A) 20
B) 10
C) 15
D) 11
Correct Answer: A
Solution :
The coefficient of\[{{x}^{2}}\]in the expansion of\[{{(1+x)}^{20}}{{(1+x)}^{20}}\]is\[^{20}{{C}_{r}}^{20}{{C}_{0}}{{+}^{20}}{{C}_{r-1}}^{20}{{C}_{1}}{{+}^{20}}{{C}_{r-2}}\]\[^{20}{{C}_{2}}+...{{+}^{20}}{{C}_{0}}^{20}{{C}_{r}},\]which is the given sum. Now, coefficient of \[{{x}^{r}}\] in \[{{(1+x)}^{40}}\]is \[^{40}{{C}_{r}}.\] Here, n = 40 and coefficient of\[{{x}^{r}}\] will be maximum when \[r=\frac{n}{2}=\frac{40}{2}=20.\]
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