JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(\{ p \}\) denotes the fractional part of the number \(p\), then \(\left\{\frac{3^{200}}{8}\right\},\) is equal to
- A \(\frac{1}{8}\)
- B \(\frac{5}{8}\)
- C \(\frac{3}{8}\)
- D \(\frac{7}{8}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{8}\)
Step-by-step Solution
Detailed explanation
\(\left\{\frac{3^{200}}{8}\right\}=\left\{\frac{\left(3^{2}\right)^{100}}{8}\right\}\) \(=\left\{\frac{(1+8)^{100}}{8}\right\}\) \(=\left\{\frac{1+{ }^{100} C _{ T } 8+{ }^{100} C _{2} \cdot 8^{2}+\ldots+{ }^{100} C _{100} 8^{100}}{8}\right\}\)…
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