Solar variability can force climate change. Which of the following statements are correct about Solar variability?
A. Flares are intense bursts of ultraviolet and X-ray emitted from the sun's outer atmosphere.
B. Sun spots are bright (hot) patches that interrupt the irregular pattern of convective cell in the photosphere.
C. Faculates are bright (hot) spots in the pattern of convective cells that often appear in conjugate with sunspots.
D. Solar activity is modulated by solar cycle of approximately 11 years.
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: