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JEE Mains · Maths · STD 11 - 7. binomial theoram
The sum of the rational terms in the binomial expansion of \({\left( {{2^{\frac{1}{2}}} + {3^{\frac{1}{5}}}} \right)^{10}}\) is
- A \(25\)
- B \(32\)
- C \(9\)
- D \(41\)
Answer & Solution
Correct Answer
(D) \(41\)
Step-by-step Solution
Detailed explanation
\(\left(2^{1 / 2}+3^{1 / 5}\right)^{10}=^{10} \mathrm{C}_{0}\left(2^{1 / 2}\right)^{10}\) \(+^{10} \mathrm{C}_{1}\left(2^{1 / 2}\right)^{9}\left(3^{1 / 5}\right)+\ldots \ldots+^{10} \mathrm{C}_{10}\left(3^{1 / 5}\right)^{10}\) There are onlytwo rational terms - first term and…
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