If x2 + y2 + 2x + 1 = 0, then the value of x31 + y35 is?

Answer: Option A

$$\begin{array}{rl}& x^2+y^2+2x+1=0\\ & \Rightarrow x^2+2x+1+y^2=0\\ & \Rightarrow {\left(x+1\right)}^2+y^2=0\end{array}$$
Hence both terms are squares and there addition is zero.
So, it can be possible only when both terms are zeros.
$$\begin{array}{rl}& \therefore x+1=0\\ & \Rightarrow x=-1\\ & y=0\\ & \therefore x^{31}+y^{35}\\ & \Rightarrow {\left(-1\right)}^{31}+{\left(0\right)}^{35}\\ & \Rightarrow -1\end{array}$$