When a positively charged rod is placed near the sphere A then due to the attraction force of rod all the electrons will come to the nearest surface of sphere A and due to deficiency of electrons on the far side of sphere B it will get positive charge
This phenomenon of charge separation is know as induction of charge
So sphere A will get negative charge and sphere B will get positive charge on its surface after they got separated
So here correct answer would be
Sphere A is negative and sphere B is positive because electrons from sphere B are attracted to the rod and move to sphere A.