JEE Mains · Maths · STD 11 - 7. binomial theoram
The number of integral terms in the expansion of \(\left(5^{\frac{1}{2}}+7^{\frac{1}{8}}\right)^{1016}\) is
- A 127
- B 130
- C 129
- D 128
Answer & Solution
Correct Answer
(D) 128
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{T}_{\mathrm{r}}={ }^{1016} \mathrm{C}_{\mathrm{r}}(5)^{\frac{1016-\mathrm{r}}{2}} 7^{\frac{\mathrm{r}}{8}} \\ & \Rightarrow \mathrm{r}=0,8,16,24, \ldots ., 1016 \\ & 1016=0+(\mathrm{n}-1) 8 \\ & \Rightarrow \mathrm{n}-1=\frac{1016}{8}=127 \end{aligned}…
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