Is it permissible to listen to beneficial television or radio programs accompanied by light music, without intending to listen to the music, and is there a difference between samāʿ (hearing) and istimāʿ (listening)?

It is permissible to listen to beneficial programs accompanied by musical instruments if the volume of the music can be lowered. Otherwise, it is not permissible to listen to them, as this falls under the general prohibition of listening to musical instruments, and the benefit of preserving the religion takes precedence over every other benefit.