A very large open tank stands on a horizontal floor and is filled with water to a depth H=1.0 m. A tiny hole is made in its vertical side wall at a…

Torricelli's theorem gives the efflux speed $v=\sqrt{2gd}$, and the jet then falls through a height $H-d$ in time $t=\sqrt{2(H-d)/g}$, so $x=vt=2\sqrt{d(H-d)}$. For $d=0.20$ m this is $2\sqrt{0.2\times0.8}=0.80$ m, so (A) is correct. The expression is symmetric under $d\to H-d$, so $d=0.80$ m gives the same range and (B) is correct. The product $d(H-d)$ is largest at $d=H/2$, giving $x_{\max}=H=1.0$ m, not $2.0$ m, so (C) is wrong. Finally $v=\sqrt{2\times10\times0.2}=2\ \mathrm{m\,s^{-1}}$, not $4$, so (D) is wrong. Answer: A, B. Because the tank is very large, the free-surface level is practically constant, so steady Bernoulli flow applies between the surface and the hole.