AP EAMCET · Maths · Binomial Theorem
If P is the greatest divisor of \(49^{\mathrm{n}}+16 n-1\) for all \(n \in \mathrm{~N}\), then the number of factors of P is
- A \(12\)
- B \(15\)
- C \(7\)
- D \(13\)
Answer & Solution
Correct Answer
(C) \(7\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & 49^n+16 n-1=(1+48)^n+16 n-1 \\ = & 1+{ }^n C_1(48)+{ }^n C_2(48)^2+\ldots .+{ }^n C_n(48)^n+16 n-1 \\ = & (48 n+16 n)+{ }^n C_2(48)^2+\ldots .+{ }^n C_n(48)^n \\ = & 64 n+8^n\left({ }^n C_2 6^2+{ }^n C_3 6^3 8+\ldots+{ }^n C_n 6^n 8^{n-2}\right) \end{aligned}…
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