Explanation:
When a conducting rod is moved with a constant velocity in a magnetic field, a potential difference appears across the two ends of the rod. This phenomenon is known as electromagnetic induction and is governed by Faraday's law of electromagnetic induction.

a) If V||I:
If the potential difference (V) is parallel to the current (I), then it means that the conducting rod is moving in a direction perpendicular to both the magnetic field (B) and the current (I). In this case, according to the right-hand rule, the force experienced by the charges in the rod will be perpendicular to both the magnetic field and the direction of motion. Therefore, no potential difference will be induced across the ends of the rod. Hence, option 'a' is incorrect.

b) If V||B:
If the potential difference (V) is parallel to the magnetic field (B), then it means that the conducting rod is moving in a direction perpendicular to both the current (I) and the magnetic field (B). In this case, according to the right-hand rule, the force experienced by the charges in the rod will be perpendicular to both the magnetic field and the direction of motion. Therefore, a potential difference will be induced across the ends of the rod. Hence, option 'b' is incorrect.

c) If I||B:
If the current (I) is parallel to the magnetic field (B), then it means that the conducting rod is moving in a direction perpendicular to both the current (I) and the magnetic field (B). In this case, according to the right-hand rule, the force experienced by the charges in the rod will be perpendicular to both the magnetic field and the direction of motion. Therefore, a potential difference will be induced across the ends of the rod. Hence, option 'c' is incorrect.

d) None of these:
The correct answer is option 'd' because none of the given options correctly describes the relationship between the direction of the potential difference (V), current (I), and magnetic field (B) in the given scenario. The potential difference is induced across the ends of the conducting rod only when it moves in a direction perpendicular to both the current and the magnetic field.