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UCEED 2024

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Q12.Shown below is a configuration of FOUR solid spheres each of radius 40 cm that are placed on four corners of a regular tetrahedron with side 120 cm. The centres of the spheres coincide with the corners of the tetrahedron. What is the radius (in cm) of the largest sphere that can be accommodated within the tetrahedron?

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Q14.What are the minimum number of tile pieces (shown on the right) that are required to create a path from tile A to tile B, such that ALL the following conditions are met: All tiles are to be used at least once. Tiles cannot overlap. The path on a tile must be connected to another path of a tile. The same type of tile cannot be used one-after-the other in a sequence. Rotation of the tiles is not allowed. Exclude tile A and tile B from the count.

UCEED2024Q13·nat·Hard159 attempts

Section P shows three views of a regular dice. TEN of such regular dice are stacked on an opaque table as shown in Section Q (two views of the same arrangement). What is the maximum sum that can be achieved adding the numbers on the visible surfaces from all angles?

Keyboards off — use the numpad, just like on exam day.