Step 1: Define the master soil horizons.
Soil scientists classify soil into layers or horizons. The main (master) horizons are designated by letters.
Step 2: List the horizons in order from the surface downward. 1. O horizon (D): The surface layer, rich in organic matter (leaf litter, humus). 2. A horizon (A): Topsoil, a mix of minerals and humus. Zone of leaching. 3. E horizon (not in this specific list, but often present below A): Zone of eluviation (leaching). 4. B horizon (B): Subsoil, zone of accumulation (illuviation) where minerals and clays from above are deposited. 5. C horizon (E): Parent material, weathered bedrock from which the soil is formed. 6. R horizon (C): Bedrock, the unweathered parent rock.
Step 3: Form the sequence based on the given letters. The correct order from top to bottom is D (O horizon), A (A horizon), B (B horizon), E (C horizon), C (R horizon).
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: