What is the minimum rank for participating in Grand slams and Masters without qualifying rounds?

What you are asking about is what they call the cutoff for direct entry into the draw. For Grand Slams, it is about 104. For Masters events, it varies. For the events with larger draws of 128 players (like Indian Wells and Miami), the cutoff is in the 80s. For all other events with draws of 64 players, the cutoff is in the 40s or 50s.

There is no blanket answer to your question, because tournaments can make their own rules about how many of the available slots (which depends on the size of the draws) will be "direct entry" (vs. qualifiers and/or wildcards). In some cases, up to 20% of the draw slots can be reserved for qualifiers and wildcards, bypassing a strict rankings-based ("direct entry") selection process.