A) \[{{2}^{5}}\]
B) \[\frac{10!}{{{2}^{5}}{{(5!)}^{2}}}\]
C) \[\frac{10!}{{{(5!)}^{2}}}\]
D) None of these
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 \[\sin \,\,2p=1\].
You need to login to perform this action.
You will be redirected in
3 sec
