AP EAMCET · Maths · Binomial Theorem
The sum of the rational terms in the expansion of \((\sqrt{2}+\sqrt[5]{3})^{10}\) is
- A 41
- B 42
- C 32
- D 39
Answer & Solution
Correct Answer
(A) 41
Step-by-step Solution
Detailed explanation
The general term is \(T_{r+1} = \binom{10}{r} (2^{1/2})^{10-r} (3^{1/5})^r = \binom{10}{r} 2^{(10-r)/2} 3^{r/5}\). For the term to be rational, \((10-r)/2\) and \(r/5\) must be integers. \(r\) must be an even multiple of 5: \(r \in \{0, 10\}\). For \(r=0\):…
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