WBJEE · Maths · Binomial Theorem
\(\left(2^{3 \mathrm{n}}-1\right)\) will be divisible by \((\forall \mathrm{n} \in \mathrm{N})\)
- A 25
- B 8
- C 7
- D 3
Answer & Solution
Correct Answer
(C) 7
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Hints: } 2^{3 \mathrm{n}}=(8)^{\mathrm{n}}=(1+7)^{\mathrm{n}}=={ }^{\mathrm{n}} \mathrm{C}_0+{ }^{\mathrm{n}} \mathrm{C}_1 7+{ }^{\mathrm{n}} \mathrm{C}_2 7^2+\ldots \ldots .+{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{n}} 7^{\mathrm{n}} \\ & \Rightarrow 2^{3…
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