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JEE Main202313 Apr 2023Evening ShiftMathematicsBinomial TheoremActual

The remainder, when 7 103 is divided by 17 , is

Correct answer

12

Step-by-step solution

Using the binomial expansion in 7 103 = 7 2 51 · 7 = 51 - 2 51 · 7 we get, 51 - 2 51 · 7 = 7 · C 0 51 51 51 · 2 0 - C 1 51 51 50 · 2 1 + . . . . . . . - C 51 51 2 51 Now 51 is divisible by 17 , so when above equation is divided by 17 we get, 7 · - 2 51 as remainder, Now again using binomial in 7 · - 2 51 = - 56 2 4 12 = - 56 17 - 1 12 we get, - 56 17 - 1 12 = - 56 C 0 12 17 12 · 1 0 - C 1 12 17 11 · 1 1 + . . . . . . . + C 12 12 1 12 Now dividing above equation by 1

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