Step 1: Recall the hierarchy of digital storage units.
The units are based on powers of 2 (or 10 in some contexts), with each major unit being approximately 1000 (or 1024) times larger than the previous one.
Step 2: List the prefixes in increasing order.
Kilo (K) < Mega (M) < Giga (G) < Tera (T)
Step 3: Apply the order to the given units. - Smallest: 1 KB (Kilobyte) (D) - Next: 1 MB (Megabyte) (B) - Next: 1 GB (Gigabyte) (A) - Largest: 1 TB (Terabyte) (C)
Step 4: Form the correct sequence. The order from smallest to largest is D, B, A, C.
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: