Will a gtx 770m work with a 201.5 2011 iMac?

Sorry it’s not that simple! The boards firmware would need to be re-flashed with the custom Apple firmware and Apple no longer offers NVIDEA drivers in the OS so you’ll need to also need to consider what macOS version you are planning on running. Your system originally came with either AMD Radeon HD 6750M or Radeon HD 6770M GPU.

While you could install it physically without addressing the firmware and OS it won’t help you.

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