I have a 1*4GB RAM installed in my dell laptop. I am going to purchase 1*8GB RAM. So, my question is if the combination of one 4GB and one 8GB RAM, will both work or not? I am confused as I have never heard about different size combinations. Are there any major issues with such a combination?
There shouldn't be any major issues with such combination given that your device supports that combination. Try to get them from the same brand and you should be fine. In fact, my ASUS N550JV, oddly tho, came with exactly that installation: 4GB + 8GB.
Since your laptop (Dell Inspiron 15) specifications say that
1x4GB + 1x8GB will not be suported. Either get a 2GB or 4GB module for upgrade. In case your manual differs than this general Inspiron 15 one, if you don't see a 12GB there, do not upgrade to 12GB. I believe values between 8GB and 16GB are not intended to be supported given that the manual says the motherboard supports 8GB and 16GB.
It depends on the type of RAM your system uses. Since it's a laptop, I would assume it uses SO-DIMM as opposed to SIMM (which usually had to be installed in matching pairs, or would treat the larger as a pair with the smaller memory). If your system operates with a single memory chip currently, then clearly you do not required paired memory. And yes, 12 GB should work in your laptop. However, if your system is running a 32-bit OS you may only be able to address 3.5 GB (depending on if your OS supports PAE).