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Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremRemainder and Divisibility ProblemsMedium2 minPYQ_2025

MathematicsMediumsingle choice

The remainder, when $7^{103}$ is divided by 23 , is equal to :

Options:

Answer:

Solution:

$7^{103} = 7 (7^{102}) = 7 (343)^{34} = 7 (345 - 2)^{34} 7^{103} = 23 K_{1} + 7. 2^{34}$ Now $7. 2^{34} = 7. 2^{2} \cdot 2^{32}$ $= 28 \cdot (256)^{4} = 28 (253 + 3)^{4} ∴ 28 \times 81 \Rightarrow (23 + 5) (69 + 12) 23 K_{2} + 60 ∴ Remainder = 14$

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

⏱ 2mℹ️ Source: PYQ_2025

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