To solve this problem, we need to analyze each statement about Phaeophyceae (brown algae) and determine which are correct.$\newline$Let's evaluate each statement:$\newline$A. Asexual reproduction occurs usually by biflagellate zoospores.$\newline$• This statement is correct. In Phaeophyceae, asexual reproduction typically involves biflagellate zoospores.$\newline$B. Sexual reproduction is by oogamous method only.$\newline$• This statement is incorrect. Phaeophyceae can exhibit isogamous, anisogamous, or oogamous sexual reproduction, not just oogamous.$\newline$C. Stored food is in the form of carbohydrates which is either mannitol or laminarin.$\newline$• This statement is correct. Mannitol and laminarin are the primary storage carbohydrates in Phaeophyceae.$\newline$D. The major pigments found are chlorophyll a, c, and carotenoids and xanthophyll.$\newline$• This statement is correct. Phaeophyceae contain chlorophyll a, chlorophyll c, carotenoids, and xanthophylls.$\newline$E. Vegetative cells have a cellulosic wall, usually covered on the outside by gelatinous coating of algin.$\newline$• This statement is correct. The cell wall of Phaeophyceae is cellulosic and often covered with algin, a gelatinous substance.$\newline$Based on the analysis, the correct statements are A, C, D, and E.$\newline$Therefore, the correct option is Option 1: A, C, D, and E only.