If (3a + 1)2 + (b - 1)2 + (2c - 3)2 = 0 then the value of (3a + b + 2c) is equal to?

Answer: Option A

$$\begin{array}{rl}& {\left(3a+1\right)}^2+{\left(b-1\right)}^2+{\left(2c-3\right)}^2=0\\ & {\left(3a+1\right)}^2=0\\ & \Rightarrow 3a=-1\\ & \Rightarrow a=-\frac{1}{3}\\ & {\left(b-1\right)}^2=0\\ & \Rightarrow b-1=0\\ & \Rightarrow b=1\\ & {\left(2c-3\right)}^2=0\\ & \Rightarrow c=\frac{3}{2}\\ & \therefore 3a+b+2c\\ & =3\times -\frac{1}{3}+1+\frac{3}{2}\times 2\\ & =-1+1+3\\ & =3\end{array}$$