Step 1: Identify the link between tanning and chromium.
Chromium, particularly hexavalent chromium, is extensively used in the leather tanning process. Improper disposal of tannery effluent is a major source of chromium contamination in soil and water.
Step 2: Identify major leather tanning hubs in India.
India has several major centers for the leather industry. The most prominent are Kanpur in Uttar Pradesh and a large cluster in Tamil Nadu (including cities like Vellore, Ambur, and Dindigul).
Step 3: Evaluate the states known for pollution from this industry.
While Kanpur (Uttar Pradesh) is also heavily polluted, the state of Tamil Nadu has a massive concentration of tanneries and a long-documented history of severe and widespread chromium pollution in the Palar river basin, making it the most cited example for this specific environmental issue in India.
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: