A) 1
B) -1
C) 0
D) 2
Correct Answer: A
Solution :
\[^{100}{{C}_{0}}{{\,}^{200}}{{C}_{100}}{{-}^{100}}{{C}_{1}}{{\,}^{199}}{{C}_{100}}{{+}^{100}}{{C}_{2}}{{\,}^{198}}{{C}_{100}}-\] \[^{100}{{C}_{3}}{{\,}^{197}}{{C}_{100}}+...{{+}^{100}}{{C}_{100}}{{\,}^{100}}{{C}_{100}}\] Coefficient ox \[{{x}^{100}}\] in \[^{100}{{C}_{0}}\,{{(1+x)}^{200}}{{-}^{100}}{{C}_{1}}\,(1+x){{\,}^{199}}\] \[{{+}^{100}}{{C}_{2}}\,{{(1+x)}^{198}}-...+{{\,}^{100}}{{C}_{100}}\,{{(1+x)}^{100}}\] = Coefficient of \[{{x}^{100}}\] in \[{{(1+x)}^{100}}{{[}^{100}}{{C}_{0}}{{(1+x)}^{100}}{{-}^{100}}{{C}_{1}}\,{{(1+x)}^{99}}+\] \[^{100}{{C}_{2}}\,{{(1+x)}^{98}}-...{{+}^{100}}{{C}_{100}}]\] = Coefficient of \[{{x}^{100}}\] in \[{{(1+x)}^{100}}\cdot {{x}^{100}}=1\]You need to login to perform this action.
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