JEE Mains · Maths · STD 11 - 7. binomial theoram
The sum of all those terms which are rational numbers in the expansion of \(\left(2^{1 / 3}+3^{1 / 4}\right)^{12}\) is:
- A \(27\)
- B \(89\)
- C \(35\)
- D \(43\)
Answer & Solution
Correct Answer
(D) \(43\)
Step-by-step Solution
Detailed explanation
\(T_{r+1}=^{12} C_{r}\left(2^{1 / 3}\right)^{r} \cdot\left(3^{1 / 4}\right)^{12-r}\) \(\mathrm{T}_{\mathrm{r}+1}\) will be rational number \(\text { Where } r=0,3,6,9,12\) \(\&\, r=0,4,8,12\) \(\Rightarrow r=0,12\) \(T_{1}+T_{13}=1 \times 3^{3}+1 \times 2^{4} \times 1\)…
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