Maths-
If
observe the following



The true statements are
Maths-General
- only I, III
- only II, III
- only I, II
- I, II, III
Answer:The correct answer is: only I, II
Book A Free Demo

Grade*
Select Grade
Related Questions to study
maths-
Statement I :
is one - one
Statement II :
are two functions such that 

Staatement III : 
Which of the above statement/s is/are true.
Statement I :
is one - one
Statement II :
are two functions such that 

Staatement III : 
Which of the above statement/s is/are true.
maths-General
physics-
A glass capillary sealed at the upper end is of length 0.11 m and internal diameter
m. The tube is immersed vertically into a liquid of surface tension
N/m. To what length has the capillary to be immersed so that the liquid level inside and outside the capillary becomes the same?

A glass capillary sealed at the upper end is of length 0.11 m and internal diameter
m. The tube is immersed vertically into a liquid of surface tension
N/m. To what length has the capillary to be immersed so that the liquid level inside and outside the capillary becomes the same?

physics-General
physics-
Water flows through a frictionless duct with a cross-section varying as shown in fig. . Pressure p at points along the axis is represented by: A resume water to be non-viscour

Application of Bernoulli’s theorem
Water flows through a frictionless duct with a cross-section varying as shown in fig. . Pressure p at points along the axis is represented by: A resume water to be non-viscour

physics-General
Application of Bernoulli’s theorem
physics-
A cubical block of wood 10 cm on a side floats at the interface between oil and water with its lower surface horizontal and 4 cm below the interface. The density of oil is
. The mass of block is

Weight of block
= Weight of displaced oil + Weight of displaced water
Þ
Þ
= 760 gm
= Weight of displaced oil + Weight of displaced water
Þ
Þ
A cubical block of wood 10 cm on a side floats at the interface between oil and water with its lower surface horizontal and 4 cm below the interface. The density of oil is
. The mass of block is

physics-General
Weight of block
= Weight of displaced oil + Weight of displaced water
Þ
Þ
= 760 gm
= Weight of displaced oil + Weight of displaced water
Þ
Þ
physics-
Water flows through a frictionless duct with a cross-section varying as shown in fig. Pressure p at points along the axis is represented by

When cross-section of duct is decreased, the velocity of water increased and in accordance with Bernoulli’s theorem, the pressure P decreased at that place
Water flows through a frictionless duct with a cross-section varying as shown in fig. Pressure p at points along the axis is represented by

physics-General
When cross-section of duct is decreased, the velocity of water increased and in accordance with Bernoulli’s theorem, the pressure P decreased at that place
physics-
The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. A graph showing the speed v with which the liquid is crossing points at a distance X from O along a radius XO would look like

When we move from centre to circumference, the velocity of liquid goes on decreasing and finally becomes zero
The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. A graph showing the speed v with which the liquid is crossing points at a distance X from O along a radius XO would look like

physics-General
When we move from centre to circumference, the velocity of liquid goes on decreasing and finally becomes zero
maths-
maths-General
maths-
maths-General
physics-
A small spherical solid ball is dropped from a great height in a viscous liquid. Its journey in the liquid is best described in the diagram given below by the

A small spherical solid ball is dropped from a great height in a viscous liquid. Its journey in the liquid is best described in the diagram given below by the

physics-General
physics-
Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel (s = relative density of mercury and
= density of water) by


If the level in narrow tube goes down by h1 then in wider tube goes up to h2,
Now,
Now, pressure at point A = pressure at point B
Þ h =
Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel (s = relative density of mercury and
= density of water) by

physics-General

If the level in narrow tube goes down by h1 then in wider tube goes up to h2,
Now,
Now, pressure at point A = pressure at point B
Þ h =
physics-
There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density
. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is


Net force (reaction) =
\
According to Bernoulli's theorem
Þ
From equation (i),
There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density
. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is

physics-General

Net force (reaction) =
\
According to Bernoulli's theorem
Þ
From equation (i),
physics-
A cylinder containing water up to a height of 25 cm has a hole of cross-section
in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out

Let A = The area of cross section of the hole
v = Initial velocity of efflux
d = Density of water,
Initial volume of water flowing out per second = Av
Initial mass of water flowing out per second = Avd
Rate of change of momentum = Adv2
Initial downward force on the flowing out water = Adv2
So equal amount of reaction acts upwards on the cylinder.
\ Initial upward reaction =
[As
]
Initial decrease in weight 
gm-wt.
v = Initial velocity of efflux
d = Density of water,
Initial volume of water flowing out per second = Av
Initial mass of water flowing out per second = Avd
Rate of change of momentum = Adv2
Initial downward force on the flowing out water = Adv2
So equal amount of reaction acts upwards on the cylinder.
\ Initial upward reaction =
A cylinder containing water up to a height of 25 cm has a hole of cross-section
in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out

physics-General
Let A = The area of cross section of the hole
v = Initial velocity of efflux
d = Density of water,
Initial volume of water flowing out per second = Av
Initial mass of water flowing out per second = Avd
Rate of change of momentum = Adv2
Initial downward force on the flowing out water = Adv2
So equal amount of reaction acts upwards on the cylinder.
\ Initial upward reaction =
[As
]
Initial decrease in weight 
gm-wt.
v = Initial velocity of efflux
d = Density of water,
Initial volume of water flowing out per second = Av
Initial mass of water flowing out per second = Avd
Rate of change of momentum = Adv2
Initial downward force on the flowing out water = Adv2
So equal amount of reaction acts upwards on the cylinder.
\ Initial upward reaction =
physics-
Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = 10 m/s2)

Let A = cross-section of tank
a = cross-section hole
V = velocity with which level decreases
v = velocity of efflux

From equation of continuity
By using Bernoulli's theorem for energy per unit volume
Energy per unit volume at point A
= Energy per unit volume at point B

Þ
a = cross-section hole
V = velocity with which level decreases
v = velocity of efflux

From equation of continuity
By using Bernoulli's theorem for energy per unit volume
Energy per unit volume at point A
= Energy per unit volume at point B
Þ
Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = 10 m/s2)

physics-General
Let A = cross-section of tank
a = cross-section hole
V = velocity with which level decreases
v = velocity of efflux

From equation of continuity
By using Bernoulli's theorem for energy per unit volume
Energy per unit volume at point A
= Energy per unit volume at point B

Þ
a = cross-section hole
V = velocity with which level decreases
v = velocity of efflux

From equation of continuity
By using Bernoulli's theorem for energy per unit volume
Energy per unit volume at point A
= Energy per unit volume at point B
Þ
physics-
A body floats in a liquid contained in a beaker. The whole system as shown falls freely under gravity. The up thrust on the body due to the liquid is

Upthrust 
where, a = downward acceleration,
V = volume of liquid displaced
But for free fall a = g
Upthrust = 0
where, a = downward acceleration,
V = volume of liquid displaced
But for free fall a = g
A body floats in a liquid contained in a beaker. The whole system as shown falls freely under gravity. The up thrust on the body due to the liquid is

physics-General
Upthrust 
where, a = downward acceleration,
V = volume of liquid displaced
But for free fall a = g
Upthrust = 0
where, a = downward acceleration,
V = volume of liquid displaced
But for free fall a = g
physics-
A wooden block, with a coin placed on its top, floats in water as shown in fig. the distance l and h are shown there. After some time the coin falls into the water. Then

As the block moves up with the fall of coin, l decreases, similarly h will also decrease because when the coin is in water, it displaces water equal to its own volume only.
A wooden block, with a coin placed on its top, floats in water as shown in fig. the distance l and h are shown there. After some time the coin falls into the water. Then

physics-General
As the block moves up with the fall of coin, l decreases, similarly h will also decrease because when the coin is in water, it displaces water equal to its own volume only.