A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?

In free space, there is no external torque acting on the sphere. According to the principle of conservation of angular momentum:
$${\vec{\tau }}_{ext}=\frac{d\vec{L}}{dt}=0⟹\vec{L}=\text{constant}$$
As the radius increases, the moment of inertia ($I=\frac{2}{5}M{R}^2$) increases. Since $L=I\omega$ is constant, the angular velocity $\omega$ must decrease, and the kinetic energy ($K=\frac{L^2}{2I}$) will also change. However, angular momentum remains constant.