AP EAMCET · Maths · Binomial Theorem
If the coefficients of \(x^5\) and \(x^6\) are equal in the expansion of \(\left(a+\frac{x}{5}\right)^{65}\), then the coefficient of \(x^2\) in the expansion of \(\left(a+\frac{x}{5}\right)^4\) is
- A 1
- B \(\frac{32}{25}\)
- C 2
- D \(\frac{24}{25}\)
Answer & Solution
Correct Answer
(D) \(\frac{24}{25}\)
Step-by-step Solution
Detailed explanation
Coefficient of \(x^5={ }^{65} \mathrm{C}_5 a^{60}\left(\frac{1}{5}\right)^5={ }^{65} \mathrm{C}_5 \frac{a^{60}}{5^5}\) Coefficient of \(x^6={ }^{65} \mathrm{C}_6\left(\frac{1}{5}\right)^6 a^{59}={ }^{65} \mathrm{C}_6 \frac{a^{59}}{5^6}\)…
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