$A$ rectangular vessel,when full of water,takes $10 \text{ minutes}$ to be emptied through an orifice in its bottom. How many minutes will it take to be emptied when half-filled with water?

$A$ cylinder containing water up to a height of $25 \ cm$ has a hole of cross-section $\frac{1}{4} \ cm^2$ in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out?

$A$ 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.

For a container open to the atmosphere,derive the velocity of the liquid exiting a narrow hole in the container wall using Bernoulli's equation and obtain Torricelli's law.

$A$ cylindrical tank has a hole of area $2 \,cm^2$ at its bottom. If water is poured into the tank from a tube above it at the rate of $100 \,cm^3 \,s^{-1}$, then the maximum height up to which water can rise in the tank is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $cm$)

Water is filled in a cylindrical vessel of height $H$. $A$ hole is made at height $z$ from the bottom,as shown in the figure. The value of $z$ for which the range $(R)$ of the emerging water through the hole will be maximum is: