As new comer in NodeJS & Mongo DB, I don't know much about its hosting and pricing. Can I host website by self on own physical server/machine. Also is there any hosting website that provide facility to have both Node JS and MongoDb configured.
Yes, yes and yes.
You can host it yourself on your own machine but it will not be as easy and efficient as using a service for hosting, unless you have a high quality symmetric internet connection with low latency and high bandwidth.
You can host it cheaply on a VPS using Digital Ocean, Vultr or AWS in which case you will have to configure Node and Mongo yourself.
Or you can use managed platforms like Heroku for Node and Compose for Mongo in which case the price will be higher but everything will be taken care of for you.
It depends on what costs are you willing to take, both in terms of service fees and your time and expertise needed to configure and maintain different layers of the system.
As for "And what will be the cost?" - for number 1 it will be whatever your ISP is charging you. For number 2 it will be around $5 for Digital Ocean or Vultr per month with few months for free with promo links (Digital Ocean, Vultr) and with number 3 it's something like $25 for Heroku and about $30 for Compose per month. Of course there are other services available, those are just examples of the most popular ones.
See these answers for more info:
来源：https://stackoverflow.com/questions/43005225/how-to-host-website-in-nodejs-and-mongodb-and-what-will-be-the-cost