AP EAMCET · Maths · Binomial Theorem
The sum of the rational term in the binomial expansion of \(\left(\sqrt{2}+3^{1 / 5}\right)^{10}\) is
- A 41
- B 39
- C 32
- D 30
Answer & Solution
Correct Answer
(A) 41
Step-by-step Solution
Detailed explanation
Rational terms are \(T_{11}, T_1\) \(\begin{aligned} & \mathrm{T}_{11}={ }^{10} \mathrm{C}_{10}\left(3^{1 / 5}\right)^{10}(\sqrt{2})^0=9 \\ & \mathrm{~T}_1={ }^{10} \mathrm{C}_0\left(3^{\frac{1}{5}}\right)^0 \cdot(\sqrt{2})^{10}=32 \end{aligned}\) Sum of rational terms \(=41\)
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