Binomial Theorem And Its Simple Applications Question 152
Question: The number of integral terms in the expansion of $ {{(\sqrt{3}+\sqrt[8]{5})}^{256}} $ is
Options:
A) 35
B) 32
C) 33
D) 34
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ {T_{r+1}}={{,}^{256}}C_{r}{{(\sqrt{3})}^{256-r}}{{(\sqrt[8]{5})}^{r}}={{,}^{256}}C_{r}{{(3)}^{\frac{256-r}{2}}}{{(5)}^{r/8}} $ Terms will be integral if $ \frac{256-r}{2}\And \frac{r}{8} $ both are +ve integer, which is so if r is an integral multiple of 8. As $ 0\le r\le 256 $
$ \therefore r=0,8,16,24,……..256, $ total 33 values.
BETA
