I want to know 'do the e-grocery company like Bigbasket has its own courier service or it takes the service from 3PL provider'

Aren't they in India? I don't know how they deliver. I'm in the US. There are occasionally people on here from India, but even so, bigbasket is just in 4 cities. I think if you study their web page and shipping methods, or use the contact link, you can find out easily. The site says to look for their signature vans, and there's a picture of one, so isn't that self explanatory?

Probably a mixture of both, dependant on location.