Step 1: Analyze Cumulus (A)
'Cumulus' comes from the Latin for 'heap' or 'pile'. These clouds have a puffy, cotton-like appearance with flat bases.
Thus, A matches with (III).
Step 2: Analyze Nimbus (B)
'Nimbus' is Latin for 'rain cloud'. When this prefix or suffix is used (e.g., Nimbostratus, Cumulonimbus), it indicates that the cloud is producing precipitation.
Thus, B matches with (I).
Step 3: Analyze Cirrus (C)
'Cirrus' is Latin for a 'curl of hair'. These are high-altitude clouds that are thin, wispy, and composed entirely of ice crystals.
Thus, C matches with (IV).
Step 4: Analyze Stratus (D)
'Stratus' comes from the Latin for 'layer' or 'sheet'. These clouds are horizontal and layered (stratified).
Thus, D matches with (II).
Conclusion: The correct matching is A-III, B-I, C-IV, 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: