Ans 2) 37 ???
[n + p sinx] is not diff at those pts where n + p sinx is an integer.
i.e is sinx = 1, -1, r/p where 0 ≤ r ≤ p-1
or x = pie/2 , - pie/2 , sin -1 (r/p) , pie - sin -1 (r/p)
But x ≠- pie/2 , 0
Therefore, the function is not diff at x = pie/2 , sin -1 (r/p) , pie - sin -1 (r/p)
So, the reqd no. of points are 1 +2 (p-1) = 2p-1
So, if p = 19, then ans is 37
Anyways, this ques can also be solved with the help of grpah.