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In the figure, there are 9 columns containing 5 cubes each, 7 columns containing 4 cubes each, 5 columns containing 3 cubes each and 1 column containing 1 cube.

∴Total number of cubes = (9 x 5) + (7 x 4) + (5 x 3) + (1 x 1) = 89

In the figure, there are 34 columns containing 2 cubes each.

 ∴ Total number cubes = (34 x 2) = 68

The figure may be labelled as shown

Rectangles :

The simplest rectangles are CVSR, VETS, RSWM and STKW i.e 4 in number.

The rectangles composed of two components each are CETR, VEKW, RTKM and CVWM i.e 4 in number.

The rectangles composed of three components each are ACRP, PRMO, EGHT and THIK i.e 4 in number.

The rectangles composed of four components each are CEKM, AVSP, PSWO,VGHS and SHIW i.e 5 in number.

The rectangles composed of five components each are AETP, PTKO, CGHR and RHIM i.e 4 in number.

The rectangles composed of six components each are ACMO and EGIK i.e 2 in number.

The rectangles composed of eight components each are AGHP, PHIO, AVWO and VGIW i.e 4 in number.

The rectangles composed of ten components each are AEKO and CGIM i.e 2 in number.

AGIO is the only rectangle having sixteen components

Total number of rectangles in the given figure = 4 + 4 + 4 + 5 + 4 + 2 + 4 + 2 + 1 = 30.

Hexagons :

The hexagons in the given figure are CDEKLM, CEUKMQ, CFHJMQ, BEUKNP and BFHJNP. So, there are 5 hexagons in the given figure.

The figure may be labelled as shown 

Triangles :

The Simplest triangles are BGM, GHM, HAM, ABM, GIN, IJN, JHN, HGN, IKO, KLO, LJO, JIO, KDP, DEP, ELP, LKP, BCD and AFE i.e 18 in number

The triangles composed of two components each are ABG, BGH, GHA, HAB, HGI, GIJ, IJH, JHG, JIK, IKL, KLJ,LJI, LKD, KDE, DEL and ELK i.e 16 in number.

The triangles composed of four components each are BHI, GJK, ILD, AGJ, HIL and JKE i.e 6 in number.

Total number of triangles in the figure = 18 + 16 + 6 =40.

Squares :

The Squares composed of two components each are MGNH, NIOJ, and OKPL i.e 3 in number

The Squares composed of four components each are BGHA, GIJH, IKJL and KDEL i.e 4 in number

Total number of squares in the figure = 3 + 4 =7

The numbers 0,1,2,3,4,5,6,7,8,9 are 10 in number while preparing telephone numbers any number can be used any number of times.

This can be done in 105ways, but '0' is there

So, the numbers starting with '0' are to be excluded is 94 numbers.

 Total 5 digit telephone numbers = 105- 94 = 3439

DESIGN = 6 letters

No consonants appear at either of the two ends. 

= 2 x 4P4 =  2 x 4 x 3 x 2 x 1=  48

CAPITAL = 7

Vowels = 3 (A, I, A)

Consonants = (C, P, T, L)

5 letters which can be arranged in  5P5=5!

Vowels A,I = 3!2!

No.of arrangements = 5! x 3!2!=360

The number of ways of arranging n beads in a necklace is (n-1)!2=(8-1)!2=7!2 = 2520 

(since n = 8)