TS EAMCET · Maths · Binomial Theorem
If \(T_4\) represents the 4th term in the expansion of \(\left(5 x+\frac{7}{x}\right)^{-3 / 2}\) and \(x \notin\left[-\sqrt{\frac{7}{5}}, \sqrt{\frac{7}{5}}\right]\), then \(\left(x^7 \sqrt{5 x}\right) T_4=\)
- A \(\frac{7^4}{2^5 5^3}\)
- B \(-\frac{7^4}{2^5 5^3}\)
- C \(-\frac{7^4}{2^4 5^3}\)
- D \(\frac{7^4}{2^4 5^3}\)
Answer & Solution
Correct Answer
(C) \(-\frac{7^4}{2^4 5^3}\)
Step-by-step Solution
Detailed explanation
We know expansion of \(\begin{aligned} & (1+x)^n=1+n x+\frac{n(n-1) x^2}{2!}+\ldots \ldots \\ & \left(5 x+\frac{7}{x}\right)^{-3 / 2}=5^{-3 / 2} x^{-3 / 2}\left(1+\frac{7}{5 x^2}\right)^{-3 / 2} \end{aligned}\) The expansion of \(\left(1+\frac{7}{5 x^2}\right)^{-3 / 2}\)…
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