TS EAMCET · Maths · Binomial Theorem
The number of rational terms in the binomial expansion of \((\sqrt[4]{5}+\sqrt[5]{4})^{100}\) is
- A \(10\)
- B \(20\)
- C \(6\)
- D \(5\)
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
\((\sqrt[4]{5}+\sqrt[5]{4})^{100}\) \(\begin{aligned} T_{r+1}= & { }^{100} C_r\left(5^{1 / 4}\right)^{100-r}\left(4^{1 / 5}\right)^r \\ = & { }^{100} C_r(5)^{\frac{100-r}{4}}(4)^{\frac{r}{5}} \end{aligned}\) For riational terms, \(100-r\) must be multiple of 4…
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