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    				| 1. | Explain on the basis of algebra that any natural number which is not a multiple of 3 when divided by 3, we get the remainder as 1. | 
| Answer» We can write the natural numbers which are not the multiple of 3 as. 3n + 1, 3n + 2 (3n + 1)2 = (3n)2 + 6n + 1 = 9n2 + 6n + 1 = 3 (3n2 + 2n) + 1 When divided by 3, remainder is 1 (3n + 2)2 = 9n2 + 6n + 4 = 9n2 + 6n + 3 + 1 = 3 (3n2 + 2n + 1) + 1 When divided by 3, remainder is 1 | |