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.

The main triangle shown is in the given figure and this the total no. of triangle is 15. remaing triangle we can find out in the drawing the triangle in the image.

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