Can the 2011 27' iMAC be used as external monitor?
Can I use my 2011 27 inch iMAC as an external monitor with my 2019 13 inch Macbook Pro?
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Yes.
https://support.apple.com/en-us/HT204592
"Use your iMac as a display with target display mode
With target display mode, you can use your iMac as an external display for another Mac.
You can connect any of these older iMac models to another Mac from 2019 or earlier for use as an external display. Learn how to identify your iMac model.
All iMac models introduced in 2011, 2012, 2013, and mid 2014: Use a Thunderbolt cable to connect your iMac to a Thunderbolt or Thunderbolt 2 port on the other Mac. If the other Mac uses Thunderbolt 3, you can use the Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter with your cable."