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If \({}^{20}\mathrm{C}_{\mathrm{r}}\) is the co-efficient of \({\mathrm{x}}^{\mathrm{r}}\) in the expansion of \((1+\mat…

Q1

If \({}^{20}\mathrm{C}_{\mathrm{r}}\) is the co-efficient of \({\mathrm{x}}^{\mathrm{r}}\) in the expansion of \((1+\mathrm{x}{)}^{20}\), then the value of \(\overset{20}{\underset{r=0}{\sum {r}^{2}}}{}^{20}C_{r}\) is equal to

[JEE Main 2021, 26 Aug (Shift 1)]

a

\(420\times {2}^{19}\)

b

\(380\times {2}^{19}\)

c

\(380\times {2}^{18}\)

d

\(420\times {2}^{18}\)

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