Question:
If $\mathrm{n}$ is the number of irrational terms in the expansion of $\left(3^{1 / 4}+5^{1 / 8}\right)^{60}$, then $(\mathrm{n}-1)$ is divisible by:
Correct Option: 1
Solution:
For rational terms.
$\frac{r}{8}=k ; 0 \leq r \leq 60$
$0 \leq 8 k \leq 60$
$0 \leq k \leq \frac{60}{8}$
$0 \leq k \leq 7.5$
$\mathrm{k}=0,1,2,3,4,5,6,7$
$\frac{60-8 \mathrm{k}}{4}$ is always divisible by 4 for all value of $\mathrm{k}$ Total rational terms $=8$ Total
terms $=61$
irrational terms $=53$
$n-1=53-1=52$
52 is divisible by 26 .