Let $z_1$ and $z_2$ be any two non-zero complex numbers such that $3|z_1| = 4|z_2|$. If $z = \frac{3z_1}{2z_2} + \frac{2z_2}{3z_1}$ then maximum value of $|z|$ is

Note: In actual paper value of $|z|$ was asked. Hence, none of the options given were correct. So we have modified the question as well as options.