Three liquids of densities \(d,\) \(2d\) and \(3d\) are mixed in equal proportions of weights. The relative density of the mixture is: 

1.	\(11d \over 7\)	2.	\(18d \over 11\)
3.	\(13d \over 9\)	4.	\(23d \over 18\)

The pressure of water in a water pipe when tap is opened and closed are respectively \(3\times10^5\) Nm^–2 and \(3.5\times10^5\) Nm^–2. With open tap, the velocity of water flowing is:
              
1. \(10\) ms^–1                           
2. \(5\) ms^–1
3. \(20\) ms^–1       
4. \(15\) ms^–1

A small spherical solid ball is dropped in a viscous liquid. Its journey in the liquid is best described in the figure by:
                        

The height of a mercury barometer is \(75 ~\text{cm}\) at sea level and \(50 ~\text{cm}\) at the top of a hill. The ratio of the density of mercury to that of air is \(10^4.\) The height of the hill is:

The value of g at a place decreases by 2%. Then, the barometric height of mercury:

A barometer kept in a stationary elevator reads \(76 ~\text{cm}.\) If the elevator starts accelerating up, the reading will be:
1. zero
2. equal to \(76 ~\text{cm}\)
3. more than \(76 ~\text{cm}\)
4. less than \(76 ~\text{cm}\)

The following figure shows the flow of liquid through a horizontal pipe. Three tubes \(A,\) \(B\) and \(C\) are connected to the pipe. The radii of the tubes  \(A,\) \(B\) and \(C\) at the junction are respectively \(2~\text{cm},1~\text{cm}\) and \(2~\text{cm}.\) It can be said that:

There is a hole in the bottom of a tank having water. If the total pressure at the bottom is \(3\) atm \((1~\text{atm}=10^5~\text{N}/\text{m}^2),\) then the velocity of water flowing from the hole is:
1. \(\sqrt{400}~~\text{m/s}\)
2. \(\sqrt{600}~~\text{m/s}\)
3. \(\sqrt{60}~~\text{m/s}\)
4. none of these

A spherical ball of radius \(r\) is falling in a viscous fluid of viscosity \(\eta\) with a velocity \(v.\) The retarding viscous force acting on the spherical ball is: