Angular momentum is the measure of the amount of rotational motion an object possesses. It is defined as the product of the moment of inertia and the angular velocity of an object. The moment of inertia depends on the distribution of mass of the object about the axis of rotation, while the angular velocity represents the rate at which the object is rotating.

When the gymnast is sitting on a rotating stool with his arms outstretched, he has a certain amount of angular momentum. The moment of inertia of the system is determined by the distribution of mass of the gymnast and the stool. The angular velocity is determined by the rate at which the system is rotating.

When the gymnast suddenly lowers his hands, the distribution of mass of the system changes. The moment of inertia decreases because the mass that was previously distributed in the outstretched arms is now closer to the axis of rotation. However, the angular velocity remains constant because there is no external torque acting on the system.

Now, let's analyze the options given:

a) Angular momentum increases: This option is incorrect because when the moment of inertia decreases and the angular velocity remains constant, the angular momentum of the system decreases. Therefore, this option is not correct.

b) Angular momentum decreases: This option is correct. As explained above, when the moment of inertia decreases and the angular velocity remains constant, the angular momentum of the system decreases. This is consistent with the conservation of angular momentum, which states that the total angular momentum of a system remains constant if no external torques are acting on it.

c) Angular momentum remains constant: This option is incorrect. The moment of inertia of the system decreases, and thus the angular momentum of the system decreases as well. Therefore, this option is not correct.

d) None of the above: This option is incorrect. As explained above, the angular momentum of the system decreases when the gymnast lowers his hands. Therefore, this option is not correct.

In conclusion, the correct answer is option 'b' - angular momentum decreases.

Since he's sitting in a Rotating stool, his Angular Velocity will increase if suddenly lowers his hands from outstretched position. Angular momentum is derived using Angular Velocity and so it's directly proportional. Thus, his Angular Momentum also increases!!! Hope, I helped you something!