Step 1: Analyze Anna Hazare (A)
While famous for his anti-corruption activism, Anna Hazare's foundational work was in transforming his drought-prone village, Ralegan Siddhi, through community-based watershed development.
Thus, A matches with (IV).
Step 2: Analyze Rajender Singh (B)
Rajender Singh, known as the "waterman of India," is renowned for his water conservation efforts in Rajasthan, primarily through the NGO Tarun Bharat Sangh.
Thus, B matches with (II).
Step 3: Analyze Chandi Prasad Bhatt (C)
Chandi Prasad Bhatt is an Indian environmentalist and social activist, who was one of the pioneers of the Chipko movement in the 1970s.
Thus, C matches with (III).
Step 4: Analyze Medha Patkar (D)
Medha Patkar is a social activist best known as a founding member of the large-scale social movement, Narmada Bachao Andolan (Save the Narmada Movement).
Thus, D matches with (I).
Conclusion: The correct matching is A-IV, B-II, C-III, D-I.
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: