Q: Macbook shutdown on unplugging the cord

Well, the battery has to be replaced anyway. So start with that, and ask the repair shop or whoever does the replacement to check the adaptor too.

Have you tried a SMC reset?

https://support.apple.com/en-us/HT201295

Ciao.

https://support.apple.com/mac-notebooks/repair/service/pricing

Those are US prices, don't know the costs elsewhere.

ankuagarwal wrote:

I try to move my mac then it shut down.

That indicates that there is a loose or intermittent connection inside the MBP.  It is possible that an Apple Hardware Test might provide a clue:

https://support.apple.com/en-us/HT201257

Note that an error free AHT is not conclusive.

Ciao.

That is unfortunate, but also an indicator of possibly different problems in the MBP.  It looks like the best option is an appointment at an Apple store genius bar for a FREE evaluation.

Ciao.