A) 12.00
B) 12.75
C) 12.25
D) 12.50
Correct Answer: C
Solution :
Here, \[{{(x+10)}^{50}}+{{(x-10)}^{50}}={{a}_{0}}+{{a}_{1}}x\]\[+{{a}_{2}}{{x}^{2}}+...+{{a}_{50}}{{x}^{50}}\] \[\Rightarrow \]\[2{{[}^{50}}{{C}_{0}}{{x}^{50}}{{+}^{50}}{{C}_{2}}{{x}^{48}}{{10}^{2}}+...{{+}^{50}}{{C}_{48}}{{x}^{2}}{{10}^{48}}\]\[{{+}^{50}}{{C}_{50}}{{10}^{50}}=\]\[{{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...+{{a}_{50}}{{x}^{50}}\] \[\Rightarrow \]\[{{a}_{0}}=2\times {{10}^{50}},{{a}_{2}}=2{{\times }^{50}}{{C}_{48}}{{10}^{48}}\] \[\therefore \]\[\frac{{{a}_{2}}}{{{a}_{0}}}=\frac{^{50}{{C}_{48}}}{{{10}^{2}}}=12.25\]
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