If by Product-based companies you mean core companies that deal directly with the manufacturing of computer based products then you will have to look for the best engineering colleges in India.
IITs, NITs, IIITs and BITS are some of the colleges that provide you with the opportunities to work with the best core companies including, HP, Microsoft, Oracle, Google, etc. However, it is not easy to get into these institutes as admissions are done strictly on the basis of merit and entrance exams like JEE Mains and JEE Advance.
Following are some Placement Records that willl give you the idea of placements:
Following are some other colleges that offer good placements:
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