what is the definition for alacrity, condescend, and diligent?

The choices are: to talk down to, enthusiasm/speed, and thorough/meticulous.

Check the definitions at Dictionary.com

http://dictionary.reference.com/

I searched there but some of them are not related to either difinition to me...

Those words' meanings should be obvious in any dictionary.

http://dictionary.reference.com

http://www.answers.com

http://www.onelook.com

http://www.yourdictionary.com

Specifically:
http://www.answers.com/alacrity
http://www.answers.com/condescend
http://www.answers.com/diligent

the got the answer however what does "to tlk down to" means?

To talk down to means to talk to someone as though he was an idiot or a young child.

To find the definitions of words, you can refer to a dictionary. There are various online dictionaries available, such as Merriam-Webster or Oxford English Dictionary, where you can search for words and get their meanings.

Let me explain the meanings of the words you mentioned:

1. Alacrity: Alacrity means enthusiasm or speed in doing something. It refers to doing something with a cheerful readiness or promptness. For example, "She accepted the challenge with alacrity," means that she eagerly and quickly embraced the challenge.

2. Condescend: Condescend means to talk down to someone or exhibit an attitude of superiority. It implies behaving in a way that suggests you are lowering yourself to interact with someone you consider inferior. For example, "He condescended to answer my questions" means that he responded with a patronizing or superior attitude.

3. Diligent: Diligent means being thorough and meticulous in one's work or effort. It describes someone who is dedicated, hardworking, and committed to achieving a high standard of performance. For example, "She was a diligent student, always submitting well-researched and detailed assignments."

Remember, if you require further clarity or detailed explanations, consulting a dictionary or referencing reputable online resources can provide additional context and usage examples.