1.basket的基本意思是“篮,筐”,指用细枝条、塑料或金属等材料编织成的盛东西的容器,是可数名词,在句中可作主语、宾语等。
2.a basket of可表示一篮〔筐〕的量。

basket case
无法照顾自己的废人 a helpless person who is unable to take care of himself
A student who studies too hard for exams may not eat, sleep or play, for so long that he becomes a basket case and must be sent to the hospital.为了考试而用功过度的学生,也可能不吃、不睡、不玩,时间久了,成了无力自理的人,只好被送进医院。

have all one's eggs in one basket
孤注一掷 place all one's money on the same risk; risk everything on one chance
〔说明〕 have all one's eggs in one basket通常不用于进行体。
To buy stock in a single company is to have all your eggs in one basket.买一家股票是孤注一掷。
With only one good pitcher this season,I'm afraid we have all our eggs in one basket.在这个季节里,我们队里只有一名好投手,胜败如何,全在他一人手里了。
Insurance firms generally spread the risk among several companies so that they don't have all their eggs in one basket.保险公司一般是把保险金额分散在几家公司,这样他们就不会冒孤注一掷的危险了。

My basket is so full that I can't carry it.我的篮子装得太满,我拿不动它。
There are two shopping baskets at home.家中有两个购物篮子。
There are two wastepaper baskets in the room.房间里有两个废纸篓。
She carried a large basket.她拎着一只大篮子。
Please carry the basket to the house.请把这只篮子提到房里去。
We ate a basket of peaches.我们吃掉了一篮桃子。

basket, hamper
basket一般是指没有盖的篮子,而有盖的则称为hamper。