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Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremRemainder and Divisibility ProblemsMedium2 minPYQ_2025

MathematicsMediumsingle choice

The remainder when $((64)^{(64)})^{(64)}$ is divided by 7 is equal to

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Answer:

Solution:

Let $N = ((64)^{64})^{64}$ $N = (64)^{6 4^{2}}$ $N = (1 + 63)^{6 4^{2}}, let 6 4^{2} = n$ Expanding by binomial $N = (1 + 63)^{n} = 1 +^{n} C_{1} 63 +^{n} C_{2} (63)^{2} + \dots . = 1 + 63 λ = 1 + 7 (9 λ)$ Remainder when divided by 7 is 1

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

⏱ 2mℹ️ Source: PYQ_2025

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