In each row, the third figure is a collection of the common elements (line segments) of the first and the second figures.

In each row, the second figure is obtained from the first figure by adding two mutually perpendicular line segments at the centre and the third figure is obtained from the first figure by adding four circles outside the main figure.

In each row, the third figure is a collection of the common elements (line segments) of the first and the second figures.

(Total numbers of cubes in a line  x  Number of stack / tower) + ...

= (6x1)+(5x2)+(4x3)+(3x4)+(5x2)+(6x1)

= 6+10+12+12+10+6 = 56

When the sheet in fig. (A) is folded, then one of the faces of the cube formed will be of the form   and this face will lie opposite the face bearing a square. Also, one of the blank faces lies opposite another blank face and the third blank face lies opposite the face bearing an '=' sign. Clearly, all the three blank faces cannot appear adjacent to each other. So, the cube shown in fig. (2) which has all the three blank faces adjacent to each other cannot be formed. Hence, only the cubes shown in figures A, C and D can be formed.

when a cube is formed by folding the sheet shown in fig. (A), then   is one of the faces of the cube and this face lies opposite to a blank face. Also, a face bearing a square lies opposite to another blank face. The remaining two blank faces lie opposite to each other. Clearly, in the cube shown in fig. (1), the face consisting of the four symbols is not the same as that formed (as shown above). Hence, the cube in fig. (1) cannot be formed

The given figure can be labelled as shown :

The spaces P, Q and R have to be shaded by three different colours definitely (since each of these three spaces lies adjacent to the other two).
Now, in order that no two adjacent spaces be shaded by the same colour, the spaces T, U and S must be shaded with the colours of the spaces P, Q and R respectively.
Also the spaces X, V and W must be shaded with the colours of the spaces S, T and U respectively i.e. with the colours of the spaces R, P and Q respectively. Thus, minimum three colour pencils are required.

The given figure can be labelled as :

Straight lines :

The number of straight lines are 19

i.e. BC, CD, BD, AF, FE, AE, AB, GH, IJ, KL, DE, AG, BH, HI, GJ, IL, JK, KE and DL.