Consider a system a system having 31 resourses of same type. There are 5 processes P₀, P₁, P₂, P₃, P₄. All resourses are shared by these process as following P₁ – 7, P₂ – 5, P, P₄ – 4, P₀ – X and P₃ – Y. What is the maximum value of X and Y to ensure that the system will be deadlock free?
(A) 100
(B) 99
(C) 72
(D) 64


Answer: (B)

Explanation: The number of resources required for the system to be deadlock-free:
(X – 1)_P0 + (7 – 1)_P11 + (5 – 1)_P2 + (Y – 1)_P3 + (4 – 1)_P4 + 1 = Total available resources.
(X – 1)_P0 + (7 – 1)_P11 + (5 – 1)_P2 + (Y – 1)_P3 + (4 – 1)_P4 + 1 = 31
X + Y = 19.
There are two possibilities for resources allowed for P₀ and P₃ is either (X – 10, Y – 9) or (X – 9, Y -10)
The maximum value of X*Y = 99
So, option (B) is correct.

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