1.—He must be busy doing his homework right now.

—I imagine____.

A. that     B. to     C. so     D. it

选C。I imagine so=I think so,

2. Mary had promised to give me a ticket for tomorrow. She failed, ____.

A. either    B. though    C. but    D. too

选B。结合上下文意思我们可以知道本题表示转折关系，先排除A、D；而but为并列连词通常放在句首或句子中间起连接作用。故选B。