a-p,r
This was a technical one. In the definition of local maxima/minima there is equal to sign also which makes several points of maxima and minima throughout the constant function. A constant function is a differentiable function with derivative as zero. Hence (p). While there are several values of x for which there is maxima/minima, the value of the function is only one. Hence, (r) also.
b-p
c-p,r,s
d-r (most got it right)
eBooklet on Applications of Derivatives containing definitions and more detailed explanation of this question is scheduled for .pdf publication in a few days. However, one can also refer to NCERT eBooklet of class 12th on Application of Derivatives page 27, Definition 4 (direct link at the moment is
this).