Binomial Theorem And Its Simple Applications Question 6
Question: The greatest value of the term independent of x in the expansion $ {{(x\sin p+{x^{-1}}\cos p)}^{10}},p\in R $ is
Options:
A) $ 2^{5} $
B) $ \frac{10!}{2^{5}{{(5!)}^{2}}} $
C) $ \frac{10!}{{{(5!)}^{2}}} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ {{(x\sin p+{x^{-1}},\cos p)}^{10}}, $ general term is $ {T_{r+1}}={{,}^{10}}C_{r}{{(x\sin p)}^{10-r}}{{({x^{-1}},\cos ,p)}^{r}} $ . For the term independent of x we have $ 10-2r=0 $ or $ r=5 $
Hence, independent term is $ ^{10}C_5{{\sin }^{5}}P,{{\cos }^{5}}P={{,}^{10}}C_5\frac{{{\sin }^{5}}2p}{32} $ which is greatest when $ \sin 2p=1 $ .
BETA
