The heating of a metal plate can be attributed to different factors related to electric currents and magnetic fields. Let's analyze each statement:

A. A direct current is passing through the plate.

• When a direct current (DC) passes through a metal plate, it can cause heating due to the resistance of the metal, which generates heat as electrical energy is converted to thermal energy. So, this statement is correct.

B. It is placed in a time-varying magnetic field.

• A time-varying magnetic field induces eddy currents in a metal plate, leading to resistive heating. So, this statement is correct.

C. It is placed in a space-varying magnetic field but doesn't vary with time.

• A space-varying magnetic field (non-time-varying) does not induce eddy currents, and the plate would not heat up in this scenario. So, this statement is not correct.

D. An alternating current passing through the plate.

• When an alternating current (AC) passes through a metal plate, it can cause heating due to the resistance of the metal, similar to the effect of a direct current. So, this statement is correct.

E. It is placed between the pole pieces of a magnet.

• Being placed between the pole pieces of a magnet doesn't necessarily mean the plate will heat up. It depends on whether there is a changing magnetic field or motion that could induce currents in the plate. This statement is not necessarily correct by itself.

So, the correct answer is:

A, B, and D Only