A) \[{{101}^{5}}\]
B) \[101\]
C) \[{{201}^{5}}\]
D) \[^{201}{{C}_{5}}\]
Correct Answer: A
Solution :
[a] \[^{505}{{C}_{5}}-5{{\times }^{404}}{{C}_{5}}+10{{\times }^{303}}{{C}_{5}}-10{{\times }^{202}}{{C}_{5}}+5{{\times }^{101}}{{C}_{5}}-1+1\]= coefficient of \[{{x}^{5}}\] in \[{{(1+x)}^{505}}-5{{(1+x)}^{404}}\] \[+10{{(1+x)}^{303}}-10{{(1+x)}^{202}}+5{{(1+x)}^{101}}-1+1\] = coefficient of \[{{x}^{5}}\] in \[{{[{{(1+x)}^{101}}-1]}^{5}}+1\] \[={{{{(}^{101}}{{C}_{1}})}^{5}}\]
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