The question involves filling in the blanks with the correct form of the verbs in parentheses. Here's how you can complete it:
The sentence "A new medicine __________ by the doctors to cure it since last month. (discover)" requires the use of the present perfect passive tense.
**Present Perfect Passive Structure**: has/have + been + past participle
- The correct sentence is: "A new medicine **has been discovered** by the doctors to cure it since last month."
For the second part, "Your sister's __________ very hard to be accepted to the university, isn't she? (work)":
This requires the present continuous tense with a question tag.
**Present Continuous Structure**: am/is/are + verb+ing
- The correct sentence is: "Your sister's **working** very hard to be accepted to the university, isn't she?"
This explanation should help you understand the usage of verb tenses in these contexts.