Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremRemainder and Divisibility ProblemsHard2 minPYQ_2009

MathematicsHardsingle choice

The remainder left out when $8^{2 n} - (62)^{2 n + 1}$ is divided by 9 is

Options:

Answer:

Solution:

$8^{2 n} - (62)^{2 n + 1} = (1 + 63)^{n} - (63 - 1)^{2 n + 1} = (1 + 63)^{n} + (1 - 63)^{2 n + 1} = (1 +^{n} c_{1} 63 +^{n} c_{2} (63)^{2} + \dots . + (63)^{n}) + (1 -^{(2 n + 1)} c_{1} 63 +^{(2 n + 1)} c_{2} (63)^{2} + \dots . + (- 1) (63)^{(2 n + 1)}) = 2 + 63 (^{n} c_{1} +^{n} c_{2} (63) + \dots . + (63)^{n - 1} -^{(2 n + 1)} c_{1} +^{(2 n + 1)} c_{2} (63) + \dots . (63)^{(2 n)})$ $∴$ Reminder is 2

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

⏱ 2mℹ️ Source: PYQ_2009

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