If the coefficients of $(2 r+6)^{\text {th }}$ and $(r-1)^{\text {th }}$ terms in the expansion of…
If the coefficients of $(2 r+6)^{\text {th }}$ and $(r-1)^{\text {th }}$ terms in the expansion of $(1+x)^{21}$ are equal, then the value of $r=$
$7$
$5$
$6$
$8$
Solution
General term of $(1+x)^{21}$ is $\mathrm{T}_{\mathrm{r}+1}={ }^{21} \mathrm{C}_{\mathrm{r}} x^{\mathrm{r}}$ Coefficient of $(2 r+6)^{\text {th }}$ term $=$ Coeff. of $(r-1)^{\text {th }}$ term $\Rightarrow 2 r+5=21-(r-2) \Rightarrow \mathrm{r}=6$