JEE Mains · Maths · STD 11 - 7. binomial theoram
The remainder when \(428^{2024}\) is divided by \(21\) is ............
- A \(1\)
- B \(2\)
- C \(3\)
- D \(11\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\( (428)^{2024}=(420+8)^{2024} \) \( =(21 \times 20+8)^{2024} \) \( =21 \mathrm{~m}+8^{2024} \) \( \text { Now } 8^{2024}=\left(8^2\right)^{1012} \) \( =(64)^{1012} \) \( =(63+1)^{1012} \) \( =(21 \times 3+1)^{1012} \) \( =21 \mathrm{n}+1 \)…
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