If n is the number of irrational terms in the expansion o

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:

  1. (1) 26

  2. (2) 30

  3. (3) 8

  4. (4) 7


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 .

 

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