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Q.

Write cubes of 5 natural numbers which are of form 3n+1 (e.g.4,7,10…) and verify the following; The cube of a natural number of the form 3n+1 is a natural number of form 3n+1.

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a

2,45,356,324,879

b

7,46,789,987,1093

c

64,343, 1000, 2197, 4096

d

None of the above

answer is C.

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Detailed Solution

The 5 natural number which are in the form of 3n+1 (for e.g 4,7,10,....) are given as:
3×1+1=3+1=4
3×2+1=6+1=7
3×3+1=9+1=10
3×4+1=12+1=13
3×5+1=15+1=16
The cubes of 5 natural numbers which are in the form of 3n+1 (for eg. 4,7,10,....)
(4)3 =4×4×4=64
(7)3 =7×7×7=343
(10)3=10×10×10=1000
(133 =13×13×13=2197
(16)3 =16×16×16=4096
The cubes of 5 natural numbers
which are in the form of 3n + 1 are 64, 343, 1000, 2197 and 4096.

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