As current grows and decays in coil B, what is the direction of induced current in coil A? Explain using lenz's law. image link : http://imgur.com/bvbra

In coil B , the nearer end of A will behave like:North pole(as current direction anti clockwise ) and at the farthest end will be like: south pole (as current direction  clockwise there ).

As current grows in coil B ,the strength of North and south poles will increase ie, the number of lines of forces per unit area will incrase with the current and that will try to induce south pole at the end of coil A which is near coil B.

But according to Lenz's law it (the effect)will be opposed by producing North pole at the near end of A. so for coil Adirection of induced current when the current grows in coil B will be:

and in the opposite direction when current starts decreasing.