I would like to know the basic difference between the Intel family processors I3, I5 and I7 since I am having some assignments to make. I heard that, inside these also, there can be difference in the no. Of cores. So someone please help me with these...

The Intel i3 and i5 series are dual core where the i7 series are quad core. Aside from that there are many different models and variations of each core that offer things like processor speed, turbo boost, and hyper threading. You can do a comparison on the Intel website if you're looking for a specific feature.