WBJEE · Maths · Binomial Theorem
The number \((101)^{100}-1\) is divisible by
- A \(10^{4}\)
- B \(10^{6}\)
- C \(10^{8}\)
- D \(10^{12}\)
Answer & Solution
Correct Answer
(A) \(10^{4}\)
Step-by-step Solution
Detailed explanation
\((101)^{100}-1=(1+100)^{100}-1\) \(=\left(1+{ }^{100} C_{1} \cdot 100+{ }^{100} C_{2} 100^{2}+\ldots \ldots\right)-1\) \(={ }^{100} C_{1} 100+{ }^{100} C_{2}(100)^{2}+\) \(\quad{ }^{100} C_{3}(100)^{3}+\ldots \ldots+{ }^{100} C_{100}(100)^{100}\)…
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