The number of integral terms in the expansion of (5^ 1 2 +7^ 1 8 … - Vidyadip

MCQ

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
✓
128

✓

Answer

Correct option: D.

128

(D) 128
$\mathrm{T}_{\mathrm{r}}={ }^{1016} \mathrm{C}_{\mathrm{r}}(5)^{\frac{1016-\mathrm{r}}{2}} 7^{\frac{\mathrm{r}}{8}}$
$\Rightarrow \mathrm{r}=0,8,16,24, \ldots ., 1016$
$1016=0+(\mathrm{n}-1) 8$
$\Rightarrow \mathrm{n}-1=\frac{1016}{8}=127$
So, $\mathrm{n}=128$.

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