will a basic dell 275W power supply that comes with a pre built dell OptiPlex 7010 mini tower handle the zotac gtx 750ti? it fits the chase and it doesn't require a power supply to GPU connector. other components being i5 3470 and 4GB ram
If it doesn't need a 6 pin, it probably can handle it... but to be honest, I wouldn't trust it. PSUs that come installed in pre-built home computers tend to fail after a while, posing a threat to any components inside, and they often can't actually provide the amount of wattage they claim to. If I were you, I'd get a 300W from a reliable brand.
The card doesn't need a 6 pin power connector, because it draws only 60W max,so it takes all of its power from the PCIe slot.
Your power supply should work fine, though it is not a great quality unit from them(like some Delta units they provide with some prebuilt PCs).
For now you can run the card on your PSU, but I'd advise upgrading to something better in the future... everything should work since your current PSU is in the ATX form factor.