Question

If the coefficients of $(r+2{)}^{th}$ and $(2r+1{)}^{th}$ terms $(r\ne 1)$ are equal in the expansion of $(1+x{)}^{43}$, then $r=$

• A. $12$
• B. $13$
• C. $14$
• D. $15$

Answer 1

The correct option is C $14$

Since coefficient of $(r+2{)}^{th}$ term is equal to coefficient of $(2r+1{)}^{th}$ term in the binomial expansion of $(1+x{)}^{43}$
Therefore ${}^{43}{C}_{r+1}={}^{43}{C}_{2r}$
Now ${}^n{C}_r={}^n{C}_{n-r}$
$\therefore 43-(r+1)=2r$
$\Rightarrow 42=3r$
$\Rightarrow r=14$