Binomial Theorem And Its Simple Applications Question 196
Question: The sum of the rational terms in the expansion of $ {{(\sqrt{2}+{3^{1/5}})}^{10}} $ is equal to
Options:
A) 40
B) 41
C) 42
D) 0
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] Here $ {T_{r+1}}={{,}^{10}}C_{r}{{(\sqrt{2})}^{10-r}}{{({3^{1/5}})}^{r}}, $
where r = 0, 1, 2, …., 10. We observe that in general term $ {T_{r+1}} $ powers of 2 and 3 are $ \frac{1}{2}(10-r) $ and $ \frac{1}{5}r $ respectively and 0 $ \le r\le 10 $ .
So, both these powers will be integers together only when $ r=0 $ or 10
$ \therefore $ Sum of required terms $ =T_1+T_{11} $
$ ={{,}^{10}}C_0{{(\sqrt{2})}^{10}}+{{,}^{10}}C_{10},{{({3^{1/5}})}^{10}}=32+9=41 $
BETA
