I have a Nikon d7100. I was shooting random shots in my room yesterday evening with my 35mm lens. I notices that if I use ISO 1000 for properly expose the image, due to grains, details of the object I was shooting was lost. Then I tried with ISO 400 and shifted my EV compensation to +3. Then the details were outstanding. My query is if EV shifting is giving me good results over ISO, then when should I increase ISO and when EV compensation? Because if I shift EV, then camera doesn't show the difference in meter. Please guide.
Not a completely technical answer, but if shooting at 1000 iso gives you too much noise in a low light situation, and using an exposure compensation of +3 with iso 400 works better, who can argue with that? It may be camera specific, but if your camera responds better with that combination, then I say use it! There's nothing right or wrong here; your results are what counts. Using exposure compensation on my camera does indeed change the exposure on the meter; either the aperture or shutter speed or iso (based on the mode) changes in order to achieve the desired exposure compensation. It is likely that yours does, too.
D7100, I presume, doesn't have a spectacular high-ISO performance compared to commercial grade ones which I have heard to produce reasonably grain-free images even at ISO 2500. As long as you can fiddle with either shutter speed or aperture to get correct exposure, it's the best bet to keep ISO as low as possible.
Aperture priority mode: If you have a fast lens, meaning that one having large maximum aperture (low f-number) allowing you to shoot at high shutter speed, leverage that to shoot wide open. However, there is one concern. Almost never you get sharpest image at maximum aperture, but one or two stops down. Increasing EV in aperture in this mode decreases the shutter speed, keeping aperture and ISO intact.
Shutter priority mode: If you are shooting hand-held, probably you can't shoot at a shutter speed slower than 1/60 unless you have VR lens. Mounting on a tripod will let you shoot at a lower speed with the chance of having motion blur for non-static objects. Increasing EV in aperture in this mode increases the aperture, keeping shutter speed and ISO intact.
Manual mode: If setting large enough aperture and slow enough shutter speed do not correctly expose the image, then you need to keep on increasing ISO which will inevitably introduce noticeable noise in the image.