Pressure in a Fluid question from JEE Main 2024 (4 Apr, Shift 1)

Answer: (a)

1. Statement I: for a fluid at rest, $P_1 + \rho g h_1 = P_2 + \rho g h_2$, so $P_1 - P_2 = \rho g(h_2 - h_1)$. Correct.
2. Statement II: Bernoulli at the same level gives $P_1 - P_2 = \tfrac{1}{2}\rho(v_2^2 - v_1^2)$, and $P_1 - P_2 = \rho g h$.
3. So $2gh = v_2^2 - v_1^2$, not $v_1^2 - v_2^2$. Statement II is incorrect.
4. So the answer is (a).