If a + b = 1 and a3 + b3 + 3ab = k, then the value of k is?

Answer: Option A

$$\begin{array}{rl}& a+b=1\\ & \text{By cubing,}\\ & a^3+b^3+3ab\left(a+b\right)=1^3\\ & \Rightarrow a^3+b^3+3ab=1\left[\because a+b=1\right]\\ & \Rightarrow a^3+b^3+3ab=k\\ & \text{From above both equations,}\\ & k=1\end{array}$$