at the end of inception,did cobb die?

did he die? no
is he still in a dream? well i guess we'll never really know, but here is some evidence that the tuktok wouldve stopped spinning had the camera not cut off:

- Cobb has no wedding ring on in the "reality" scenes and he does iin the dreams. When he wakes up on the plane and the whole way through immigration he doesnt have a ring on, suggesting he is in reality.

- was the immigration man staring because he was a projection? No, after seeing it twice, it appears to just be the normal scrutiny that officers do at airports

- The totem began to wobble ever so slightly before it cut to black- in a dream it never wobbled, even slightly.

Throughout the film, Cobb continues to obsess about spinning the tuktok and verifying reality – however, at the end of movie, he spins the tuktok and walks away from it before he can verify if it stops spinning or not. His kids come running in and Cobb could care less about about the tuktok or “true reality” or extraction/inception anymore. He just wants to be with his children, in whatever place he can be with them. That emotional connection and desire is “reality” enough for him.

In the end, Cobb walking away from the tuktok is a statement in itself that also completes the arc of his character.
So whether or not its reality, Cobb doesnt care anymore, as long as he is with his children.

Short answer? No. Cobb did not die at the end of the movie.

We do not know If the tuktok keeps spinning or if it falls, it cuts out at that point. So we don't know If he's dreaming or in reality

No Cobb did not die, but I believe he remained in limbo.