The correct answer is (d) Will the cake have been baked by my mother?
In this sentence, the verb "bake" is in the perfect tense, which is used to describe an action that was completed in the past but has consequences or relevance in the present. The perfect tense is formed using the auxiliary verb "have" plus the past participle of the main verb.
In the sentence "Will the cake have been baked by my mother?", the auxiliary verb "have" is in the present tense, which indicates that the action of baking is still relevant in the present moment. The past participle "been" indicates that the action of baking was completed in the past.
Option (a) "Will the cake have baked by my mother?" is incorrect because it does not use the past participle "been," which is necessary to form the perfect tense.
Option (b) "Will the cake has being baked by my mother?" is incorrect because it uses the incorrect form of the auxiliary verb "have." The correct form is "has," not "has being."
Option (c) "Will the cake be baked by my mother?" is incorrect because it uses the present tense verb "be," which does not indicate that the action of baking was completed in the past. It describes a present or future action.
Therefore, the correct answer is (d) Will the cake have been baked by my mother?