Step 1: Statement A is true. Surface tension occurs due to excess molecular energy at the surface.
Step 2: Statement B is incorrect. As the temperature of a liquid increases, the coefficient of viscosity decreases.
Step 3: Statement C is true. As the temperature of a gas increases, the coefficient of viscosity increases.
Step 4: Statement D is true. Reynolds number determines whether the flow is laminar or turbulent.
Step 5: Statement E is true. In a steady flow, streamlines do not intersect. Final Conclusion: The correct statements are A, D, and E, which corresponds to Option (4).
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: