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: , 2
Solution:
$\mathrm{T}_{\mathrm{r}+1}={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}(3)^{\frac{\mathrm{n}-\mathrm{r}}{2}}(5)^{\frac{\mathrm{r}}{8}} \quad(\mathrm{n} \geq \mathrm{r})$
Clearly $\mathrm{r}$ should be a multiple of $8 .$
$\because$ there are exactly 33 integral terms
Possible values of $\mathrm{r}$ can be
$0,8,16, \ldots \ldots \ldots, 32 \times 8$
$\therefore$ least value of $\mathrm{n}=256$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.