How to find the maximum and minimum value of an array without using any For Loop or any inbuild function in C#

If you can't use loops or inbuilt functions, then you can't do anything: because you have a set of data of unknown size where you need to examine each element in order to find the largest or smallest.

If it's just a for loop your homework disallows, then try a foreach loop instead.

Otherwise, you have to use some inbuilt functions: Max, Min, Linq based iterative functions, or a Sorting function - you can't just "look" at a whole array and "see" the largest, any more that you physically could with a pack of cards in front of you.