Can I buy an Option after the strike price has crossed?

For eg. Nifty index is at 11800 pts., So can i buy a call option of Nifty 11750 strike price? Would there be any charges other than the normal brokerage, normal STT etc.?

why not , you can buy any strike price option :slight_smile:
check span page for today allowed range

You can buy or sell options of all strike prices available(both in the money and out of the money).
You can start with reading about options on Varsity.