(i) When a positively charged rod is brought near A, the free electrons in the sphere A are attracted toward the rod and moved to the leftside of A. This movement leaves unbalanced positive charged on B. If the rod is removed before the spheres are soparated. the excess electrons on spjere A would flow back to B. Both the electrons will becone uncharged.
(ii) Yes, net charge is conserved. Before the rod is brought near A both A and B were neutral. They will remain so even if they have different sizes or materials.
(iii) If the rod is removed after the spheres are separated, then sphere A will have net negative charge and sphere B will have net positive charge of same magnitude as shown in figure.

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