1)Two coils of self inductance 4 Henry and 16 Henry are wound on the same iron core. What is the coefficient of mutual inductance for them?
Can anyone give an idea on how to go about this problem?

http://farside.ph.utexas.edu/teaching/em/lectures/node83.html

Mutual inductance is the magnetic flux phi through coil 2, due to current i in coil 1. The mutual inductance is then M = phi/i.

Assume a current of i amps in the first coil.

What is the flux through it, given its self-inductance?
Therefore, what is the flux through the second coil?
Divide by i, and you've got M.

Thanks for the guidance.