In the expansion of $(1 + x)^{43}$, the coefficients of the (2r+1)th and the (r + 2)th terms are equal, then the value of r, is

$\begin{aligned} T_{n+1} & ={ }^{n} C_{n} \cdot a^{n-n} \cdot b^{n} \\ T_{n+1} & ={ }^{43} C_{n} x^{n} \\ T_{2 n+1} & =43 C_{2 n} \cdot x^{2 n} \\ T_{n+2} & =T_{(n+1)+1} \cdot x^{n+1} \\ & =43 C_{n+1} \end{aligned}$

Coefficients are equal

$43 c_{2 r}={ }^{43} c_{n+1}$

$\begin{aligned} 2 r= & r+1 \quad \text { or } \\ 2 n+r+1 & =43 \\ r & =1 \text { or } \begin{aligned} 3 r & =42 \\ r & =14 \end{aligned} \end{aligned}$

$\left[\begin{array}{c} n c_{x}={ }^{n} c_{y} \text {, then } x=y \text { or } \\ x+y=n \end{array}\right]$

Option (A) is correct