$A$ large tank filled with water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from $h$ to $h/2$ and from $h/2$ to zero is

$A$ large vessel with a small hole at the bottom is filled with water and kerosene, with kerosene floating on water. The length of the water column is $20 \,cm$ and that of the kerosene is $25 \,cm$. The velocity with which water flows out of the hole is (density of kerosene $= 0.8 \,g/cm^3$, density of water $= 1.0 \,g/cm^3$, neglect viscous force). (in $\,m/s$)

$A$ person in a lift is holding a water jar,which has a small hole at the lower end of its side. When the lift is at rest,the water jet coming out of the hole hits the floor of the lift at a distance $d$ of $1.2 \ m$ from the person. In the following,the state of the lift's motion is given in List-$I$ and the distance where the water jet hits the floor of the lift is given in List-$II$. Match the statements from List-$I$ with those in List-$II$ and select the correct answer using the code given below the lists.

List-$I$	List-$II$
$P$. Lift is accelerating vertically up.	$1$. $d = 1.2 \ m$
$Q$. Lift is accelerating vertically down with an acceleration less than the gravitational acceleration.	$2$. $d < 1.2 \ m$
$R$. Lift is moving vertically up with constant speed.	$3$. $d > 1.2 \ m$
$S$. Lift is falling freely.	$4$. No water leaks out of the jar.

$A$ cylinder of height $h$ is filled with water and is kept on a block of height $h/2$. The level of water in the cylinder is kept constant. Four holes numbered $1, 2, 3$ and $4$ are at the side of the cylinder and at heights $0, h/4, h/2$ and $3h/4$ from the base of the cylinder, respectively. When all four holes are opened together, the hole from which water will reach the farthest distance on the plane $PQ$ is the hole number:

State Torricelli's law.

$A$ closed pipe containing liquid showed a pressure $P_{1}$ by gauge. When the valve is opened,the pressure was reduced to $P_{2}$. The speed of water flowing out of the pipe is $[\rho = \text{density of water}]$