A) \[\left( 16,\frac{251}{3} \right)\]
B) \[\left( 14,\frac{251}{3} \right)\]
C) \[\left( 14,\frac{272}{3} \right)\]
D) \[\left( 16,\frac{272}{3} \right)\]
Correct Answer: D
Solution :
\[(1+ax+b{{x}^{2}})\] \[[1{{-}^{18}}{{C}_{1}}2x{{+}^{18}}{{C}_{2}}{{(2x)}^{2}}{{-}^{18}}{{C}_{3}}{{(2x)}^{3}}{{+}^{18}}{{C}_{4}}{{(2x)}^{4}}...]\]Coefficient of \[{{x}^{3}}\]is \[{{-}^{18}}{{C}_{3}}({{2}^{3}})+a{{(}^{18}}{{C}_{2}}\times 4)-b{{(}^{18}}{{C}_{1}}\times 2)=0\] ?(i) Coefficient of is \[^{18}{{C}_{4}}({{2}^{4}})+a({{-}^{18}}{{C}_{3}}{{2}^{3}}){{+}^{18}}{{C}_{2}}b{{2}^{2}}=0\] ?(ii) or solving both these equation a = 16 and b = 272/3.
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