Step 1: Analyze Blue baby syndrome (A)
This condition (methemoglobinemia) is caused by decreased oxygen-carrying capacity of hemoglobin. In infants, it is classically linked to high concentrations of nitrate in drinking water.
Thus, A matches with (III).
Step 2: Analyze Keshan disease (B)
Keshan disease is a congestive cardiomyopathy (a heart condition) caused by a dietary deficiency of the mineral selenium.
Thus, B matches with (IV).
Step 3: Analyze Gas bubble disease (C)
This is a condition primarily affecting aquatic organisms like fish, caused by environmental supersaturation with gases, typically nitrogen or oxygen. This can be considered as "Excess dissolved oxygen".
Thus, C matches with (I).
Step 4: Analyze Itai-itai disease (D)
"Itai-itai" (Japanese for "it hurts, it hurts") is a painful bone disease caused by chronic poisoning from excess cadmium (Cd) in drinking water and food, first identified in Japan.
Thus, D matches with (II).
Conclusion: The correct matching is A-III, B-IV, C-I, D-II.
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: