Step 1: Identify the main atmospheric layers.
The atmosphere is divided into layers based on temperature profiles. The main layers from the ground up are the Troposphere, Stratosphere, Mesosphere, and Thermosphere.
Step 2: Identify the boundary regions ('pauses').
The 'pauses' are the boundaries that separate the main layers. The tropopause separates the troposphere and stratosphere. The stratopause separates the stratosphere and mesosphere.
Step 3: Construct the sequence from the Earth's surface upwards. 1. Troposphere (A): The lowest layer, where we live and weather occurs. 2. Tropopause (C): The boundary at the top of the troposphere. 3. Stratosphere (B): The layer above the troposphere, containing the ozone layer. 4. Stratopause (D): The boundary at the top of the stratosphere. 5. Mesosphere (E): The layer above the stratosphere. Conclusion: The correct order from the surface up is A, C, B, D, E.
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: