Step 1: Analyze the definition of a process.
In computer science, a program is a passive collection of instructions. A process is the active instance of a computer program that is being executed by one or more threads. It contains the program code and its activity.
Step 2: Evaluate the given options.
(A) A reusable resource is hardware (like a printer) or software (like a library) that can be used by multiple processes, but it is not the process itself.
(B) A variable timer is a mechanism used for scheduling or managing time within the OS, but it is not a process.
(C) "Program in execution" is the standard definition of a process. It represents the dynamic execution of a program's code.
(D) Allocation and de-allocation of memory are functions performed by the operating system's memory manager, often on behalf of a process, but this is an action, not the process itself.
Conclusion: The correct definition is a program in execution.
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: