TS EAMCET · Maths · Binomial Theorem
The number of integral terms in the expansion of \((\sqrt{3}+\sqrt[8]{5})^{256}\) is
- A \(32\)
- B \(33\)
- C \(34\)
- D \(35\)
Answer & Solution
Correct Answer
(B) \(33\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & (\sqrt{3}+\sqrt[8]{5})^{256} \\ T_{r+1} & ={ }^{256} C_r\left(3^{1 / 2}\right)^{256-r}\left(5^{1 / 8}\right)^r \end{aligned} \] For integral terms, \(r\) must be divisible by 2 and 8 . \(\therefore \quad r\) must be divisible by 8 i.e.…
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