In given attachment, a decreasing magnetic field acts perpendicularly into the plane of paper. . Please explain why no induced current flows into the connector AB.....

Dear student,

A couple of things here are unclear.
Is the circular loop shown also a conductor?
Is the magnetic field present inside the coil also?

If it is a circular coil too with another straight conductor passing through AB and magnetic field is passing through the coil, clockwise current would flow through the upper half, due to which the current in AB would be from B to A. But in the lower coil also it would be clockwise, due to which same amount of current will from from A to B.