Maximum value of (2sinθ + 3cosθ) is?

Answer: Option B

$$\begin{array}{rl}& \left(2\sin \theta +3\cos \theta \right)\\ & \text{Maximum value of}\\ & a\sin \theta +b\cos \theta \\ & =\sqrt{a^2+b^2}\\ & =\sqrt{2^2+3^2}\\ & =\sqrt{4+9}\\ & =\sqrt{13}\end{array}$$