A) 1
B) n
C) nx
D) ny
Correct Answer: C
Solution :
[c] We have, \[\sum\limits_{r=0}^{n}{r{{\,}^{n}}{{C}_{r}}{{x}^{r}}\,{{y}^{n-r}}=\sum\limits_{r=0}^{n}{r\frac{n}{r}{{\,}^{n-1}}{{C}_{r-1}}{{x}^{r-1}}{{x}^{1}}{{y}^{n-r}}}}\] \[=\,\,nx\,\,\sum\limits_{r=0}^{n}{^{n-1}{{C}_{r-1}}{{x}^{r-1}}{{y}^{(n-1)-(r-1)}}}\] \[=\,\,\,\,nx{{(x+y)}^{n-1}}=nx\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[\because \,\,\,\,x+y=1]\]You need to login to perform this action.
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