Operational amplifier when the non-inverting terminal is open
The opamp will not work because the transistors will not be able to draw their input bias current.
The first stage of an opamp is a differential pair.

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The inputs of the opamp are connected to the gates of Q1 and Q2. The transistors need to be able to draw current through the gate to work. If one of the inputs is open, one of the two transistors will not function properly. Thus you need to ensure that their is a DC path for both opamp inputs.