Question:
The value of r for which
${ }^{20} \mathrm{C}_{\mathrm{r}}{ }^{20} \mathrm{C}_{0}+{ }^{20} \mathrm{C}_{\mathrm{r}-1}{ }^{20} \mathrm{C}_{1}+{ }^{20} \mathrm{C}_{\mathrm{r}-2}{ }^{20} \mathrm{C}_{2}+\ldots{ }^{20} \mathrm{C}_{0}{ }^{20} \mathrm{C}_{\mathrm{r}}$ is maximum, is
Correct Option: 1
Solution:
Given sum = coefficient of xr in the expansion
of $(1+x)^{20}(1+x)^{20}$,
which is equal to ${ }^{40} \mathrm{C}_{\mathrm{r}}$
It is maximum when $r=20$
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