Can rockets fly without burning any fuel with the help of gases under extreme pressure only? Why is it necessary to burn the hydrogen fuel coming out of the engine for the lift of rockets?
If it is done to create a greater reaction force on the rocket then why can't we get the same lift with just adjusting the speed of the hydrogen gas going out of the engine like we can release them at a great pressure (and also by adjusting the size of the nozzle opening) and thus at a greater speed?
Is it possible for rockets to fly without burning the fuel and just releasing the fuel with a great force? (I know the rockets are too massive).
How does the ISP of the ordinary rocket engines compare with the one in my question ? Most of the answers have done the comparison (and a great thanks for that), but help me with the numerical difference in the ISP's.
(Compare it using any desired values of the amount of fuel and other required things for taking off.)
 A: It will produce thrust, but think about it this way:
You need to throw some mass out the back anyway. If you can get the mass to react with itself so that it heats itself up and increases its velocity, all the better.
A: Cold gas thrusters, generally using compressed nitrogen, are sometimes used for control, such as adjusting orientation in orbit.
In that case the low thrust is, if anything, an advantage, as it makes precise control easier.
A: 
Why is it necessary to burn the hydrogen fuel coming out of the engine for the lift of the rockets ?

Hydrogen isn't the only fuel possible, so I presume your question is more general, why is any fuel burned?

If it is done to create a greater reaction force on the rocket then why can't we do the same lift with just adjusting the speed of the hydrogen gas going out of the engine like we can release them at a great pressure and thus at a greater speed?

You need two things for a rocket:  a reaction mass to expel, and a source of power to accelerate it.  Combustion rockets combine these two into a single source.  The fuel/oxidizer burns generating energy.  The energy from combustion heats and then, via the nozzle configuration, accelerates the combustion products as the reaction mass.
Just about anything could be put onboard as the reaction mass, but getting the power to accelerate it is much harder.  Batteries and compressed gas hold a bit of energy, but the density is much lower than rocket fuels.  Solar panels can gather a nearly unlimited amount of energy, but you have to wait for a long time to collect it.  Nuclear fuels could release a lot of power, but putting a nuclear reactor on a rocket takes a lot of mass and is difficult to convince everyone that it can be done safely.
Even if you had sufficient electrical power, converting it into thrust isn't simple.  Ion engines can be used, but they have orders of magnitude less thrust than a chemical rocket.  The acceleration can be useful in space, but is too small to help lift a rocket off the surface of the earth.
So the fuel is burned because it can be stored on the rocket with a fairly high energy density, and the reaction can take place at a high rate, giving large amounts of thrust.
A: All of the other answers here make important points.
A way to think of this question in simple terms is to think of it purely in terms of temperature.
Temperature is the average velocity of particles (whether they be a solid, liquid, gas or plasma).
So from here on I will use the terms temperature and velocity interchangeably.
A rocket motor design seeks to optimize the following parameters:

*

*maximize power by expelling the maximum number of particles per second at the highest possible velocity.  A higher particle velocity is equivalent to a higher temperature.


*don’t melt the motor by raising the motor’s temperature above about 3000 degrees Celsius.  All materials start turning to plasma above ~3000C.


*the motor itself can’t be too heavy in ratio to the fuel it is expelling
If you increase the velocity of the fuel you are expelling above ~3000 degrees, then the fuel will start melting/vaporizing the motor.
Ion rocket motors do accelerate the fuel to high velocity (a temperature of about a million degrees).  However, the ion rocket motor parts themselves, that are accelerating the plasma ion fuel, can only be heated up to about 300 degrees Celsius before failing.  So ion rockets are much more efficient, but they can only expel a small amount of fuel per second before overheating.
In comparison, the materials near a hydrogen/oxygen burning rocket motor nozzle can withstand about 3000C before failing.  These motors can expel a lot more fuel per second before overheating.
So in answer to your question, ion rockets cannot be used to launch rockets from the ground because they overheat too easily.
A: Releasing compressed gas will produce some thrust. But when the gasses are combusted they expand much more. This produces a much higher exhaust velocity which gives a much greater thrust.
A: "Cold gas" thrusters (i.e. pressurized gas released through a nozzle without combustion) are used for attitude control on some rockets (notably on the Falcon 9 first-stage, for attitude control in the recovery phase), but they have a much lower specific impulse than hydrogen-oxygen combustion. Their advantage is their extreme simplicity in small systems.
Cold hydrogen specific impulse: ~270 sec; hydrogen-oxygen combustion: ~440 sec. Nitrogen is more commonly used in cold-gas setups (easier to produce and store, more thrust per volume of tankage) but yields only about 70 sec.
Increasing the pressure to get better performance requires more weight in tankage to contain the pressure, so you get a net performance loss.
A: Surely you can. The power (thrust) of rocket motor in first order depends only on speed and mass flow of gas coming out of engine:
$$
F=\Phi_m v
$$
Where $\Phi_m$ is mass flow from the motor and $v$ is the velocity of flow relative to the rocket.
But we have to somehow produce this mass flow, eg. we have to produce high pressure of gas. This can be done with compressing gas into container. But we can get even higher pressure, if we burn the fuel.
We actually use chemical reaction, which produces heat and consequently higher pressure (have in mind equation of state for ideal gas). So burning is used just to increase temperature and consequently higher pressure.
$$
P=\frac{n R T}{V}
$$
A: There is a limit to how much you can pressurize gas. Past a certain point, they cease to be gasses, and turn into liquids. Rockets have already reached this limit; oxygen is stored as a liquid. And while it is possible to store energy in liquids by pressurizing them, this is much more difficult to do than with gasses.

and also by adjusting the size of the nozzle opening

Pressurized gas has only so much energy. You can't get more than the energy stored, regardless of nozzle size, and decreasing the nozzle size decreases the amount of gas released per time.

Is it possible for rockets to fly without burning the fuel and also without affecting the volume of the total fuel i.e. with the same amount of fuel used in general propellers ??

This is confusingly worded, but you seem to be asking whether it's possible to get the same energy without burning the fuel. Releasing the pressure of a gas and burning it is going to release more energy than just releasing the pressure, so of course the amount of fuel needed will increase if it's not burned. It is possible to fly a rocket a short distance just from release of pressure (there are toy rockets that have water as a propellant and pressurized air as fuel), but I don't think it's possible to reach orbit from them.

(I know they are too massive but consider a lighter one.)

It's really not clear what "they" refers to here.
A: Of course a rocket, loosely defined, can accelerate under gas pressure alone.  That is what blowing up a balloon and letting it go does.
The problem is that there is not enough energy in compressed gas to provide much thrust.  Take for instance scuba tanks, perhaps the most familiar instance of high-pressure gas for most of us.  A typical tank (rough numbers because there's a lot of variation) will weigh about 30 lbs/15 kg empty, and will hold 4-6 lbs/2-3 kg of air compressed to 3000/3500 psi.  So you've got a container weighing about 5 times as much as the gas it holds.
That amount of compressed gas holds roughly 1 kWh of energy. (The relatively small compressor of a typical dive shop can fill a tank in 15 minutes or so.) That's not very much when compared to the energy generated by burning the same mass of hydrogen (or other fuel) and oxygen.
There's a second problem with compressed gas.  Compressing a gas creates heat. (One reason dive shops fill tanks in water is to keep them cool.)  Conversely, uncompressing that gas requires absorbing heat from the environment.  With scuba tanks, the uncompression is slow (at least you hope so!), and the tank is in water that it can absorb heat from.  Try to decompress the gas quickly, in atmosphere or vacuum, and you will cool the remaining gas to the point where it no longer evaporates.  Indeed, this is the principle on which many refrigerators, air conditioners, and gas liquifiers work.
A: Yes, a rocket powered by any pressurized gas may fly (you must have blown  balloons and left them to fly), but the problem is distance to be traveled and the maximum payload capacity.
A: Newton's third law applies whatever the action.  You could generate thrust by chucking rocks, but it wouldn't be very efficient.
A: The energy that can be stored in a pressure tank is limited by the strength of the tank material, which ultimately depends on the energy needed to break the chemical bonds between its molecules.
The energy that can be stored in a chemical fueled rocket is limited by the energy of the chemical bonds of the combustion products.
In both, the energy (per molecule) of chemical bonds are of similar magnitude, but I'm pretty sure the combustion rocket wins out, for the same reason we do not have compressed gas powered cars.
