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If (101)n = 65, where n represent the base of the respective number system, then the value of n is

If (101)n = 65, where n represent the base of the respective number system, then the value of n is Correct Answer 8

For n = 2

(101)2 = 1 × 22 + 0 × 21 + 1 × 20 = 22 + 20 = 4 + 1 = 5

For n = 4

(101)4 = 1 × 42 + 0 × 41 + 1 × 40 = 42 + 40 = 16 + 1 = 17

For n = 8

(101)8 = 1 × 82 + 0 × 81 + 1 × 80 = 82 + 80 = 64 + 1 = 65

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