Remember the four necessary conditions for deadlock (Coffman conditions):
1. Mutual Exclusion: Resources cannot be shared.
2. Hold and Wait: A process holds at least one resource and is waiting for another.
3. No Preemption: Resources cannot be forcibly taken from a process. 4. Circular Wait: A closed chain of processes exists, such that each process holds at least one resource needed by the next process in the chain.
Step 1: Define deadlock.
A deadlock is a state in which each member of a group of processes is waiting for some other member to release a resource. Since all processes are waiting, none of them can proceed, and they are stuck in a permanent state of waiting. This situation is also known as a circular wait.
Step 2: Evaluate the options based on the definition.
(A) This statement perfectly describes the deadlock condition, specifically the circular wait condition where Process 1 waits for a resource held by Process 2, and Process 2 waits for a resource held by Process 1.
(B) A process exceeding its time slice is handled by the scheduler, which will preempt the process. This is related to scheduling, not deadlock.
(C) Running out of memory is a memory management issue that can cause processes to fail or the system to slow down (thrash), but it is not a deadlock.
(D) A process entering the running state is a normal part of the process life cycle.
Conclusion: The defining characteristic of a deadlock is a set of blocked processes each holding a resource and waiting to acquire a resource held by another process in the set.
If \(f(t)\) is the inverse Laplace transform of \( F(s) = \frac{s+1+s^{-2}}{s^2-1} \), then \(f(t)\) is
Match LIST-I with LIST-II
LIST-I (Differential Equation)
(A) \(\frac{dy}{dx} = 2x(y-x^2+1)\)
(B) \(x\frac{dy}{dx} + 2(x^2+1)y=6\)
(C) \((x^2+1)\frac{dy}{dx} + 2xy = x \sin x\)
(D) \(x^3\frac{dy}{dx} + 2xy = 2x^2e^{x^2}\)
LIST-II (Integrating Factor)
(I) \(x^2\)
(II) \(e^{-x^2}\)
(III) \(x^2e^x\)
(IV) \(1+x^2\)
Choose the correct answer from the options given below: