JEE Mains · Maths · STD 11 - 7. binomial theoram
If the fractional part of the number \(\frac{{{2^{403}}}}{{15}}\) is \(\frac{k}{{15}}\), then \(k\) is equal to
- A \(6\)
- B \(8\)
- C \(4\)
- D \(14\)
Answer & Solution
Correct Answer
(B) \(8\)
Step-by-step Solution
Detailed explanation
\(\frac{2^{403}}{15}=\frac{2^{3} \cdot 2^{400}}{15}=\frac{8 \cdot(1+15)^{100}}{15}\) \( = \frac{{8\left( {^{100}{{\text{C}}_0}{ + ^{100}}{{\text{C}}_1}(15){ + ^{100}}{{\text{C}}_2}{{(15)}^2} + \ldots \ldots } \right)}}{{15}}\)…
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