Looking at the question figure, we can observe these elements:

• A square frame
• A diagonal line from top-left to bottom-right
• Two small circles at the top corners
• A quarter-circle arc connecting the top-left corner to the middle of the top edge

Option 3 maintains the same pattern but rotated 180 degrees:

• It preserves the square frame
• It shows a diagonal line from top-left to bottom-right
• It has two small circles at the bottom corners
• It has a quarter-circle arc connecting the bottom-left corner to the middle of the left edge

This follows the pattern of rotation while maintaining the essential elements of the design.

To solve this problem, we need to identify the pattern in the first three quadrants and determine what should be in the fourth quadrant.

Analyzing the pattern:

• In the top-left quadrant: We have a circle with a vertical and horizontal line forming a plus (+) sign.
• In the top-right quadrant: We have a circle with a structure that resembles the top half of a triangle pointing upward (∧).
• In the bottom-left quadrant: We have a circle with a structure that resembles the right half of a triangle pointing right (▷).

If we follow the pattern of rotation:

• The top-left has a plus (+) sign
• Moving clockwise, the top-right has an upward pointing angle (∧)
• Continuing clockwise, the bottom-left has a rightward pointing angle (▷)
• For the bottom-right, we should have a downward pointing angle (∨)

Option C shows this pattern with an upside-down V shape (∨) and a line connecting to the left, which completes the rotation pattern. Each quadrant rotates the angle structure by 90 degrees clockwise.

To determine which face will be opposite to the face marked ‘X’ when the net is folded into a cube, we need to visualize the folding process.

In a cube, opposite faces are those that are on opposite sides of the cube. When a net is folded, faces that are adjacent in the net (sharing an edge) cannot be opposite in the cube.

Looking at the given net:

• Face X is in the center of the cross-shaped net.
• Face A is above X.
• Face B is to the left of X.
• Face C is to the right of X.
• Face D is to the right of C.
• Face E is below X.

When folded into a cube:

• Faces A, B, C, and E are all adjacent to X in the net, so they will be adjacent to X in the cube (sharing an edge).
• Face D is not adjacent to X in the net. Instead, it is adjacent to C.
• When the net is folded, face D will fold to become the back face of the cube, while X is the front face.

Thus, the face opposite to X (front) is D (back).

In the original figure, we have:

• A square with a circle in the center
• Lines connecting each corner of the square to the center of the circle
• One line (the bottom-right one) is thicker than the others

If we rotate this figure 90 degrees counterclockwise, the thick line will move from the bottom-right position to the top-right position.

Looking at the options:

• Option A shows the original figure without any rotation
• Option B shows the figure with the thick line at the bottom-left
• Option C shows the figure with the thick line at the top-left
• Option D shows the figure with the thick line at the top-right

Option D matches what we would see after rotating the original figure 90 degrees counterclockwise.

In this sequence, we need to identify the pattern of how the figure evolves from left to right.

Analyzing the sequence:

• The first figure has a square, a circle in the center (radius 20), and one line connecting the top edge of the square to the circle.
• The second figure adds a second line, connecting the right edge of the square to the circle.
• The third figure adds a third line, connecting the bottom edge of the square to the circle.

Following this pattern, the fourth figure should add a fourth line connecting the left edge of the square to the circle, completing the pattern of lines connecting all four sides of the square to the circle.

Looking at the options:

• Option A has all four lines (top, right, bottom, left) connecting the square to the circle, with the same circle radius (20) and line lengths as the previous figures.
• Option B has all four lines but with a larger circle (radius 30) and shorter lines, which breaks the pattern.
• Option C is missing the line from the left side, so it only has three lines.
• Option D has all four lines but a filled (black) circle, which deviates from the unfilled circle in the sequence.

Option A maintains the exact pattern established in the sequence, with the same size circle, unfilled circle, and consistent line lengths.