MAT Exam 2023 Paper

Concept:Cubes showing red, green and black colours are the corner cubes formed at the ends of both the length and the breadth.Explanation:The block has dimensions $6\ \text{cm} \times 4\ \text{cm} \times 1\ \text{cm}$.The green faces are the top and bottom faces, each of size $6 \times 4$.Since height is $1\ \text{cm}$, every small cube has green on at least one face.Black colour appears only on cubes at the two ends along the $6\ \text{cm}$ length.Red colour appears only on cubes at the two ends along the $4\ \text{cm}$ breadth.Thus, a cube having all three colours must be at the intersection of the black ends and the red ends.Number of such cubes $= 2 \times 2 = 4$.Answer:$4$ cubes; option D.