A) 120
B) 330
C) 420
D) 210
Correct Answer: B
Solution :
[b] \[{{(1+x)}^{10}}+x{{(1+x)}^{9}}+{{x}^{2}}{{(1+x)}^{8}}+\text{ }\ldots \text{ }+\text{ }{{x}^{10}}\] \[=\frac{{{(1+x)}^{10}}\left( 1-{{\left( \frac{x}{1+x} \right)}^{11}} \right)}{1-\frac{x}{1+x}}\] \[={{(1+x)}^{11}}{{x}^{11}}\] \[\therefore \] Coeff. of \[{{x}^{7}}={{\,}^{11}}{{C}_{7}}=\,{{\,}^{11}}{{C}_{4}}\] \[=\,\frac{11\times 10\times 9\times 8}{4\times 3\times 2\times 1}\] \[=330\]
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