AP EAMCET · Maths · Binomial Theorem
In the expansion of \((\sqrt[5]{3}+\sqrt[3]{2})^{15}\)
- A Number of rational terms is 3
- B Sum of all rational terms is 58
- C Sum of all rational terms is greater than the sum of all irrational terms
- D Sum of all irrational terms is greater than the sum of all rational terms
Answer & Solution
Correct Answer
(D) Sum of all irrational terms is greater than the sum of all rational terms
Step-by-step Solution
Detailed explanation
Given binomial is \((\sqrt[5]{3}+\sqrt[3]{2})^{15}\) \(\because\) The general term \(T_{r+1}={ }^{15} C_r 3^{\frac{15-r}{5}} 2^{\frac{r}{3}}\) \(={ }^{15} C_r 3^{3-r / 5} 2^{1 / 3}\) For rational terms \(r\) must be multiple of 15 , so possible values of \(r=0\) and…
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