Step 1: Define the Mohorovičić Discontinuity (Moho).
The Moho is the boundary surface between the Earth's crust and the mantle.
Step 2: Describe how it is identified.
It is identified by a distinct and rapid increase in the velocity of seismic waves (both P-waves and S-waves). This is because the mantle below is significantly denser and more rigid than the crust above.
Step 3: Quantify the velocity change.
P-wave (primary wave) velocity in the lower crust is typically 6.7–7.2 km/s. Upon crossing the Moho into the mantle, it abruptly increases to 7.6–8.6 km/s. Therefore, the depth where the P-wave velocity sharply increases to over 7.6 km/s is the defining characteristic of the Moho.
Conclusion: Option (B) provides the best description of this seismic velocity jump.
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: