The correct answer is option 1 - "1 only".

Statement 1 is correct, which states that if the net external torque acting on an object is switched off, then the linear momentum will remain unchanged. This is based on the concept of the conservation of linear momentum, which states that the total momentum of an isolated system remains constant if no external forces act upon it. Since torque is the rotational counterpart of force, when the net external torque is switched off, there are no external forces acting on the object, and hence the linear momentum remains unchanged.

Statement 2 is incorrect, as it states that the angular momentum will remain unchanged. This is not necessarily true. When the net external torque is switched off, the angular momentum will only remain unchanged if the object is in a state of purely rotational motion with no angular acceleration. If there is any angular acceleration present, the angular momentum can change even if the torque is switched off.

Therefore, the correct answer is option 1 - "1 only".