Identify Wrong statement

Dear student,
In the elastic collision, both the kinetic energy and momentum remain conserved. And in an inelastic collision, only momentum remains conserved. so statement 3 and 4 are correct.
If a body of mass m is moving is placed at a height h, then potential energy stored in it =$mgh$
and if it is in rest, then velocity =0 and thus kinetic energy =0
so total energy ==$mgh$
but its momentum =0
so a body can have finite energy with zero momentum.
statement 2 is correct.

Now, if a body has a finite momentum value, that means both its mass and velocity is non-zero, so the kinetic energy is also non-zero.
thus a body having momentum must have kinetic energy.
statement 1 is wrong.
Regards