$($Maximum $20$ points$)$ Consider the beam shown in figure $1.$ The end $A$ is fixed, while there are rollers at $B$ and $C.$ The beam is subjected to a uniformly distributed load of magnitude $w.$ Answer the following:

$($a$)(4$ points$)$ Neglecting the axial components, identify the degree of static and kinematic indeterminacy.

$($b$)(10$ points$)$ Calculate the support reactions at $A,B$ and $C$ using slope deflection method.

$($c$)(6$ points$)$ Draw the bending moment and shear force diagram for the beam.

Figure $1$: Structure for Question $2.$