Step 1: Define "Criteria Pollutants".
Criteria air pollutants are a set of common air pollutants that are regulated by national environmental agencies because they can harm public health and the environment.
Step 2: List the criteria pollutants in India (under NAAQS).
India's National Ambient Air Quality Standards (NAAQS) regulate 12 pollutants: PM\(_10\), PM\(_2.5\) (A), Sulphur Dioxide (SO\(_2\)) (E), Nitrogen Dioxide (NO\(_2\)) (B, as part of NO\(_x\)), Ozone (O\(_3\)), Carbon Monoxide (CO), Lead (Pb) (C), Ammonia (NH\(_3\)), Benzene, Benzo(a)Pyrene, Arsenic, and Nickel.
Step 3: Evaluate the given options against the list. - A (PM\(_2.5\)), B (NO\(_x\)), C (Lead), and E (Sulphur dioxide) are all on the list. - D (Methane) is a major greenhouse gas but is not regulated as a criteria pollutant for direct ambient air quality in the same way. Conclusion: The correct combination from the options is A, B, C, and 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: