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Consider a system with five processes $P_0$ through $P_4$ and three resource types $A, B$ and $C$. Resource type $A$ has seven instances, resource type $B$ has two instances and resource type $C$ has six instances suppose at time $T_0$ we have the following allocation.

If we implement Deadlock detection algorithm we claim that system is ________

1. Semaphore
3. Circular wait

The deadlock detection algo investigates every possible allocation sequences for the processes that remain to be completed.

The total allocated resources to all processes of resource type B doesn't match with that mentioned in the question. If we ignore the statement and take the tables as the right one then the solution is as follows:

Process P0 and P2 have been allocated all its resources and hence will run till completion. They will give up the resources they were allocated. This is the state:

Available:  A = 3    B = 1    C = 3

Processes left: P1   P3   P4

Process P1 requires: A = 2   B = 0   C = 2

We can fulfill its request. It will be allocated all the resources and will run till completion. Then it will give up all the resources. Now this will be the state:

Available: A = 5    B = 1    C = 3

Processes left: P3   P4

Similarly, next process P3 will be executed first and then P4.

Ans: option 4.

In the last state of processes:

How C=3 it should be 5, like A=5 (3+2) B=1(1+0)  then C=5 (3+2).
Before executing process P1 available resources:

A = 3    B = 1     C = 3

For process P1, we allocate the resources it requires which is:

A = 2   B = 0    C=2

After P1 completes execution we get back the resources it was allocated recently + the resources it was already holding. Resources P1 was already holding:

A = 2    B = 0     C = 0

Thus total available resources after P1

A = (3 - 2 + 2 + 2)

B = (1 + 0)

C = (3 - 2 + 2 + 0)

This is a very common mistake people make solving these type of questions. Try solving the question on your own, you'll find out the mistake you made. I allocated the resources it required by the process, ran it till execution, got back the recently allocated resources + the already allocated resources it had got earlier.
Now I got it right. I usually did this miscalculation in other questions too. Its all sorted. Thanks a lot.
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