TheDellGamer :
clutchc :
PCI Express is a backward-compatible interface. So that is of no concern. Very few (if any) gfx cards today can saturate the PCIe version 2.0 interface at 16 lanes. The GTX 750 Ti won't even come close to that. You are good.
There is one caveat, however. The GTX 750 Ti uses a UEFI BIOS. The Dell server probably still uses a legacy BIOS. Nvidia cards are pretty good about interfacing with older legacy BIOSs, but it is something you won't know until you try it. I suspect all will be fine, but no guarantees. You may want to hop over to the Dell forum and post that question. I'm sure other T3400 owners (and possibly a rep) will have the definitive answer.
What about a AMD's Radeon HD7750 or R7 360?Also im pllaning to upgrade my PSU ,will any standard ATX PSU fit in Precision's T3400 case ?
If this is the nameplate on your PSU:
http://g02.a.alicdn.com/kf/HTB1MZTdIVXXXXa5XVXXq6xXFXXXs/Original-YY922-525W-Power-Supply-N525E-00-for-Dell-Precision-390-T3400-T5400.jpg
It has enough power for the GTX 750 Ti, HD-7750, and the R7-360 as it is. You would have to use a 6-pin adapter for the R7-360, but with a +12v rail rated for 500W, you are fine.
But to answer your question, yes the PSU is a std. ATX.
The HD-7750 uses a conventional legacy BIOS, so it should work for sure. The R7-360 may use a UEFI BIOS, not sure. I know the R7-370 I used to have does. But of course, the GTX 750 Ti is the fastest of all three.