Step 1: Recall the hardness values of the given minerals on the Mohs scale. - Corundum (C): 9 - Orthoclase (A): 6 - Fluorite (D): 4 - Calcite (B): 3
Step 2: Arrange these minerals in decreasing order of hardness. The order from hardest to softest is: 1. Corundum (9) 2. Orthoclase (6) 3. Fluorite (4) 4. Calcite (3)
Step 3: Write the final sequence using the letters. The sequence is C, A, D, B.
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: