Let the harmonic mean of two positive real numbers $a$ and $b$ be 4. If $q$ is a positive real number such that $a, \ 5, \ q, \ b$ is an arithmetic progression, then find the value(s) of $|q-a|$ . \[\begin{array}{} (1) \, 1 \quad \quad \quad \quad \quad \quad \quad \quad & (2) \, 2 \\ (3) \, 3 & (4) \, 5 \end{array}\] Note:

• Submit your answer as the increasing order of the serial numbers of all the correct options.

• For eg, if your answer is $(1),(2)$ , then submit 12 as the correct answer, if your answer is $(2),(3),(4)$ , then submit 234 as the correct answer.