Cubes
 Find the minimum number of cuts required to get 50 pieces.

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For minimum number of cuts we will get 50 from 2 x 5 x 5 and cuts is 1 + 4 + 4 = 9
Correct Option: C
For minimum number of cuts we will get 50 from 2 x 5 x 5 and cuts is 1 + 4 + 4 = 9
 Find the maximum number of cuts required to get 50 pieces.

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For maximum number of cuts it has to be in one cut only, so number of cuts is 49
Correct Option: A
For maximum number of cuts it has to be in one cut only, so number of cuts is 49
 If total number of pieces (Smaller cubes/cuboids) is 45 then find the possible number of cuts.

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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.Correct Option: B
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.
 If total number of cuts is 20 then find the ratio of maximum and minimum of pieces that can be obtained.

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For maximum number of pieces cuts has to be 6, 7 and 7 and maximum number of pieces is (6 + 1)(7 + 1)(7 + 1) = 7 x 8 x 8 = 448.
Minimum number of pieces is 20 + 1 = 21.Correct Option: B
For maximum number of pieces cuts has to be 6, 7 and 7 and maximum number of pieces is (6 + 1)(7 + 1)(7 + 1) = 7 x 8 x 8 = 448.
Minimum number of pieces is 20 + 1 = 21.
Hence required ratio is 448:21
 If total number of cuts is 10 then find the maximum number of pieces that can be obtained.

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If total number of cut is 10 then for maximum number of pieces these cuts have to be well distributed in three planes. For 10 cuts,
3,3 and 4 is the distribution of cuts.Correct Option: A
If total number of cut is 10 then for maximum number of pieces these cuts have to be well distributed in three planes. For 10 cuts, 3,3 and 4 is the distribution of cuts.
Hence total number of pieces is
(3 + 3)(3 + 1)(4 + 1) = 4 x 4 5 = 80