In the figure the simplest Triangles are GLK, DLJ, DJM,HMN,QRE,IRA,IPA, and FPO is the 8 triangle

and another is BDO,CDQ,DLM, PRA, KFI, NEI, HJI, GJI,DKI, and DNI is the 10 triangle

and another is DIE, DFI, DOA, DQA, and GHI is the 5 triangle

and DCA, DBA is the 2 triangle and DEF and ABC so that according to the figure the total no. of triangle is 8+10+5+2+1+1=27

Answer: A) 30, 5 Explanation: 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.

In this figure counting the squares and we get the 27 squares.

Answer: A) 35/36 Explanation: When two dice are thrown simultaneously, the probability is n(S) = 6x6 = 36 Required, the sum of the two numbers that turn up is less than 12 That can be done as n(E) = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)(6,1), (6,2), (6,3), (6,4), (6,5) } = 35 Hence, required probability = n(E)/n(S) = 35/36.

Answer: B) 1/9 Explanation: S = { (1, 1), (1, 2), (1, 3), (1, 4),(1, 5), (1, 6), (2, 1), (2, 2),.........(6, 5), (6, 6) } => n(S) = 6 x 6 = 36 E = {(6, 3), (5, 4), (4, 5), (3, 6) } => n(E) = 4 Therefore, P(E) = 4/36 = 1/9

3+3+3=9 triangle 

Triangle ABD +Triangle ADC =2

Same as 2+2+2=6

And Triangle ABC=1 

So that total no of triangle in this figure is 9+6+1=16