Choose a figure which would most closely resemble the unfolded form of Figure (3).

For least number of cuts 120 = 4 x 5 x 6 i.e number of cuts must be 3, 4 and 5 in three planes in this case number of cubes on a face is either 6 x 5 = 30 or 6 x 4 = 24 or 4 x 5 = 20 cubes . And number of cuboids on an edge is 4 or 5 or 6
Maximum number of cuboid with red colour is possible when cube is painted with red colour in 3 sides with minimum number of common edges (which is equal to 2)
Hence required maximum value is 6 (5 + 5 + 4 - 2) = 72
For minimum number of such cuboid Red colour is used only once and minimum number of cubes in that case is 20
Hence required ratio is 72 : 20 = 18 : 5

NA

Here on each face 6 x 6 = 36 cubes that are painted with one colour.
Case (i): when these three colour are adjacent to each other then from one face we will get 6 x 6 = 36 cubes but out them 6 x 3 = 18 cubes from common edge is common so number of cubes are 3 x 6 x 6 - 6 x 3 = 90
Case (ii): When red and blue are opposite to each other (or any two of the given three) then required number of cubes is 3 x 6 x 6 - 2 x 6 = 96

Except in figure (1) in all others the number of pins is one less than the number of sides of the geometrical figure.

The design (+) is encircled by two different designs in figure (2). But all three figures are in same .

From first figure to second figure in the first pair of Question Figures the triangle is converted into a square, i.e., one side is added. The elongated side moves to opposite direction.

From first figure to second figure the designs move half step to the left and the left most design moves to the right. Again, the arrow gets inverted, the double lines becomes horizontal and the curve turn into circle.

From first figure to second, one side of the main design is deleted and the inner circles move out of the main design and the outer circle moves inside the main design.