Step 1: Differentiate between high-level and low-level languages.
High-level languages (like Java, Python, C++) are designed to be easier for humans to read and write. They provide strong abstraction from the details of the computer's hardware. Low-level languages provide little or no abstraction and are very close to the machine's native instruction set.
Step 2: Define machine dependence.
A language is machine-dependent if its programs can only be executed on the specific type of computer hardware for which they were written. Machine-independent languages can be run on many different types of hardware.
Step 3: Evaluate the options.
(A), (B), (D): Java, C++, and Python are high-level languages. They are designed to be portable (machine-independent). Code written in these languages is compiled or interpreted into machine code for the target platform, but the source code itself is not tied to a specific machine.
(C) Assembly language is a low-level language that is a human-readable representation of a specific computer's machine code. Each processor family (e.g., x86, ARM) has its own unique assembly language. Therefore, it is machine-dependent.
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: