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Highly selective Backlog Qs for JEE MainMathematicsBinomial Theorem

The remainder when 2021 2023 is divided by 7 is

Options

  1. A2
  2. B3
  3. C4
  4. D5

Correct answer

D. 5

Step-by-step solution

The remainder when 2021 divided by 7 is - 2 . Hence, the problem reduces to finding the remainder when - 2 2023 is divided by 7 . = - 2 2022 × - 2 7 = - 2 × 2 2022 7 = - 2 × 2 3 674 7 = - 2 × 8 674 7 = - 2 × 1 + 7 674 7 Using binomial theorem, we get = - 2 × 1 + 7 k 7 where k is an integer. = - 2 - 14 k 7 Clearly, the remainder when - 14 k is divisible by 7 is 0 . = - 2 7 = - 2 - 5 + 5 7 = 5 7 Hence, the remainder is 5 .

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