Question

the kinetic energy of a freely falling object. increase yet it holds law of conservation of energy

Answer 1

when an object is placed at some height.
this means that it have potential energy.and zero kinetic energy.
when the object is dropped from that height,the potential energy decreases and kinetic energy increases.But the sum of both is equal to the potential energy at the initial height.so,whenever an object is dropped the law of conservation is maintained and is true.

Answer 2

when a body falls freely under the force of gravity, the kinetic energy increase because of the increase in its velocity however the potential energy decreases as the height of the body from the earth surface decreases.
here at the potential energy stored in the body get converted to kinetic energy.
when the body reaches the earth's surface whole of the stored potential energy changes to kinetic energy.
hence at every instance of the motion of the body the total mechanical energy remains constant.
therefore it holds law of conservation of energy.