In a game playing search tree, upto which depth 𝛼−𝛽 pruning can be applied?…

Short answer: Alpha–beta pruning can be applied at any internal node during a minimax search; it is not limited to fixed depths such as level 6 or level 8.

• What alpha–beta does: It keeps track of two bounds (alpha and beta) and prunes branches that cannot affect the final minimax value.

• Where it applies: Pruning can occur at any depth while performing the minimax calculations (typically during depth‑first exploration). There is no intrinsic restriction to the root or to specific numbered levels.

• What affects pruning effectiveness: Good move ordering (examining strong moves first) increases pruning; alpha–beta is most effective with depth‑first search and iterative deepening. It does not depend on evaluating utility values in a breadth‑first order.

Implication for the provided choices: Any answer that restricts alpha–beta pruning to particular fixed depths (for example, only level 6 or only level 8) is incorrect. The statement that pruning depends on utility values in a breadth‑first order is misleading; pruning effectiveness depends on move ordering and search strategy (depth‑first), not on breadth‑first utility evaluation. Therefore the question's provided combined choices do not accurately capture the correct conceptual answer.