house with a triangular roof and a door. We need to determine which of the given options (I, II, III) correctly represents the front view of the house.

1. Understanding the House:
- The house has a triangular roof and a rectangular door.
- The front view will show the full height of the house, including the roof and the door.

2. Analyzing the Options:
- (I) Shows a complete front view with a triangular roof and a door.
- (II) Shows a cross-sectional view (cut through the house), revealing internal details.
- (III) Shows a simplified front view with a triangular roof but no door.

3. Correct Answer:
- The front view should include both the triangular roof and the door.
- Option (I) matches this description.

Conclusion for Part (b):
The correct answer is (I).

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#### Part (c): Table Representation
The image shows a 3D representation of a table with a circular top and four legs. We need to determine which of the given options (I, II, III) correctly represents the side view of the table.

1. Understanding the Table:
- The table has a circular top and four legs.
- The side view will show the circular top as an ellipse and the legs as vertical lines.

2. Analyzing the Options:
- (I) Shows a side view with a rectangular top and two legs.
- (II) Shows a top-down view of the circular top.
- (III) Shows a side view with a rectangular top and two legs.

3. Correct Answer:
- The side view should show the circular top as an ellipse and the legs as vertical lines.
- Neither option (I) nor (III) shows a circular top; they both depict a rectangular top.
- Option (II) shows a top-down view, not a side view.

Conclusion for Part (c):
None of the options (I, II, III) correctly represent the side view of the table. The correct side view should show an elliptical top and vertical legs.

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Final Answers:

- Part (a): There is an issue with the options provided. None match the correct side view.
- Part (b): The correct answer is (I).
- Part (c): There is an issue with the options provided. None match the correct side view.

If you have any further clarification or need adjustments, feel free to ask!