NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

If λ is the remainder when 2 2021 is divided by 17 , then the value of λ must be equal to

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Correct answer

D. 15

Step-by-step solution

2 2021 = 2 . 2 2020 = 2 . 2 4 505 = 2 16 505 = 2 17 - 1 505 = 2 1 7 505 - 505 C 1 1 7 504 + 505 C 2 1 7 503 . . . . . . . . . . . . + 505 C 504 1 7 1 - 505 C 505 1 = 2 17 k - 1 = 17 ⋅ 2 k - 2 = 17 ⋅ 2 k - 17 + 1 5 = 17 2 k - 1 + 1 5

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