Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremRemainder and Divisibility ProblemsHard2 minPYQ_2021

MathematicsHardnumerical

If the remainder when $x$ is divided by $4$ is $3$ , then the remainder when ${(2020 + x)}^{2022}$ is divided by $8$ is ___ .

Answer:

1.00

Solution:

$x = 4 k + 3$

$∴ {(2020 + x)}^{2022} = {(2020 + 4 k + 3)}^{2022}$

$= {(4 (505 + k) + 3)}^{2022}$

$= {(4 λ + 3)}^{2022} = {(16 λ^{2} + 24 λ + 9)}^{1011}$

$= {(8 (2 λ^{2} + 3 λ + 1) + 1)}^{1011}$

$= {(8 p + 1)}^{1011}$

$∴$ Remainder when divided by $8 = 1$ .

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Remainder and Divisibility Problems

⏱ 2mℹ️ Source: PYQ_2021

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