are you seeing this voltage at opamp out pin with a meter ?Testing with 200mV injected into pin 10 (non-inv input of Opamp1, Gain of 10) should
: see 2V at pin 8 output. When set as buffer should see 200mV. Both tests show 0V.
your description is not clear whether the opamp is not working or the adc measurement .
working with opamps with inputs near rail potentials is never easy unless chip is designed to have rail to rail capability
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