WBJEE · Maths · Mathematical Induction
The expression \(2^{4 n}-15 n-1\), where \(n \in \mathbb{N}\) (the set of natural numbers) is divisible by
- A \(125\)
- B \(225\)
- C \(325\)
- D \(425\)
Answer & Solution
Correct Answer
(B) \(225\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } 2^{4 n}-15 n-1=(1+15)^n-15 n-1=\left({ }^n C_0+{ }^n C_1 \cdot 15+{ }^n C_2 15^2+\ldots \ldots \ldots . .+{ }^n C_n \cdot 15^n\right)-15 n-1 \\ & =15^2\left({ }^n C_2+{ }^n C_3 \cdot 15 \ldots \ldots \ldots .+{ }^n C_n \cdot 15^{n-2}\right) \\ & =225…
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