Step 1: Understand "contribution to global warming".
This contribution depends on two factors: the gas's atmospheric concentration and its global warming potential (GWP) per molecule. The overall effect is the product of these factors.
Step 2: Rank the gases by their overall contribution. 1. Carbon Dioxide (CO\(_2\)): Although it has the lowest GWP of the main greenhouse gases (by definition, GWP=1), its atmospheric concentration is vastly higher than the others, making it the largest contributor to modern global warming (typically over 60%). 2. Methane (CH\(_4\)): It has a much higher GWP than CO\(_2\) but a lower concentration. It is the second-largest contributor. 3. Nitrous Oxide (N\(_2\)O): It has a very high GWP and a longer atmospheric lifetime than methane, but its concentration is lower, making it the third-largest contributor. 4. Chlorofluorocarbons (CFCs) and other halocarbons: They have extremely high GWPs but are present in very small concentrations. Their contribution is smaller than the others listed.
Step 3: Form the sequence. The order in decreasing contribution is: B (Carbon dioxide) \(\rightarrow\) D (Methane) \(\rightarrow\) A (Nitrous oxide) \(\rightarrow\) C (Chlorofluorocarbon). The sequence is B, D, 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: