Binomial Theorem And Its Simple Applications Question 164
Question: The term independent of x in $ {{( \sqrt{x}-\frac{2}{x} )}^{18}} $ is
[EAMCET 1990]
Options:
A) $ ^{18}C_62^{6} $
B) $ ^{18}C_62^{12} $
C) $ ^{18}C_{18}2^{18} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- $ {T_{r+1}}={{,}^{18}}C_{r}{{(\sqrt{x})}^{18-r}}{{( -\frac{2}{x} )}^{r}}={{,}^{18}}C_{r}{x^{9-r/2-r}}{{(-2)}^{r}} $
If $ {T_{r+1}} $ is independent of x, then $ 9-\frac{r}{2}-r=0\Rightarrow r=6 $ .
So term independent of $ x=T_7={{,}^{18}}C_62^{6} $
BETA
