Four pairs of flower pots are given below. Among them only one pair is similar in all respects. Identify the pair numbers which represent that pair:

Correct Answer: 40 triangles, 7 Squares

Explanation:

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

Correct Answer: 1

Explanation:

Correct Answer: 10

Explanation:

The given figure can be labelled as :

   

The simplest triangles are AJF, FBG, HDI, GCH and JEI i.e 5 in number.
The triangles composed of the three components each are AIC, FCE, ADG, EBH and DJB i.e 5 in number.
Thus, there are 5 + 5 = 10 triangles in the given figure.

Correct Answer: C

Explanation:

Correct Answer: o

Explanation:

Correct Answer: A

Explanation:

Correct Answer: yellow

Explanation:

We may label the figure as shown.

The Simplest triangles are AFB, FEB, EBC, DEC, DFB and AFD i.e 6 in number.

The triangles composed of two components each are AEB, FBC, DFC, ADE, DBE and ABD i.e 6 in number.

The triangles composed of three components each are ADC and ABC i.e 2 in number.

There is only one triangle i.e DBC which is composed of four components.

Thus, there are 6 + 6 + 2 + 1 = 15 triangles in the figure

Correct Answer: 342

Explanation:

Out of 6 faces of 3 faces are exposed and those were painted.
Number of vertices with three faces exposed (Painted) is 1
Number of vertices with 2 faces exposed (Painted) is 3
Number of vertices with 1 faces exposed (Painted) is 3
Number of vertices with 0 faces exposed (Painted) is 1
Number of sides with 2 sides exposed (Painted) is 3
Number of sides with 1 sides exposed (Painted) is 6
Number of sides with no sides exposed (Painted) is 3
From the above observation
Number of cubes with 3 faces Painted is 1
Number of cubes with 2 faces Painted is given by sides which is exposed from two sides and there are 3 such sides and from one we will get 6 such cubes hence required number of cubes is 6 x 3 = 18
Number of cubes with 1 face Painted is given by faces which is exposed from one sides and there are 3 such faces hence required number of cubes is 36 x 3 = 108
Number of cubes with 0 face Painted is given by difference between total number of cubes - number of cubes with at least 1 face painted = 343 - 1- 18 - 108 = 216
In other words number of cubes with 0 painted is (7 - 1)³ = 216.
From the above explanation number of the cubes with at most 2 faces painted is 216 + 108 + 18 = 342.
Or else 343 - 1 = 342

Correct Answer: 1

Explanation:

NA

Correct Answer: 8 or 12

Explanation:

If 45 = 1 x 1 x 45 then we require only 44 cuts in one plane.
If 1 x 3 x 15 then we require 2 cuts in one plane and 14 cuts in other plane so total number of cuts is 2 + 14 = 16.
If 1 x 5 x 9 the we require 4 cuts in one plane and 8 cuts in other plane so total number of cuts is 4 + 8 = 12
If 3 x 3 x 5 then we require 2 cuts in one plane, 2 cuts in 2^nd plane and 4 cuts in 3^rd plane so total number of cuts is 2 + 2 + 4 = 8.