A) \[^{6}{{C}_{3}}\]
B) \[8{{(}^{6}}{{C}_{3}})\]
C) \[8{{(}^{6}}{{C}_{4}})\]
D) \[^{6}{{C}_{4}}\]
E) \[8{{(}^{6}}{{C}_{5}})\]
Correct Answer: B
Solution :
Middle term in the expansion of\[{{(x+2y)}^{6}}\] \[=\left( \frac{n}{2}+1 \right)\]th term \[=\left( \frac{6}{2}+1 \right)\]th term = 4th term \[\therefore \]Coefficient of middle term = coefficient of \[{{T}_{4}}\] = coefficient of \[{{T}_{3+1}}\] \[{{=}^{6}}{{C}_{3}}{{.2}^{6-3}}\] \[{{=}^{6}}{{C}_{3}}.8\] \[=8{{\,}^{6}}{{C}_{3}}\]
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