True$/$False

A$).$ Breadth$-$first search is complete if the state space has infinite depth but finite branching factor.

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B$).$ Assume that a king can move one square in any of the $8$ directions in a chess board.$$ Manhattan distance is then an admissible heuristic for the problem of moving the king from square A to Square B$.$

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C$)$ A$*$ search with heuristic h $=0$ will always have to search the entire tree before finding the optimal solution.

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D$)$ Suppose A$*$ search uses an evaluation function f$($n$)=(1-$w$)$ g$($n$)+$ w h$($n$).$ For any value of w between $0$ and $1($inclusive$),$ A$*$ will terminate and return optimal solution.