Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremRemainder and Divisibility ProblemsMedium2 minPYQ_2021

MathematicsMediumnumerical

If $(2021)^{3762}$ is divided by $17,$ then the remainder is _______.

Answer:

4.00

Solution:

$(2023 - 2)^{3762} = 2023 k_{1} + 2^{3762}$

$= 17 k_{2} + 2^{3762}$ (as $2023 = 17 \times 17 \times 9$ )

$= 17 k_{2} + 4 \times 16^{940}$

$= 17 k_{2} + 4 \times (17 - 1)^{940}$

$= 17 k_{2} + 4 (17 k_{3} + 1)$

$= 17 k + 4 \Rightarrow$ remainder $= 4$

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

⏱ 2mℹ️ Source: PYQ_2021

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