State whether the following statements are true or false.
$(a)$. An electric motor converts mechanical energy into electrical energy.
$(b)$. An electric generator works on the principle of electromagnetic induction.
$(c)$. The field at the centre of a long circular coil carrying current will be parallel straight lines.
$(d)$. A wire with a green insulation is usually the live wire of an electric supply.

$(a)$. "An electric motor converts mechanical energy into electrical energy."

This statement is false.

Reason:

An electric motor does not convert mechanical energy into electrical energy. An electric motor converts electrical energy into mechanical energy. When an electric current is passed into a coil placed in a magnetic field, it starts rotating. 

$(b)$. "An electric generator works on the principle of electromagnetic induction."

This statement is true.

Reason:

When a coil is rotated by some external mechanical energy in a magnetic field magnetic flux is changed, then an induced emf in the coil is produced by changing the flux. Thus induced current starts to flow.

$(c)$. "The field at the center of a long circular coil carrying current will be parallel straight lines."

This statement is true.

Reason:

By the right-hand thumb rule, it can be proved that the field at the center of a long circular coil carrying current will be parallel straight lines.

$(d)$. "A wire with green insulation is usually the live wire of an electric supply."

This statement is false.

Reason:

In domestic wiring, the earth wire has a green insulation cover,  while live wire has a red insulation cover.