AP EAMCET · Maths · Binomial Theorem
The number of rational terms in the expansion of \(\left(3^{\frac{1}{4}}+7^{\frac{1}{6}}\right)^{144}\) is
- A 33
- B 23
- C 12
- D 13
Answer & Solution
Correct Answer
(D) 13
Step-by-step Solution
Detailed explanation
In the expansion of \(\left(3^{1 / 4}+7^{1 / 6}\right)^{144}\) General term is \[ \begin{aligned} T_{r+1} & ={ }^{144} C_r\left(3^{1 / 4}\right)^{144-r}\left(7^{1 / 6}\right)^r \\ & ={ }^{144} C_r(3)^{\frac{144-r}{4}} 7^{\frac{r}{6}} \end{aligned} \] For rational terms \(144-r\)…
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