Mass and free fall speed under gravity

[Orrin]

If mass increases with speed then what is the mass and speed of a particle falling from a large distance into a black hole or onto a neutron star?

 

[weirdoguy]

mass increases with speed

It does not. Read this please:
https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

 

[PeroK]

If mass increases with speed then what is the mass and speed of a particle falling from a large distance into a black hole or onto a neutron star?

You're probably thinking of "relativistic mass", which is now a largely obsolete concept. See:

https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/