A) \[7\]
B) \[6\]
C) \[5\]
D) None of these
Correct Answer: B
Solution :
The general term in the expansion of\[{{({{y}^{1/5}}+{{x}^{1/10}})}^{55}}\]is\[{{T}_{r+1}}{{=}^{55}}{{C}_{r}}{{({{y}^{1/5}})}^{55-r}}{{({{x}^{1/10}})}^{r}}\] \[{{=}^{55}}{{C}_{r}}{{y}^{11-r/5}}{{x}^{r/10}}\] Since, \[{{T}_{r+1}}\] will be independent of radicals, so the exponents \[r/5\] and \[r/10\] are integers for\[0\le r\le 55\], which is possible only when\[r=0,\,\,10,\,\,20,\,\,30,\,\,40,\,\,50\]. There are six terms viz\[{{T}_{1}},\,\,{{T}_{11}},\,\,{{T}_{21}},\,\,{{T}_{31}},\,\,{{T}_{41}},\,\,{{T}_{51}}\]which are independent of radicals.
You need to login to perform this action.
You will be redirected in
3 sec
