选A,
allow doing sth.允许做某事
例：The hospital does not allow smoking.医院里不允许吸烟.
例句中No photos is allowed taking here.和这里的语法是一样的,photos和take构成被动,所以用allowed.
allow sb to do sth .允许某人做某事
例：Teacher allow students to have a short break after long trainning.
老师允许学生在长时间的训练以后稍作休息.
be allowed sb to do sth 被允许做某事
例：He is allowed to go to university for his good performance.
他因为表现好而被允许进入大学.
I didn't notice 表示我过去没注意到,当说话人告诉我的时候我已经注意到了,所以不能用B中的完成时,也不能用过去进行时.