JEE Mains · Maths · STD 11 - 7. binomial theoram
If the remainder when \(x\) is divided by \(4\) is \(3 ,\) then the remainder when \((2020+ x )^{2022}\) is divided by \(8\) is ....... .
- A \(1\)
- B \(6\)
- C \(2\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(x=4 k+3\) \(\therefore(2020+ x )^{2022}=(2020+4 k +3)^{2022}\) \(=(4(505+ k )+3)^{2022}\) \(=(4 \lambda+3)^{2022}=\left(16 \lambda^{2}+24 \lambda+9\right)^{1011}\) \(=\left(8\left(2 \lambda^{2}+3 \lambda+1\right)+1\right)^{1011}\) \(=(8 p +1)^{1011}\) \(\therefore\) Remainder…
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