$A$ tank is filled up to a height $2H$ with a liquid and is placed on a platform of height $H$ from the ground. The distance $x$ from the ground where a small hole is punched to get the maximum range $R$ is:

$A$ vessel completely filled with water has two holes $P$ and $Q$ at depths $2h$ and $8h$ from the top,respectively. Hole $P$ is a square of side $a$ and hole $Q$ is a circle of radius $r$. If the volume of water flowing out per second from both holes is the same,then the side $a$ of hole $P$ is:

$A$ vessel completely filled with water has holes $A$ and $B$ at depths $h$ and $3h$ from the top respectively. The hole $A$ is a square of side $L$ and $B$ is a circle of radius $r$. The water flowing out per second from both the holes is same. Then $L$ is equal to

$A$ cylindrical vessel of height $50 \,cm$ is filled with water and rests on a table. $A$ small hole is made at a height $h$ from the bottom of the vessel so that the water jet hits the table surface at a maximum distance $x_{\max }$ from the vessel as shown in the figure. The value of $x_{\max }$ will be (Neglect the viscosity of water.) (in $\,cm$)

$A$ cylindrical vessel is filled with water up to a height of $1 \,m$ from the base. $A$ small orifice is opened at some height in the cylinder, and the water level is reduced to the height of the orifice in $20 \,s$. If the base area of the cylinder is $100$ times the area of the orifice, then the height of the orifice from the base is (take $g = 10 \,m/s^2$): (in $\,cm$)

$A$ water barrel having water up to a depth $d$ is placed on a table of height $h$. $A$ small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel, then the value of $d$ is