JEE Mains · Maths · STD 11 - 7. binomial theoram
The remainder when \((2021)^{2023}\) is divided by \(7\) is
- A \(1\)
- B \(2\)
- C \(5\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
\((2021)^{2023}=(7 \lambda-2)^{2023}\) \(={ }^{2023} C_{0}(7 A )^{2023}-\ldots{ }^{2023} C _{2023} 2^{2023}\) \(=7 t -2^{2023}\) \(\therefore-2^{2023}=-2 \times 2^{2022}\) \(=-2 \times\left(2^{3}\right)^{674}\) \(=-2(1+7 \mu)^{674}\) \(=-(7 \alpha+2)\)…
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