If { p } denotes the fractional part of the number p , then 3 200 8 is equal to

3 200 = 9 100 ⇒ ( 1 + 8 ) 100 = 1 + C 1 100 8 + C 2 100 8 2 + . . . 8 100 ⇒ 3 200 = 1 + 8 λ , where λ is some integer. ⇒ 3 200 8 = λ + 1 8 ⇒ 3 200 8 = 1 8

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Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremRemainder and Divisibility ProblemsHard2 minPYQ_2020

MathematicsHardsingle choice

If ${p}$ denotes the fractional part of the number $p,$ then $\{\frac{3^{200}}{8}\}$ is equal to

Options:

Answer:

Solution:

$3^{200} = 9^{100}$

$\Rightarrow (1 + 8)^{100} = 1 + {}^{100}C_{1} 8 + {}^{100}C_{2} {(8)}^{2} + . . . 8^{100}$
$\Rightarrow 3^{200} = 1 + 8 λ$ , where $λ$ is some integer.
$\Rightarrow \frac{3^{200}}{8} = λ + \frac{1}{8}$
$\Rightarrow \{\frac{3^{200}}{8}\} = \frac{1}{8}$

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

⏱ 2mℹ️ Source: PYQ_2020

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