Can this graphic card support multiple 4K monitors simultaneously through its Mini DisplayPort outputs?

Yes, the graphic card has 4 Mini DisplayPort 1.4 outputs, which can support multiple 4K monitors.

Does the NVIDIA T1000 4 GB GDDR6 graphics card require additional power connectors, or is it powered solely through the PCIe slot?

The NVIDIA T1000 4 GB GDDR6 graphics card has a max power consumption of 50W, which suggests it is likely powered solely through the PCIe slot.

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NVIDIA T1000 4 GB GDDR6 - PCIe 3.0 x16 low profile - 4 x Mini DisplayPort Graphic Card