Q: Mac graphic card? Mid 2012

Just hoping that it is a laptop that you have dropped a few times and not a Mac Pro.

This is the Mac Pro desktop forum. Do you have a MacBook Pro laptop?

If a laptop the problem, if this

http://www.apple.com/support/macbookpro-videoissues/

is with the solder connections between the GPU chip and the logic board.

Se if this helps:

http://apple.stackexchange.com/questions/128180/how-to-disable-discrete-graphics -card-and-use-only-integrated-graphics-m…

From you description, if a laptop, it appears you have a hardware problem. Make an appointment at the Genius Bar of an Apple store.

  Apple Retail Store - Genius Bar

https://www.apple.com/retail/geniusbar/ 

You can also try:

- Try resetting the SMC and NVRAM/PRAM

Intel-based Macs: Resetting the System Management Controller (SMC)

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

About NVRAM and PRAM 

https://support.apple.com/en-us/HT204063

- Try starting in Safe Mode

OS X: What is Safe Boot, Safe Mode?

https://support.apple.com/en-us/HT201262

It likely will work in Safe Mode since the GPU integral with the CPU chip is used instead of discrete Nvidia GPU

- Boot to Recovery and repair the startup disk

OS X: About OS X Recovery - Apple Support

https://support.apple.com/en-us/HT201314

- If it is repairable reinstall the OSX

How to reinstall OS X on your Mac - Apple Support

https://support.apple.com/en-us/HT204904

- If you do not have a backup use disk utility to restore the internal disk to an external disk so you can try to recover data.

Then format the startup disk and do a fresh install of OSX

What specific MacBook Pro?

What do yo mean by "It was not working well even to let me select that option"?

This is the Mac Pro desktop forum. I requested your post be moved to the MacBook Pro laptop forum.