On which two factors does the escape velocity of an object projected from the Earth $NOT$ depend?

$A$ particle falls towards the Earth from infinity. Its velocity on reaching the Earth would be:

The angular velocity of rotation of a star (of mass $M$ and radius $R$) at which the matter starts to escape from its equator will be:

The escape speed of a projectile on the earth's surface is $11.2 \; km/s$. $A$ body is projected out with thrice this speed. What is the speed (in $km/s$) of the body far away from the earth? Ignore the presence of the sun and other planets.

$A$ satellite is moving with a constant speed '$V$' in a circular orbit about the Earth. An object of mass '$m$' is ejected from the satellite such that it just escapes from the gravitational pull of the Earth. At the time of its ejection,the kinetic energy of the object is

The magnitude of potential energy per unit mass of an object at the surface of the Earth is $E$. Then,the escape velocity of the object is ..........