"Jakie są opcje?"

Translation: What are the options?

[va-diim]

Why isn't the word opcje in instrumental case after być in this exercise?

[CelioFM]

va-diim: Because "być" is not predicative, as "Jakie" is not subject of the sentence. Not everything that comes after "być" goes to instrumental; only predicatives do. E.g.: Jestem tutaj (I am here). Być tutaj. Być wesoły = to be happy, Być w domu = to be at home, etc.

[Volizione]

Can "możność" be used as a synonym for "opcja?"

[immery]

maybe "możliwość" ,

opcja http://sjp.pwn.pl/szukaj/opcja.html
możliwość http://sjp.pwn.pl/szukaj/możliwość.html

Możność is rarely used word, meaning circumstances allowing something to happen/ be acomplished

[Volizione]

thank you

[br0d4]

A small addendum: możność , możliwość i możność

P.S. you use some interesting words :)

[Volizione]

haha, thank you.

[va-diim]

Or would jakie need to be jakimi?

[br0d4]

Jakimi is a totally different thing. It would be clearly question about the properties of something, but posing such a question correctly is not evident, often unnatural and sometimes is quite difficult. It is not a typical question, it may be posed while asking about someone's preferences. eg.

• Jakimi dziewczętami się interesujesz? [What (sort of) girls are you interested in?]
• Jakimi samochodami lubisz jeździć? [What (type of) cars do you like to drive?]

or in singular:

• Jakim on jest mężem? - [What (kind of) husband is he?]
• Jaką mnie wolisz? [What do you prefer me like?] - (clearly a woman asking her closely related man, and it may concern eg. the colour of hair dye, dress, attitude and a whole range of other things including intime behaviour) - therefore it is often necessary to narrow the question down, eg. Jaką mnie wolisz, w rudym czy blond? [What do you prefer me like, in red or in blonde? (showing off with her hair dyed)]

[Lanosh_Meriem]

can be "variants"?

[br0d4]

No. It is something different.