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
\begin{aligned}\text {Hints: } & (101)^{100}-1={ }^{100} \mathrm{C}_1 100+{ }^{100} \mathrm{C}_2 100^2+{ }^{100} \mathrm{C}_3 100^3+\ldots \ldots +{ }^{100} \mathrm{C}_{100} 100^{100} \\ & =100^2\left[1+{ }^{100} \mathrm{C}_2+{ }^{100} \mathrm{C}_3 100+\ldots \ldots .\right] \\…
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