Question:
If the number of integral terms in the expansion of $\left(3^{1 / 2}+5^{1 / 8}\right)^{n}$ is exactly 33 , then the least value of $n$ is :
Correct Option: , 3
Solution:
Here, $\left(3^{2}+5^{8}\right)$
$T_{r+1}={ }^{n} C_{r}(3)^{\frac{n-r}{2}}(5)^{\frac{r}{8}}$
$\because \frac{n-r}{2}$ and $\frac{r}{8}$ are integer
So, $r$ must be $0,8,16,24 \ldots \ldots$
Now $n=t_{33}=a+(n-1) d=0+32 \times 8=256$
$\Rightarrow n=256$