Explanation:
Statement 1 :
Current is the total amount of charge that passes through a conductor's full cross section at any point per unit of time. Current flowing is given by :
[tex]I=\dfrac{q}{t}[/tex]
This statement is true.
Statement 2 :
When an electric field is applied to a conductor, the free electrons move only in the direction opposite the applied electric field. It is false because due to electric field the force is applied in the direction of electric field.
Statement 3 :
By convention, the direction of a current is taken to be the direction of flow for negative charges. It is false because the direction of electric current is opposite direction to the flow of negative charges.
Statement 4 :
In a circuit, current is delivered by the positive terminal of a battery, and it is used up by the time it returns to the negative terminal of the battery. It is false because current is delivered by the positive terminal of a battery, and it is used up by the time it returns to the positive terminal of the battery itself.
Statement 5 :
In order to maintain a steady flow of current in a conductor, a steady force must be maintained on the mobile charges. It is true.
Hence, statements 1 and 5 are correct.